Multiscale Deformation and Fracture in Materials and Structures the James R

MULTISCALE DEFORMATION AND FRACTURE IN MATERIALS

AND STRUCTURES SOLID MECHANICS AND ITS APPLICATIONS Volume 84

Series Editor: G.M.L. GLADWELL Department of Civil Engineering University of Waterloo Waterloo, Ontario, Canada N2L 3GI

Aims and Scope of the Series The fundamental questions arising in mechanics are: Why?, How?, and How much? The aim of this series is to provide lucid accounts written by authoritative researchers giving vision and insight in answering these questions on the subject of mechanics as it relates to solids.

The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations; computational mechanics; statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and structures; dynamical systems and chaos; the theories of elasticity, plasticity and viscoelasticity; composite materials; rods, beams, shells and membranes; structural control and stability; soils, rocks and geomechanics; fracture; tribology; experimental mechanics; biomechanics and machine design.

The median level of presentation is the first year graduate student. Some texts are mono- graphs defining the current state of the field; others are accessible to final year under- graduates; but essentially the emphasis is on readability and clarity. Multiscale Deformation and Fracture in Materials and Structures The James R. Rice 60th Anniversary Volume

Edited by

T.-J. Chuang National Institute of Standards & Technology, Gaithersburg, U.S.A. and J. W. Rudnicki Northwestern University, Evanston, Illinois, U.S.A.

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The work of J. R. Rice has been central to developments in solid mechanics over the last thirty years. This volume collects 21 articles on deformation and fracture in honor of J.R. Rice on the occasion of his 60th birthday.Contributors include students (P. M. Anderson, G. Beltz, T.-J. Chuang, W.J. Drugan, H. Gao, M. Kachanov, V. C. Li, R. M. McMeeking, S. D. Mesarovic, J. Pan, A. Rubinstein, and J. W. Rudnicki), post-docs (L. B. Sills, Y. Huang, J.Yu, J.-S. Wang), visiting scholars (B. Cotterell, S. Kubo, H. Riedel) and co-authors (R. M. Thomson and Z. Suo). These articles provide a window on the diverse applications of modern solid mechanics to problems of deformation and fracture and insight into recent developments. The last thirty years have seen many changes to the practice and applications of solid mechanics. Some are due to the end of the Cold War and changes in the economy. The drive for competitiveness has accelerated the need to develop new types of materials without the costly and time-consuming process of trial and error. An essential element is a better understanding of the interaction of macroscopic material behavior with microscale processes, not only mechanical interactions, but also chemical and diffusive mass transfer. Unprecedented growth in the power of computing has made it possible to attack increasingly complex problems. In turn, this ability demands more sophisticated and realistic material models. A consistent theme in modern solid mechanics, and in this volume, is the effort to integrate information from different size scales. In particular, there is an increasing emphasis on understanding the role of microstructural and even atomistic processes on macroscopic material behavior. Despite the great advances in computational power, current levels do not approach that needed to employ atomic level formulations in practical applications. Consequently, idealized problems that link behavior at small, even atomic, size scales to macroscopic behavior remain essential. It would be presumptuous to hope that the articles here are as original, rigorous, clear and as strongly connected to observations as the work of the man they are meant to honor. Nevertheless, we hope that they do reflect the high standards that he has set. That they do is in no small measure a consequence of the interaction, both formal and informal, of the authors with J. R. Rice and the inspiration that his work has provided. The articles in this volume are grouped into sections on Deformation and Fracture although, obviously, there is some overlap in these topics. As is evident by reading the titles, the scope and subjects of the articles are diverse. This reflects not only the extensive impact of Rice’s work but also the broad applicability of certain fundamental tools of solid mechanics. vi EDITORS’ PREFACE

FRACTURE: Arguably, Rice’s most well-known contribution is the introduction of the J-integral in 1968 and its application to problems of fracture. Because of its path-independent property, the integral has become a standard tool of fracture mechanics that makes it possible to link processes at the crack-tip to applied loads. Three of the papers in the Fracture section discuss this J-integral (and several others use it). Kubo gives a concise catalog of various versions of the integral and related extensions. Li discusses applications of the J-integral to characterization and tailoring of cementitious materials. A special feature of these materials is the presence of fibers or aggregate particles that transmit tractions across the crack-faces behind the tip. In his 1968 paper, Rice showed that the J-integral is equal to the energy released per unit area of crack advance for elastic materials. Consequently, this energy or the value of J could be used as criterion for fracture. Haug and McMeeking use the J-integral to study the effect of an extrinsic surface charge on the energy release rate for a piezoelectric compact tension specimen. They find that the presence of the free charge diminishes the effect of the electric field and suggest that this will complicate attempts to infer the portions of the crack tip singularity that are due to stress and to the electric field. A related path-independent integral, the M-integral, is used by Banks-Sills and Boniface to determine the stress intensity factors for a crack on the interface between two transversely isotropic materials. A finite element analysis is used to determine the asymptotic near-field displacements needed to evaluate the M-integral. Interpretation of the J-integral as an energy release is rigorous only for nonlinear elastic materials. But much of its usefulness arises from applications to elastic-plastic materials whose response, for proportional loading paths, is indistinguishable from a hypothetical nonlinear elastic one. For significant deviations from proportional loading, the interpretation of J in terms of fracture energy is approximate. Cotterell et al. present a method for accounting for the extra work arising from deviations from proportional loading due to significant crack growth in elastic plastic materials. Crack growth is affected not only by mechanical loading (or coupled piezoelectric loading as considered by Haug and McMeeking) but also by chemical processes. Numerical simulations by Tang et al. show that the presence of chemical activity at the crack tip can lead to blunting, stable steady crack growth or unstable sharpening of the crack tip. In the steady state regime, the computed crack velocity as a function of applied load agrees qualitatively with experiments but uncertainties in material parameters make quantitative comparison difficult. Consistent with previous studies, Tang et al. find the existence of a threshold stress level that leads to sharpening and fracture, but, contrary to previous studies, this threshold depends not only on the mechanical driving force, but also on the chemical kinetics. A classic problem of material behavior is to delineate the conditions for which materials fail ductilely or brittlely. Rice and Thomson addressed this problem by considering the interaction of a dislocation with a sharp crack-tip and arguing that ductile behavior occurred when the energetics of the interaction favored emission of a dislocation. In a concise analysis, Beltz and Fischer extend this formulation to consider the effect of the T-stress, that is , the non-singular portion of the crack-tip stress field. They show that the EDITORS’ PREFACE vii effect of this stress can be significant for small cracks, with lengths on the order of 100 atomic spacings. Klein and Gao present an innovative approach to the problem of dynamic fracture instability. They suggest that the discrepancy between predictions and observations could be resolved by including non-linear deformations near the crack-tip. They do this by a cohesive potential model that bridges the gap between continuum scale and atomistic scale calculations. Using as a measure of failure the loss of strong ellipticity, they suggest that crack branching may be associated with a loss of stiffness in biaxial stretching near the crack-tip. Several pioneering papers by Rice have considered the problem of determining the stress and deformation fields near the tip of a crack in a ductile material. The chapter by Drugan extends consideration to the case of a crack propagating along the interface of two ductile (elastic-ideally plastic) materials. An interesting by-product of the analysis for anti-plane deformation of bimaterials is a family of admissible solutions for homogeneous materials (including the well-known Chitaley -McClintock solution). Analysis reveals that beyond a certain level of material mismatch (ratio of yield stresses) a single term of the asymptotic expansion is not sufficient to characterize accurately the near-tip field. This suggests that the number of terms required will depend on some microstructural distance. Yu and Cho present detailed observations of the crack-tip fields in plastically deforming copper single crystals and compare them with fields predicted by Rice (Mechanics of Materials, 1987). They suggest that discrepancies could be due to absence of latent hardening in the elastic ideally plastic model analyzed by Rice. Rubinstein presents the results of numerical calculations based on a complex variable formulation for a variety of micromechanical models of composites. Though the calculations are elastic, they take explicit account of various reinforcing fibers, particles, etc. and, as a result the solutions depend on the ratio of fiber size to spacing, an important design variable. DEFORMATION: Another major contribution of Rice has been the development of shear localization theory as a model of failure in ductile materials. In contrast to fracture, where the stress intensification caused by acute geometry plays a dominant role, the approach of shear localization is based on the constitutive description of homogeneous deformation. The constitutive relation developed by Gurson, under Rice’s direction, has seen much application in this context because it includes softening due to the nucleation and growth of micro-voids, an important microscale feature of ductile metal deformation. Chen et al. discuss modifications of the Gurson model that are necessary to describe the anisotropy of aluminum sheets. A related chapter by Chien et al. uses a three dimensional finite element analysis of a unit cell to confirm the accuracy of a phenomenological anisotropic yield condition for porous metal and apply the phenomenological condition to analyze failure in a fender forming operation. The chapter by Rudnicki discusses shear localization of porous materials in a quite different context: the effects of coupling between pore fluid diffusion and deformation on the development of shear localization in geomaterials. viii EDITORS’ PREFACE

Although the constitutive model developed by Gurson and those used by Chien et al., Chen et al. and Rudnicki are more complex than classic elastic-plastic relations, they include microstructural information simply by means of the void volume fraction or porosity. The paper by Riedel and Blug presents an example of the type of sophisticated constitutive model needed for implementation in a finite element code to model a complex technology, solid state sintering. Application of the model to silicon carbide demonstrates the level of detail and accuracy this kind of material modelling combined with finite element analysis can bring to technological processes. Elastic-plastic contact is an example of the fruitful application of continuum mechanics to microscale processes. Applications include indentation hardness testing, atomic force microscopy, powder compaction, friction and wear. Mesarovic reviews and summarizes the current understanding in this area and identifies a number of problems in need of further work. Recent computational advances have improved understanding but further work is needed in several areas. Hydrogen is an element whose presence on an interface or at a crack-tip can lead to embrittlement. In an elegant analysis that combined thermodynamics and fracture mechanics and extended the introduction of surface energy into fracture analysis by Griffith, Rice showed how the presence and mobility of segregants can alter the surface energy.Wang reviews the analysis of Rice and co-workers and shows that the predictions are consistent with observations of hydrogen embrittlement in iron single crystals. Anderson and Xin address the classic problem of the stress needed to drive a dislocation. In particular, they examine how this stress is affected by a welded interface using a model that allows them to vary independently the unstable stacking fault energy gus, the peak shear strength and the slip at peak shear. Using a numerical solution, they find that the critical resolved shear stress increases with gus, but is relatively insensitive to the maximum shear strength. Suo and Lu present a model for the growth of a two-phase epilayer on an elastic substrate. By means of a linear perturbation analysis and numerical computations, they show that the competition between phase coarsening, due to phase boundary energy, and phase refining, due to concentration dependent surface stress, can lead to a variety of growth patterns, including a stable periodic structure. The chapter by Kachanov et al. gives a complete solution for the problem of translation and rotation of ellipsoidal inclusions in an elastic space. Although they do not pursue applications of the solution, the solution is relevant to deformation around hard particles in a matrix, motion of embedded anchors, etc. Thomson et al. present a percolation theory approach to addressing the inevitable inhomogeneous deformation on the microscale. They show how it can be used to construct stress/ strain response and give insight into processes of microlocalization. We consider it an honor and privilege to have had the opportunity to edit this volume. In the preparation of the biography, H. Gao, W. Drugan and Y. Ben-Zion provided extra needed information. Jim himself provided autobiographical source material and helped proofread it to assure its correctness and completeness. We are grateful to the individual authors for their contributions and timely cooperation, and to the technical review EDITORS’ PREFACE ix board members who enhanced the quality of the volume by providing critical reviews on the articles. Our special thanks are due to Kluwer Academic Publishers, Dordrecht Office and its professional staff for their editing and production, and for their agreement to publish the Volume given even when it was still unwritten, but existed simply as a proposal in the form of a list of authors and titles. Financial support and encouragement from NIST management team, S. Freiman, G. White and E. R. Fuller, Jr. are gratefully acknowledged. Finally, we would like to express our appreciation to Drs. W. Luecke, X. Gu and J. Guyer for their help in the editing of this book.

T-J. CHUANG, Gaithersburg, MD J. W. RUDNICKI, Evanston, IL 25 August 2000 TABLE OF CONTENTS

Editors’ Preface v

Biography of James R. Rice xv T.-J. Chuang and J. W. Rudnicki

List of Publications by James R. Rice xxvii

List of Contributors xli

PART I: DEFORMATION

Approximate Yield Criterion for Anisotropic Porous Sheet Metals and its 1 Applications to Failure Prediction of Sheet Metals under Forming Processes W. Y. Chien, H.-M. Huang, J. Pan and S. C. Tang

A Dilatational Plasticity Theory for Aluminum Sheets 17 B. Chen, P. D. Wu, Z. C. Xia, S. R. MacEwan, S. C. Tang and Y. Huang

Internal Hydrogen-Induced Embrittlement in Iron Single Crystals 31 J.-S. Wang

A Comprehensive Model for Solid State Sintering and its Application 49 to Silicon Carbide H. Riedel and B. Blug

Mapping the Elastic-Plastic Contact and Adhesion 71 S. Dj. Mesarovic

The Critical Shear Stress to Transmit a Peierls Screw Dislocation 87 across a Non-Slipping Interface P. M. Anderson and X.J. Xin xii TABLE OF CONTENTS

Self-Organizing Nanophases on a Solid Surface 107 Z. Suo and W. Lu

Elastic Space Containing a Rigid Ellipsoidal Inclusion 123 Subjected to Translation and Rotation M. Kachanov, E. Karapetian, and I. Sevostianov

Strain Percolation in Metal Deformation 145 R. M. Thomson, L. E. Levine and Y. Shim

Diffusive Instabilities in Dilating and Compacting Geomaterials 159 J. W. Rudnicki

PART II: FRACTURE

Fracture Mechanics of an Interface Crack between a Special Pair of 183 Transversely Isotropic Materials L. Banks-Sills and V. Boniface

Path-Independent Integrals Related to the J-Integral and Their Evaluations 205 S. Kubo

On the Extension of the JR Concept to Significant Crack Growth 223 B. Cotterell, Z. Chen and A. G. Atkins

Effect of T-Stress on Edge Dislocation Formation at a Crack Tip under 237 Mode I Loading G. E. Beltz and L. L. Fischer

Elastic-Plastic Crack Growth along Ductile/Ductile Interfaces 243 W. J. Drugan

Study of Crack Dynamics Using Virtual Internal Bond Method 275 P. A. Klein and H. Gao

Crack Tip Plasticity in Copper Single Crystals 311 J. Yu and J. W. Cho TABLE OF CONTENTS xiii

Numerical Simulations of SubCritical Crack Growth 331 by Stress Corrosion in an Elastic Solid Z. Tang, A. F. Bower and T.-J. Chuang

Energy Release Rate for a Crack with Extrinsic Surface Charge 349 in a Piezoelectric Compact Tension Specimen A. Haug and R. M. McMeeking

Micromechanics of Failure in Composites 361 -An Analytical Study A. A. Rubinstein

J-Integral Applications to Characterization and Tailoring 385 of Cementitious Materials V. C. Li

Author Index 407

Subject Index 415 James R. Rice Biography of James R. Rice

James Robert Rice (JRR) was born on 3 December 1940 in Frederick, Maryland to Donald Blessing Rice and Mary Celia (Santangelo) Rice. Located some 50 miles northwest of the nation’s capital, Frederick was then a small city of about 20,000 people, set in a rural, farming area. Commemorated in Whittier’s poem about Dame Barbara Fritchie’s patriotism, Frederick was a crossroads for troop movements during the Civil War (1861-1865) and the birthplace of Francis Scott Key who wrote the American National Anthem. JRR’s mother Mary was the child of a Sicilian immigrant family and now resides in Adamstown, Maryland. The family of JRR’s father, Donald, had long lived in that part of the USA. Donald, who died in 1987, operated a gasoline station, served 3 terms as alderman and a term as mayor of Frederick City in the early 1950s, later founded a successful tire company, and, like Mary, was highly active in Frederick community affairs. JRR was raised in Frederick, and was the second of three children. His older brother, Donald Blessing Rice Jr., served as corporate CEO of several companies (such as the RAND Corporation) in the private sector and one term as Secretary of the U.S. Air Force under the Bush Administration. He now resides in Los Angeles. JRR’s younger brother, Kenneth Walter Rice, continues to live in Frederick and runs the business started by his father. JRR attended primary and secondary school at St. John’s Literary Institute, a local parish school in Frederick. He played baseball and basketball, worked part-time delivering newspapers and in his father’s businesses, and read a lot. Influenced by his high school teachers of math and physics, recruited from Fort Dieterich, a local army base, JRR’s early interest in auto mechanics gradually evolved into an interest in mechanical engineering. Armed with several scholarships, he began undergraduate studies in that subject at Lehigh University in Bethlehem, PA, in 1958, one year after the launch of Sputnik propelled the U.S. into a keen competition in outer space with the then-USSR. During his undergraduate studies at Lehigh, JRR realized his particular interest was in theoretical mechanics, especially fluid and solid mechanics, and applied mathematics. Under the influence of inspiring teachers including Ferdinand Beer, Fazil Erdogan, Paul Paris, Jerzy Owczarek, George Sih, and Gerry Smith, he did his subsequent studies in the engineering mechanics and applied mechanics programs. Paul Paris has said that for the courses JRR took from him, half of Paul’s preparation for each lecture consisted of answering the questions JRR had posed during the previous class meeting. Because of his proficiency in math and physics, JRR earned all his academic degrees, from B.S. to Ph.D in only six years (1958-1964), the shortest time in Lehigh’s record. Ferdinand Beer directed JRR’s M.S. and Ph.D. theses on stochastic processes, specifically on the statistics of highly correlated noise. The results were summarized in 1964 in his Ph.D. thesis, entitled “Theoretical Prediction of Some Statistical Characteristics of Random Loadings Relevant xvi BIOGRAPHY OF J. R. RICE to Fatigue and Fracture”. At the same time, he continued working with George Sih on the subject of his undergraduate research project, elastic stress analysis of cracks along a bi- material interface. He independently developed a simple elastic-plastic crack model, which turned out to be the same as D. S. Dugdale had already published, and then extended the model to the case of cyclic loads. His work on “The Mechanics of Crack Tip Deformation and Extension by Fatigue” was published in ASTM STP 415 in 1967, and was awarded the ASTM Charles B. Dudley Medal in 1969. In the late 1950s, fracture mechanics was still in the early stages of development. Egon Orowan of MIT and George Irwin of Naval Research Laboratory were beginning to advocate using stress analysis of cracks to solve fracture and fatigue problems in conventional metals and metal alloys. Motivated by the problems encountered while working at Boeing in the summers, Paul Paris was especially keen to work in this field. Together Paris, George Sih and Erdogan offered the first graduate course on fracture mechanics, which JRR took in his senior year. In addition, they recruited bright graduate students, including JRR, to do thesis research in this area. This environment cultivated JRR’s interest in fracture mechanics, which became a major focus of his teaching and research. After JRR’s graduation from Lehigh in 1964, his advisor, Ferdinand Beer, suggested he accept an offer from Daniel C. Drucker to be a post-doctoral research fellow in the Solid Mechanics Group of the Division of Engineering at Brown University. Brown was (and still is) well known internationally in the solid mechanics community. At that time many world-renowned researchers in solid mechanics were members of the faculty. They included, among others, Daniel C. Drucker, Morton E. Gurtin, Harry Kolsky, Joseph Kestin, Alan C. Pipkin, Ronald S. Rivlin, Richard T. Shield, and Paul S. Symonds. At Brown, JRR, armed with enthusiasm, energy, and innovative ideas, pursued his research on many critical fronts in fracture mechanics. He continued to collaborate with his former professors on the unfinished work from Lehigh, including characterization of fatigue loadings, plastic yielding at a crack tip and stress analysis of cracks and notches in elastic and work-hardening plastic materials under longitudinal shear loading. At Lehigh, he had also obtained some results for determining energy changes due to material removal, such as cracking or cavitation, in a linear elastic solid. At Brown, Drucker opened his eyes to the importance of generalizing these results to the widest possible class of materials; thus, JRR developed this work into a procedure for calculating energy changes in a general class of solids. This work led to JRR’s discovery of the well-known J-integral a few years later. With these impressive achievements, he was offered a tenure-track faculty job as Assistant Professor in 1965. As an assistant professor at Brown, JRR devoted his energy and efforts not only to research but also to teaching. He always believed that a good professor must excel in teaching and research. He offered many courses in applied mechanics. He developed his own lecture notes in each course without relying on specific text books. During lecturing in a typical class, he memorized every important piece of information and used the blackboard to convey the concepts to students. He was an excellent and effective BIOGRAPHY OF J. R. RICE xvii communicator. Students were always welcome and encouraged to ask questions or engage in discussions. Copies of his lecture notes highlighting the key information including methods of derivations and final resulting formulae were distributed to his students. In research, he obtained federal funding from agencies such as NSF, DARPA, NASA, ONR, and the DOE to support project initiatives on mechanics of deformation and fracture. At this time, fracture mechanics was still in the early stages of development. JRR seized the opportunity to work out many unsolved problems in stress and deformation fields around a crack in various materials systems, mostly in 2D. Some examples are: elastic- plastic mechanics of crack extension, stresses in an infinite strip containing a semi-infinite crack, plane-strain deformation near a crack in a power-law hardening material (with G.F. Rosengren), energy changes in stressed bodies due to void and crack growth (with D.C. Drucker), a path independent integral and the approximate analysis of strain concentration by notches and cracks. At the invitation of H. Liebowitz, this work was summarized in a classic review article entitled “Mathematical Analysis in the Mechanics of Fracture”, which appeared in 1968 as Chapter 3, in Volume 2, Mathematical Fundamentals of Fracture, of the book series, Fracture: An Advanced Treatise. Of particular significance was the discovery of a path-independent integral resulting from his prior probe into energy variations due to cracking of a nonlinear elastic solid. He named this particular integral the “J-Integral” with the upper case letter “J” inadvertently coinciding with his nickname “big Jim” respectfully used by his students. This integral turned out to coincide with a 2D version of the general 3D energy momentum tensor proposed by J. D. Eshelby in England in 1956. A similar concept was also developed by Cherepanov in Russia at about the same time as Rice’s J-integral, but JRR exploited the integral’s usefulness more fully in fracture analysis, especially by focusing on aspects relating to path-independence. Because of its path independence, the J-integral is a powerful tool to evaluate energy release due to cracking, bypassing the difficulties arising from strain concentration at the crack-tip. Using the procedure he developed with Drucker, JRR showed that the J-Integral is identical to the rate of reduction of potential energy with respect to crack extension. In addition, JRR, together with the late Göran F. Rosengren, showed in 1968 that the J-integral plays the role of a single unique parameter that governs the amplitude of the nonlinear deformation and stress fields inside the plastic zone near a crack tip. This result established criticality of the J-integral as a criterion for fracture even for an elastic-plastic material and made possible its use for practical engineering applications. Simultaneously, John Hutchinson at Harvard also derived a similar result. Based on their studies, the nonlinear stress distribution in the crack tip zone is now referred to as the “Huchinson-Rice-Rosengren” or “HRR” field. Over the next decade, criticality of the J- Integral was adopted as the major design criterion against failure. It is used in the ASME Pressure Vessel and Piping Design Code, and in general purpose finite element codes such as ABAQUS and ANSYS. JRR’s paper on the J-integral, which appeared in the Journal of Applied Mechanics in 1968, received the ASME Henry Hess Award in 1969 and has become a classic, attracting more than 1000 citations and references. The J-Integral forms an essential part of the subject matter contained in any textbook on fracture mechanics. xviii BIOGRAPHY OF J. R. RICE

Because of this and other contributions, JRR was promoted to Associate Professor in Engineering in 1968 and received the ASME Pi Tau Sigma Gold Medal Award for outstanding achievement in mechanical engineering within 10 years following graduation in 1971. As Associate Professor at Brown, JRR extended his research interests from mechanics to the physics and thermodynamics aspects of fracture phenomena. He worked with his student N. Levy on the prediction of temperature rise by plastic deformation at a moving or stationary crack-tip. When applied to a set of aluminum and mild steel alloys, this work helped to explain the experimentally observed relationship between the temperature- dependent toughness and the loading rate. Other accomplishments included his work with his student Dennis Tracey on the ductile void growth in a triaxial stress field. This work clarified the mechanism of void growth under applied stress in ductile metals. The role of large crack tip geometry changes in plane strain fracture was quantified in a paper with M. Johnson. He also actively participated in the development of formulations for finite element computations. He directed Ph.D. thesis research in computational fracture mechanics by Dennis Tracey. He interacted with Pedro Marcal, a faculty colleague and the founding developer of the MARC finite element code, and with Dave Hibbitt, Marcal’s graduate student and the co-developer of the ABAQUS code. Together, they developed an appropriate numerical algorithm to compute large strains and large displacements in the finite element code. This scheme has been implemented in many general purpose finite element codes such as MARC, ABAQUS and ANSYS. With another faculty colleague, Joseph Kestin, JRR worked on the application of thermodynamics to strained solids. For example, although the chemical potential is well- defined in fluids, the proper definition in solids is not clear. A paper by Kestin and Rice helped to clarify the concept and served as a starting point to extend JRR’s developing interest in high temperature fracture, namely, creep and creep rupture. In 1970, JRR was promoted to Full Professor of Engineering. With financial support from federal funding agencies such as the National Aeronautic and Space Administration (NASA), Office of Naval Research (ONR), DARPA, National Science Foundation (NSF) and Atomic Energy Commission (AEC, the predecessor of ERDA and the Department of Energy (DOE)), he was directing a research team of 7 Ph.D. graduate students. The team participated in the Materials Research Laboratory, a large-scale, interdisciplinary research program, funded by DARPA and NSF, and in a program of the AEC Basic Sciences Division directed by Joseph Gurland. JRR’s students worked in a wide range of areas in the mechanics of solids and fracture: Dennis Tracey, Dave Parks, and Bob McMeeking in (1) theoretical and computational fracture mechanics; Art Gurson in (2) constitutive relationships in metals and metallic alloys; Glenn Brown and (Jerry) T.- j. Chuang in (3) creep and creep rupture in the high temperature range; and Mike Cleary in (4) mechanics of geomaterials. Representative work in (1) included an alternative formulation of Bueckner’s (1970) weight function method to evaluate the stress intensity factor KI of a given 2D linear elastic cracked solid subject to arbitrary loading, based on any known solution to the same geometry; a finite element analysis of small scale yielding near BIOGRAPHY OF J. R. RICE xix a crack in plane-strain (with N. Levy, P.V. Marcal and W.J.Ostergren); an approximate method for analysis of a part-through surface crack in an elastic plate (with N. Levy); and 3D elastic-plastic stress analysis for fracture mechanics (with N. Levy and P. V. Marcal). In (2) JRR worked out the fundamental structure for the time-dependent stress-strain relationship of a metal in the plastic deformation range and proposed an internal variable theory for the inelastic constitutive relations in metal plasticity. In 1971-72, JRR took a year of sabbatical leave with support from a NSF Senior Postdoctoral Fellowship. He spent the year at the Department of Applied Mathematics and Theoretical Physics of the University of Cambridge, where he was affiliated with Churchill College under the support of a Churchill College Overseas Fellowship. At Cambridge, he worked with a number of people, including Rodney Hill, one of the pioneers in classical plasticity, Andrew C. Palmer in soil mechanics, and John Knott and his student Rob Ritchie on elastic-plastic fracture. With Hill, JRR developed a general structure of inelastic constitutive relations assuming the existence of elastic potentials, and gave a special implementation for elastic/plastic crystals at finite strain. In the latter case, crystallographic slip along a set of active slip planes was considered as the sole deformation mechanism responsible for the inelastic behavior. This theory successfully explained various aspects of plasticity such as strain hardening, the existence of a flow rule and normality. With Knott and Ritchie, JRR proposed a relationship between the critical tensile stress and the fracture toughness of mild steel. The analysis predicts the observed temperature dependence of K IC in the brittle to ductile transition range. With Andrew Palmer, JRR used his newly developed J-integral to develop a mode-II “shear crack” model for the growth of slip surfaces in over-consolidated clay slopes. Returning to Brown in 1972, JRR continued to pursue research on many aspects of fracture mechanics. John Landes and Jim Begley of the Westinghouse R&D Center became keen advocates of using the J-Integral as a design criterion in the nuclear energy business, and in a paper with Landes and Paul Paris, JRR developed an elegantly simple procedure to estimate the value of J-Integrals from experiments. Eventually, this procedure became the ASTM standard and part of the ASME Pressure Vessels and Piping design code. Besides analysis on the continuum level, JRR strongly felt that there was a need to study fracture at the microstructural level in order to bridge the atomic and engineering scales. One important area that required such a treatment is high temperature creep and creep rupture where mass transport plays an important role. At that time, a group at Harvard led by Mike Ashby was also interested in this topic. As a result, there was much interaction between Harvard and Brown during 1972-74: JRR and Ashby and their students made frequent mutual visits to give seminars and to exchange ideas. One important result, jointly developed in 1973 with his student, T.- J. Chuang, was the discovery of creep crack-like cavity shapes induced by surface diffusion. This type of cavity, referred to as a Chuang-Rice crack-like cavity, is frequently observed at the grain boundaries of a ruptured tensile specimen. This work defines the boundary conditions at the cavity apex and satisfactorily explained non-linear stress dependence on cavity growth rate. The degree of non-linearity depends on the deformability of the grains, and JRR obtained solutions for the stress xx BIOGRAPHY OF J. R. RICE dependence on creep cavity growth in rigid grains (with Chuang, Kagawa, Sills and Sham), in elastic grains (with Chuang) and in plastic grains (with Needleman). The predicted stress dependence was verified experimentally by Bill Nix and his students at Stanford in the late 1970s using implanted water vapor cavities at grain boundaries in pure silver and nickel-tin alloys. Later in the 1980s and 90s, this work was used by many researchers to predict cavity growth induced by electromigration in aluminum interconnect wires. In 1973, JRR was offered a Chair by the Brown President, Donald Hornig with the title L. Herbert Ballou Professor of Theoretical and Applied Mechanics. This privileged title is an honor comparable to a University Professorship, which is the highest rank of teaching professors at Brown. In physical metallurgy, it had become well-known that dislocations at the atomic level are fully responsible for the room temperature plastic behavior in metals. Since the early 1960s, many researchers (such as Hirth, Lothe, Mura and Weertman) devoted their efforts to this area and helped to build the foundation of dislocation theory. JRR was among those cutting edge scholars who excelled in mathematical dislocation theory. In 1972, he met Robb Thomson of SUNY-Stony Brook at a conference and they puzzled over the ductile versus brittle transition phenomenon in crystals. Since dislocation movement leads to ductility and rapid crack growth leads to catastrophic failure, they believed the interactions of both must play a dominant role in ductile/brittle behavior. They proposed that the ability to emit dislocations from a pre-existing sharp crack tip is the source of ductility in metals. On the other hand, the resistance of a crack tip to dislocation emission leads to brittleness in ionic or covalent crystals like ceramics. By analyzing the energetic forces between a dislocation and a crack, they derived an important parameter that governs the ductility. If this parameter, which is shear modulus times Burgers vector over surface energy, exceeds 8.5 to 10, then the crystal exhibits intrinsically brittle behavior. If less, it is generally ductile. The Rice -Thomson theory has become a classic in the Science Citation Index with more than 200 citations. In the late 1970’s, Mike Ohr of Oak Ridge National Laboratory provided direct experimental evidence for the theory by observing emission of dislocations from the crack tip in a variety of metal specimens in situ under TEM. In another noteworthy work, JRR helped his student Art Gurson to develop in 1975 the plasticity theory of porous media, in which yield criteria and flow rules were predicted in stress space using 2D or 3D unit cell models. The model predicts the effect of porosity on the plastic behavior of ductile materials and has come to be known as the “Gurson” model. It is well-known in the metallurgy and mechanics communities and is one of the major yield criteria adopted in the commercial general purpose finite element codes for assessing inelastic behavior of metallic materials. Motivated by his studies of shear bands with Andrew Palmer, JRR became interested in the fundamental question of why deformation would localize in a narrow zone. A basic premise of fracture mechanics, going back to the ideas of Griffith, is that the presence of flaws in a material causes a local elevation of the stress and leads to propagation of the flaw and, eventually, to failure. Although this process provides a satisfactory explanation of failure in many materials, it does not explain why macroscopically uniform BIOGRAPHY OF J. R. RICE xxi deformation should give way to localized deformation in very ductile materials or under conditions of compressive stress that suppress flaw propagation. Based on antecedents in the work of Hadamard, Hill, Thomas and Mandel, JRR and his student Rudnicki treated the initiation of localized deformation as a bifurcation from homogeneous deformation and showed that its onset was promoted by certain subtle features of the constitutive behavior. This work, which was published in the Journal of the Mechanics and Physics of Solids in 1975, received the Award for Outstanding Research in Rock Mechanics from the U. S. National Committee on Rock Mechanics in 1977. Although this work was originally intended to describe fault formation in rock, JRR extended the approach to consider localized necking in thin sheets (with S. Storen), strain localization in ductile single crystals (with R. J. Asaro), and limits to ductility in sheet metal forming (with A. Needleman). He summarized the state of the subject in a keynote lecture on “The Localization of Plastic Deformation” at the 14th International Congress on Theoretical and Applied Mechanics in Delft in 1976. The printed version of this lecture is a widely-cited classic. In the early 1970’s, there were many reports of observations precursory to earthquakes that were attributed to the coupling of deformation with the diffusion of pore fluid. A series of papers, by JRR with students (Cleary and Rudnicki) and Don Simons, an Assistant Professor at Brown, analyzed the effects of this coupling on models for earthquake instability and for quasi-statically propagating creep events. One of these papers (“Some basic stress-diffusion solutions for fluid-saturated elastic porous media with compressible constituents”, with M. P. Cleary, Rev. Geophys. Space Phys., 14, pp. 227-241, 1976) reformulated, in a particularly insightful way, the equations first derived by Biot for a linear elastic, porous, fluid-infiltrated solid. This version of the equations has proven so advantageous that it is now the standard form. The models of the earthquake instability formulated to study these effects were among the first in which the instability was not postulated but arose in a mechanically consistent way from the interaction of the fault zone material behavior and the surroundings. JRR’s interest in the mechanics of earthquakes proved durable and became a major branch of his work. With Florian Lehner and Victor Li, he worked on time-dependent effects due to coupling of the shallow, elastic portion of the Earth’s lithosphere with deeper viscoelastic portions. This work was based on a generalization of an earlier thin plate model by Elsasser. This work demonstrated that the viscous deformation of the lower crust and upper mantle following large earthquakes could affect surface deformation for decades and provided a new model for the interpretation of increasingly detailed surface deformation measurements. In the early 90s, JRR used the finite element code ABAQUS together with Yehuda Ben-Zion, Renata Dmowska, Mark Linker, and Mark Taylor to explore the behavior of this model in 3D and to compare model predictions with geophysical observations. JRR’s growing interest in the mechanics of earthquakes complemented nicely the interests of his spouse, Renata Dmowska, a seismologist. Together, Renata's analysis of data and JRR’s mathematical models have been combined in several papers on aspects of earthquakes, particularly in subduction zones. JRR’s interest in the mechanics of earthquakes soon led to a study of frictional xxii BIOGRAPHY OF J. R. RICE stability. Stick-slip is a widely observed phenomenon and has long been regarded as a physical analog for the earthquake instability. But the standard constitutive description, static and dynamic friction, was inconsistent with the steady sliding often observed and contained no mechanism for restrengthening that would allow repeated events on the same surface. Based on experimental observations of Dieterich at the U.S. Geological Survey, JRR and his student Andy Ruina formulated a rate- and state-dependent constitutive relationship for sliding on a frictional surface. By examining the stability of a one degree-of- freedom system with this relationship, they were able to predict the variety of behaviors observed in rock friction experiments: steady sliding, damped oscillations, stick-slip and sustained periodic oscillations. Other papers with Tse and Gu examined the dynamics and nonlinear stability of these systems. JRR and his student Tse showed that when this type of relationship was applied on a surface between two elastic solids and modified to include a depth dependence appropriate for the temperature and pressure dependence in the earth, the calculations produced periodic events with a depth dependence remarkably similar to that of observed earthquakes. In the late 1970s and early 1980s, JRR also continued to work on many aspects of inelasticity and fracture. With Joop Nagtegaal and Dave Parks, he developed a numerical scheme to improve the accuracy of finite element computations in the fully plastic range. With Bob McMeeking, he worked out the proper finite element formulation in the large elastic-plastic deformation regime. With a colleague at Brown, Ben Freund, and a student, Dave Parks, he helped solve the problem of a running crack in a pressurized pipeline. In materials science, he studied stress corrosion and hydrogen embrittlement problems. He also orchestrated a remarkable multidirectional attack on the problem of quasi- static crack growth in elastic-plastic materials. This began with a paper with Paul Sorensen in 1978 that proposed an elegant way of using near-tip elastic-plastic fields to derive theoretical predictions for crack growth resistance curves (J R curves). Then, he and his student Walt Drugan derived asymptotic analytical elastic-ideally plastic solutions for the stress and deformation fields near a plane strain growing crack which showed the necessity of an elastic unloading sector in the near-tip field. [Independent work by L. I. Slepyan in the then-USSR and Y. C. Gao in China also addressed this problem, for incompressible material and steady-state conditions.] The detailed numerical finite element elastic-plastic growing crack solutions of JRR’s student T-L. Sham confirmed the analytical predictions, and in a 1980 paper with Drugan and Sham, JRR combined the method proposed earlier with Sorensen, with the new analytical asymptotic solutions and Sham’s numerical results, to produce a comprehensive and fundamentals-based model of stable ductile crack growth and predictions of plane strain crack growth resistance curves. Then, with Lawrence Hermann, JRR conducted and analyzed “plane strain” crack growth tests and showed that this theory was indeed capable of describing the experimentally-measured crack growth resistance curves under contained yielding conditions. The asymptotic analysis of elastic-ideally plastic growing crack fields, involving the assembling of different possible types of near-tip solution sectors into complete near-tip solutions, prompted JRR and Drugan to inquire more fundamentally about what continuity BIOGRAPHY OF J. R. RICE xxiii and jump conditions are required across quasi-statically propagating surfaces in elastic- plastic materials by the fundamental laws of continuum mechanics and broad, realistic constitutive constraints (such as the maximum plastic work inequality). Their resulting restrictions (published in the D. C. Drucker Anniversary Volume), and the later generalization of these to dynamic conditions by Drugan and Shen, have been utilized repeatedly in elastic-plastic crack growth studies. Not surprisingly, perhaps the most important applications of these discontinuity results are due to JRR himself, in his fundamental studies of stationary and growing crack fields in ductile single crystals, wherein JRR showed that a precise understanding of possible discontinuity types is absolutely essential in deriving correct solutions. Beginning in 1985 with his student R. Nikolic on the anti-plane shear crack problem, and in a landmark, pioneering 1987 paper on plane strain tensile cracks, JRR produced fascinating analytical solutions for the near-tip fields in elastic-ideally plastic ductile single crystals. These fields differ dramatically from crack fields in isotropic (i.e., polycrystalline) ductile materials, being characterized by discontinuous displacements and stresses for stationary cracks, discontinuous velocities for quasi-statically growing cracks, and, in another fascinating paper with Nikolic in 1988, JRR showed that the near-tip field for a dynamically propagating anti-plane shear crack in a ductile single crystal must involve shock surfaces across which stress and velocity jump. JRR and his student M. Saeedvafa generalized the stationary crack ductile single crystal solutions to incorporate Taylor hardening, revealing even more complex near-tip behavior. Other major work in the late 1970s and early 1980s included two important papers with visiting faculty members: one on the crack tip stress and deformation fields for a crack in a creeping solid, with Hermann Riedel; and another heavily-cited paper on crack curving and kinking in elastic materials, with Brian Cotterell. For his significant contributions to sciences and engineering, JRR was elected to Fellow grade of the American Academy of Arts and Sciences in 1978, Fellow of the American Society of Mechanical Engineers and Membership in the National Academy of Engineering in 1980, and membership in the National Academy of Sciences in 1981. The next move was to Harvard University in September 1981. A Gordon McKay Chaired Professorship in Engineering Sciences and Geophysics was created for JRR, jointly in the Division of Applied Sciences and the Department of Earth and Planetary Sciences. He further expanded the scope of his research activities along two major branches in mechanics, namely, fracture of engineering materials and geological materials. At Harvard, he recruited many bright students from all over the world to work on topical fracture problems in engineering and geology. He directed Peter Anderson to study constrained creep cavitation and the Rice-Thomson model, supervised Huajian Gao on three dimensional crack problems, worked with Jwo Pan, Ruzica Nikolic and Maryam Saeedvafa on inelastic behaviors of cracks in single crystal metals, and collaborated with Renata Dmowska, Victor Li, Paul Segall, Andy Ruina, Yehuda Ben-Zion, G. Perrin, J.-c. Gu, Mark Linker, Simon T. Tse , G. Zheng, and F. K. Lehner in developing friction laws and shear crack models of geological faults as related to earthquake events in seismology. JRR’s recent work on earthquakes has focused on several important aspects of the xxiv BIOGRAPHY OF J. R. RICE process. One issue is the origin of earthquake complexity, that is, the distribution of events of various sizes, as described by the well-established Gutenberg-Richter relationship. One previous explanation was that fault slip, as modeled by friction between two elastic solids, was an inherently chaotic process. In a series of papers that combine elegant analysis and prodigious calculations, JRR and his post-doc, Yehuda Ben-Zion, showed that the chaotic behavior predicted in these models was the subtle result of numerical discretization and oversimplification of the frictional constitutive relation. Other work was motivated by observations that slip during an earthquake does not propagate in the fashion predicted by classical dynamic fracture mechanics with most of the surface slipping for the entire duration of the event. Instead, slip is pulse-like and any point on the surface slips only for a short time. Papers with Zheng and Perrin showed that only certain types of frictional constitutive relations were consistent with these observations. Another, very influential paper, “Fault Stress States, Pore pressure Distributions and the Weakness of the San Andreas Fault” addresses a long-standing paradox in earthquake mechanics: A variety of measurements indicate that the San Andreas fault in southern California is much weaker, both in an absolute sense and relative to the surrounding crust, than would be expected from a straightforward interpretation of laboratory friction experiments. JRR showed that the discrepancy could be resolved by high fluid pressures within the fault zone and summarized a variety of evidence for this possibility. Another mechanism that can explain the discrepancy and produce slip in a pulse-like form is dynamic rupture along a bi-material interface. JRR has been studying this problem recently together with his student K. Ranjith and Post-Doc A. Cochard, following earlier works of Weertman, Adams, and Andrews and Ben-Zion, thus returning to a subject he investigated statically as an undergrad at Lehigh. In the mid-1980’s, JRR and other faculty members including John Hutchinson and Bernie Budiansky formed a joint research team with Tony Evans at the University of California at Santa Barbara to study mechanical behavior and toughening mechanisms of ceramics. Between 1988 and 1994, faculty and students at Harvard regularly visited and exchanged ideas with Tony Evans and his research group at UCSB. The Harvard-UCSB collaboration generated tremendous research output. During this period, JRR worked with John Hutchinson, Jian-Sheng Wang, Mark E. Mear and Zhigang Suo on crack growth on or near a bi-material interface. With Jian-Sheng Wang, he developed a model of interfacial embrittlement by hydrogen and solute segregation. This model has been referred to as the Rice-Wang Model which provided a basis for the materials community in pursuit of better design of steels. Between 1989 and 1995, JRR worked with Glenn Beltz, Y. Sun and L. Truskinovsky to reformulate the Rice-Thomson model in terms of interactions between a crack and a Peierls dislocation being emitted from the crack tip. This study eliminated the need to define a core cut-off radius for dislocations and instead established unstable stacking fault energy as the new physical parameter governing the intrinsic ductility of crystals. Rice’s new model caused an instant sensation among materials scientists and physicists and is now used as the new paradigm for understanding brittle-ductile transition of crystals. Separate from his other activities at Harvard, JRR began to develop a growing interest in three dimensional crack problems, starting around 1984. Together with Huajian BIOGRAPHY OF J. R. RICE xxv

Gao, the first of his graduate students at Harvard to work on 3-D crack problems, he developed a series of ingenious methods of analysis based on the idea of 3-D weight functions, generalizing a 2-D concept he and Hans Bueckner had developed in the early 1970’s. These methods were used to study configurational stability of crack fronts, crack interaction with dislocation loops and transformation strains, and trapping of crack fronts by tough particles. In 1987, he began to work with K. S. Kim, who spent a year of sabbatical at Harvard, to generalize these methods to model dynamically propagating 3-D crack fronts. This then led to a burst of his interests in the following years in the spontaneous dynamics of 3-D tensile crack propagation and of slip ruptures in earthquake dynamics. He directed a number of graduate students, post-docs and visiting scientists on those areas, including K. S. Kim, Yehuda Ben-Zion, G. Perrin, G. Zheng, Phillipe Geubelle, A. Cochard, J. W. Morrissey, and Nadia Lapusta. He also encouraged other leading scientists such as John Willis and Daniel Fisher to work in this field. An example of significant discoveries coming out of these activities is a new kind of wave which propagates along the crack front at a velocity different from the usual body and surface elastic wave speeds. JRR continues today to lead an international research effort in crack and fault dynamics. Needless to say, the output of his research group is of the highest quality and generates significant impact on the engineering, materials science and geophysics communities. As a result of his contributions to science and engineering, JRR received numerous awards and recognitions by professional societies and academic institutions. In 1981, he was elected to Fellow of AAAS. Next year in 1982, he received the George R. Irwin Medal from ASTM Committee E-24, shared with John Hutchinson, for “significant contributions to the development of nonlinear fracture mechanics”. In 1985, he was one of the recipients of an Honorary Doctor of Science Degree at his alma mater, Lehigh University. In 1988, he was elected Fellow of the American Geophysical Union, and received the William Prager Medal from the Society of Engineering Science for his “outstanding achievements in solid mechanics”. Two years later, he was elected Fellow of the American Academy of Mechanics and the Royal Society of Edinburgh. In 1992, he received an award from AAM for “Distinguished Service to the Field of Theoretical and Applied Mechanics”. The following year he served as Francis Birch Lecturer on “Problems on Earthquake Source Mechanics” at the American Geophysics Union. The next year he received the ASME Timoshenko Medal with the following citation: “for seminal contributions to the understanding of plasticity and fracture of engineering materials and applications in the development in the computational and experimental methods of broad significance in mechanical engineering practice”. In 1996, he was elected as a Foreign Member of the Royal Society of London for his work on “earthquakes and solid mechanics” and received an honorary degree from Northwestern University. In addition, he received the ASME Nadai Award for major contributions to the fundamental understanding of plastic flow and fracture processes in engineering and geophysical materials and for the invention of the J- Integral which forms the basis for the practical application of nonlinear fracture mechanics to the development of standards for the safety of structures. He also received the Francis J. Clamer Medal from the Franklin Institute for Advances in Metallurgy with the citation: “for xxvi BIOGRAPHY OF J. R. RICE development of the J-Integral for the accurate prediction of elastic-plastic fracture behavior in metal from easily obtained data”. In 1997, he received an honorary Doctor of Science degree from Brown University. In 1998, a donation from David Hibbitt and Paul Sorensen of HKS, Inc. established the Rice Professorship at Brown in his honor. Recently, he was awarded the Blaise Pascal Professorship by the Region Ile-de-France for the 1999 calendar year for research on “Rupture Dynamics in Seismology and Materials Physics”, and he was the recipient of an Honorary Doctoral Degree at the University of Paris VI in March 1999. He was elected a Foreign Member (Associé Étrager) of the French Academy of Sciences in April 2000. There is no need to place complimentary words here on the impact of his work. The recognitions described in the previous paragraph speak for themselves. His standards of scholarship and intellectual honesty are the highest. He is always ready to appreciate the good work of other colleagues, and to give them proper credit. On the other hand, he does not hesitate to dispense candid criticism of inconsistent or misguided thinking, though in a gentle rather than harsh manner -- as some oral comments in conferences or written book reviews testify. A man is as young as he thinks. JRR enjoys long walks, whether in urban or mountain settings, reads broadly in science, history and social commentary, and likes listening to classical and folk music in his spare time.. He has an excellent sense of humor, a razor-sharp wit and a cheerful disposition. His wife Renata Dmowska, in addition to being a regular and important scientific collaborator, is an excellent influence on Jim. Renata is an enthusiastic polymath with a warm and cheerful personality and a seemingly endless array of interests. She insists that he take much-deserved breaks from his research to attend concerts, to visit art museums, to travel, to read literature, and to socialize with their large circle of friends. JRR is increasingly active in his research, full of curiosity, creativity and persistence. As his students can attest, he is also an excellent teacher in the classroom. He gives lectures in a humorous, but comprehensive way that can be easily digested by his audience. As a thesis advisor, he defines the scope of a research area in which he sees the potential for advancement. He inspires and encourages, but does not push his students. When a student heads in a wrong direction or reaches a dead end, he wastes no time to steer him or her back to the right track. His good qualities as an advisor were recognized by his recent Excellence in Mentoring Award conferred by the Graduate Student Council of Harvard University in April 1999. JRR recently returned from his full year sabbatical leave (January 1999 to January 2000) in Paris, France, working in the Département Terre Atmosphère Océan of École Normale Supérieure, and also part time at École Polytechnique in Paliseau. His flow of publications shows no sign of diminishing and his friends and colleagues surely will hope that the short legend “J. R. Rice” will appear again and again in the scientific literature for many years to come.

TZE-JER CHUANG JOHN W. RUDNICKI Gaithersburg, MD Evanston, IL List of Publications by James R. Rice

1. G. C. Sih and J. R. Rice, “The Bending of Plates of Dissimilar Materials with Cracks”, Journal of Applied Mechanics, 31, (1964), pp. 477-482. 2. J. R. Rice and E. J. Brown, “Discussion of ‘Random Fatigue Failure of a Multiple Load Path Redundant Structure’ by Heller, Heller and Freudenthal”, in Fatigue: An Interdisciplinary Approach (eds. J. Burke, N. Reed and V. Weiss), Syracuse University Press, (1974), pp. 202-206. 3. J. R. Rice and F. P. Beer, “On the Distribution of Rises and Falls in a Continuous Random Process”, Transactions ASME (Journal of Basic Engineering), 87D, (1965), pp. 398-404. 4. J. R. Rice and G. C. Sih, “Plane Problems of Cracks in Dissimilar Materials”, Journal of Applied Mechanics, 32, (1965), pp. 418-423. 5. J. R. Rice, F. P. Beer and P. C. Paris, “On the Prediction of Some Random Loading Characteristics Relevant to Fatigue”, in Acoustical Fatigue in Aerospace Structures (eds. W. Trapp and D. Forney), Syracuse University Press, (1965), pp. 121-144. 6. J. R. Rice, “Starting Transients in the Response on Linear Systems to Stationary Random Loadings”, Journal of Applied Mechanics, 32, (1965) pp. 200-201. 7. J. R. Rice, “Plastic Yielding at a Crack Tip”, in Proceedings of the 1st International Conference on Fracture, Sendai, 1965 (eds. T. Yokobori, T. Kawasaki, and J. L. Swedlow), Vol. I, Japanese Society for Strength and Fracture of Materials, Tokyo, (1966), pp. 283-308. 8. J. R. Rice, “An Examination of the Fracture Mechanics Energy Balance from the Point of View of Continuum Mechanics”, in Proceedings of the 1st International Conference on Fracture, Sendai, 1965 (eds. T. Yokobori, T. Kawasaki, and J. L. Swedlow),Vol. I, Japanese Society for Strength and Fracture of Materials, Tokyo, (1966) pp. 309-340. 9. J. R. Rice and F. P. Beer, “First Occurrence Time of High Level Crossings in a Continuous Random Process”, Journal of the Acoustical Society of America, 39, (1966) pp. 323-335. 10. J. R. Rice, “Contained Plastic Deformation Near Cracks and Notches Under Longitudinal Shear”, International Journal of Fracture Mechanics, 2, (1966) pp. 426-447. 11. J. R. Rice and D. C. Drucker, “Energy Changes in Stressed Bodies due to Void and Crack Growth”, International Journal of Fracture Mechanics, 3, (1967) pp. 19-27. 12. J. R. Rice, “Stresses due to a Sharp Notch in a Work Hardening Elastic-Plastic Material Loaded by Longitudinal Shear”, Journal of Applied Mechanics, 34, (1967), pp. 287-298. xxviii LIST OF PUBLICATIONS BY J. R. RICE

13. J. R. Rice, “The Mechanics of Crack Tip Deformation and Extension by Fatigue”, in Fatigue Crack Propagation, Special Technical Publication 415, ASTM, Philadelphia, (1967), pp. 247-311. 14. J. R. Rice, “Discussion of ‘Stresses in an Infinite Strip Containing a Semi-Infinite Crack’ by W.G. Knauss”, Journal of Applied Mechanics, 34, (1967), pp. 248-250. 15. J. R. Rice, “A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks”, Journal of Applied Mechanics, 35, (1968), pp. 379-386. 16. J. R. Rice and G. F. Rosengren, “Plane Strain Deformation Near a Crack in a Power Law Hardening Material”, Journal of the Mechanics and Physics of Solids, 16, (1968), pp. 1-12. 17. J. R. Rice, “The Elastic-Plastic Mechanics of Crack Extension”, International Journal of Fracture Mechanics, 4, (1968), pp. 41-49 (also published in International Symposium on Fracture Mechanics, Wolters-Noordhoff Publ., Groningen, 1968,41-49). 18. J. R. Rice, “Mathematical Analysis in the Mechanics of Fracture”, Chapter 3 of Fracture: An Advanced Treatise (Vol. 2, Mathematical Fundamentals) (ed. H. Liebowitz), Academic Press, N.Y., (1968), pp. 191-311. 19. J. R. Rice and N. Levy, “Local Heating by Plastic Deformation at a Crack Tip”, in Physics of Strength and Plasticity (ed. A. S. Argon), M.I.T. Press, Cambridge, Mass., (1969), pp. 277-293. 20. J. R. Rice and D. M. Tracey, “On the Ductile Enlargement of Voids in Triaxial Stress Fields”, Journal of the Mechanics and Physics of Solids, 17, (1969), pp. 201-217. 21. D. C. Drucker and J. R. Rice, “Plastic Deformation on Brittle and Ductile Fracture”, Engineering Fracture Mechanics, 1, (1970), pp. 577-602. 22. J. Kestin and J. R. Rice, “Paradoxes in the Application of Thermodynamics to Strained Solids”, in A Critical Review of Thermodynamics (eds. E.G. Stuart, B. Gal-Or and A.J. Brainard), Mono Book Corp., Baltimore, MD (1970), pp. 275- 298. 23. H. D. Hibbitt, P. V. Marcal and J. R. Rice, “A Finite Element Formulation for Problems of Large Strain and Large Displacement”, International Journal of Solids and Structures, 6, (1970), pp. 1069-1086. 24. J. R. Rice, “On the Structure of Stress-Strain Relations for Time-Dependent Plastic Deformation in Metals”, Journal of Applied Mechanics, 37, (1970), pp. 728-737. 25. J. R. Rice and M. A. Johnson, “The Role of Large Crack Tip Geometry Changes in Plane Strain Fracture”, in Inelastic Behavior of Solids (eds. M. F. Kanninen, et al.), McGraw-Hill, N.Y., (1970), pp. 641-672. 26. N. Levy, P. V. Marcal, W. J. Ostergren and J. R. Rice, “Small Scale Yielding Near a Crack in Plane Strain: A Finite Element Analysis”, International Journal of Fracture Mechanics, 7, (1971), pp. 143-156. LIST OF PUBLICATIONS BY J. R. RICE xxix

27. J. R. Rice and N. Levy, “The Part-Through Surface Crack in an Elastic Plate”, Journal of Applied Mechanics, 39, (1972), pp. 185-194. 28. N. Levy, P. V. Marcal and J. R. Rice, “Progress in Three-Dimensional Elastic- Plastic Stress Analysis for Fracture Mechanics”, Nuclear Engineering and Design, 17, (1971), pp. 64-75. 29. J. R. Rice, “Inelastic Constitutive Relations for Solids: An Internal Variable Theory and Its Application to Metal Plasticity”, Journal of the Mechanics and Physics of Solids, 19, (1971), pp. 433-455. 30. J. R. Rice, “Some Remarks on Elastic Crack Tip Stress Fields”, International Journal of Solids and Structures, 8, (1972), pp. 571-578. 31. J. R. Rice and D. M. Tracey, “Computational Fracture Mechanics”, in Numerical and Computer Methods in Structural Mechanics (eds. S. J. Fenves et al.), Academic Press, N.Y., (1973), pp. 585-623. 32. B. Budiansky and J. R. Rice, “Conservation Laws and Energy-Release Rates”, Journal of Applied Mechanics, 40, (1973), pp. 201-203. 33. J. R. Rice and M. A. Chinnery, “On the Calculation of Changes in the Earth’s Inertia Tensor due to Faulting”, Geophysical Journal of the Royal Astronomical Society, 29, (1972), pp. 79-90. 34. R. J. Bucci, P. C. Paris, J. D. Landes and J. R. Rice, “J Integral Estimation Procedures”, in Fracture Toughness, Special Technical Publication 514, Part 2, ASTM, Philadelphia, (1972), pp. 40-69. 35. J. R. Rice, “The Line Spring Model for Surface Flaws”, in The Surface Crack: Physical Problems and Computational Solutions (ed. J.L. Swedlow), ASME, N.Y., (1972), pp. 171-185. 36. R. Hill and J. R. Rice, “Constitutive Analysis of Elastic/Plastic Crystals at Arbitrary Strain”, Journal of the Mechanics and Physics of Solids, 20, (1972), pp. 401-413. 37. J. R. Rice, “Elastic-Plastic Fracture Mechanics (Remarks for Round Table Discusison on Fracture at the 13th International Congress of Theoretical and Applied Mechanics, Moscow, 1972)“, Engineering Fracture Mechanics, 5, (1973), pp. 1019-1022. 38. A. C. Palmer and J. R. Rice, “The Growth of Slip Surfaces in the Progressive Failure of Overconsolidated Clay”, Proceedings of the Royal Society of London, A 332, (1973), pp. 527-548. 39. J. R. Rice, “Plane Strain Slip Line Theory for Anisotropic Rigic/Plastic Materials”, Journal of the Mechanics and Physics of Solids, 21, (1973), pp. 63-74. 40. J. R. Rice, P. C. Paris and J. G. Merkle, “Some Further Results of J-Integral Analysis and Estimates”, in Progress in Flaw Growth and Fracture Toughness Testing, Special Tech. Publication 536, ASTM, Philadelphia, PA (1973), pp. 231- 245. xxx LIST OF PUBLICATIONS BY J. R. RICE

41. R. Hill and J. R. Rice, “Elastic Potentials and the Structure of Inelastic Constitutive Laws”, SIAM Journal of Applied Mathematics, 25, (1973), pp. 448- 461. 42. J. R. Rice, “Continuum Plasticity in Relation to Microscale Deformation Mechanisms”, in Metallurgical Effects at High Strain Rate (eds. R.W. Rohde et al.), Plenum Press, (1973), pp. 93-106. 43. J. R. Rice, “Elastic-Plastic Models for Stable Crack Growth”, in Mechanics and Mechanisms of Crack Growth (ed. M.J. May), British Steel Corporation Physical Metallurgy Centre Publication, April 1973 (issued 1975), pp. 14-39. 44. T.- J. Chuang and J. R. Rice, “The Shape of Intergranular Creep Cracks Growing by Surface Diffusion”, Acta Metallurgica, 21, (1973), pp. 1625-1628. 45. R. O. Ritchie, J. F. Knott and J. R. Rice, “On the Relationship Between Critical Tensile Stress and Fracture Toughness in Mild Steel”, Journal of the Mechanics and Physics of Solids, 21, (1973), pp. 395-410. 46. L. B. Freund and J. R. Rice, “On the Determination of Elastodynamic Crack Tip Stress Fields, International Journal of Solids and Structures, 10, (1974), pp. 411- 417. 47. J. R. Rice, “Limitations to the Small Scale Yielding Approximation for Crack Tip Plasticity”, Journal of the Mechanics and Physics of Solids, 22, (1974), pp. 17-26. 48. J. R. Rice and R. M. Thomson, “Ductile vs. Brittle Behavior of Crystals”, Philosophical Magazine, 29, (1974), 73-97. 49. J. R. Rice, “The Initiation and Growth of Shear Bands”, in Plasticity and Soil Mechanics (edited by A. C. Palmer), Cambridge University Engineering Department, Cambridge, (1973) pp. 263-274. 50. J. C. Nagtegaal, D. M. Parks and J. R. Rice, “On Numerically Accurate Finite Element Solutions in the Fully Plastic Range”, Computer Methods in Applied Mechanics and Engineering, 4, (1974) pp. 153-177. 51. J. R. Rice, “Continuum Mechanics and Thermodynamics of Plasticity in Relation to Microscale Deformation Mechanisms”, Chapter 2 of Constitutive Equations in Plasticity (ed. A. S. Argon), M.I.T. Press, (1975), pp. 23-79. 52. R. M. McMeeking and J. R. Rice, “Finite-Element Formulations for Problems of Large Elastic-Plastic Deformation”, International Journal of Solids and Structures, 11, (1975), pp. 601-616. 53. J. R. Rice, “On the Stability of Dilatant Hardening for Saturated Rock Masses”, Journal of Geophysical Research, 80, (1975), pp. 1531-1536. 54. J. R. Rice, “Discussion of ‘The Path Independence of the J-Contour Integral’ by G. G. Chell and P. T. Heald”, International Journal of Fracture, 11, (1975), pp. 352- 353. 55. J. W. Rudnicki and J. R. Rice, “Conditions for the Localization of Deformation in Pressure-Sensitive Dilatant Materials”, Journal of the Mechanics and Physics of Solids, 23, (1975) pp. 371-394. LIST OF PUBLICATIONS BY J. R. RICE xxxi

56. S. Storen and J. R. Rice, “Localized Necking in Thin Sheets”, Journal of the Mechanics and Physics of Solids, 23, (1975), pp. 421-441. 57. J. R. Rice, “Some Mechanics Research Topics Related to the Hydrogen Embrittlement of Metals” (discussion appended to paper by J. P. Hirth and H. H. Johnson); Corrosion, 32, (1976), pp. 22-26. 58. J. R. Rice and M. P. Cleary, “Some Basic Stress-Diffusion Solutions for Fluid- Saturated Elastic Porous Media with Compressible Constituents”, Reviews of Geophysics and Space Physics, 14, (1976), pp. 227-241. 59. J. R. Rice, “Hydrogen and Interfacial Cohesion”, in Effect of Hydrogen on Behavior of Materials (eds. A.W. Thompson and I.M. Bernstein), Metallurgical Society of AIME, (1976), pp. 455-466. 60. L.B. Freund, D.M. Parks and J. R. Rice, “Running Ductile Fracture in a Pressurized Line Pipe”, in Mechanics of Crack Growth, Special Technical Publication 590, ASTM, Philadephia, (1976), pp. 243-262. 61. J. R. Rice, “The Localization of Plastic Deformation”, in Theoretical and Applied Mechanics (Proceedings of the 14th International Congress on Theoretical and Applied Mechanics, Delft, 1976, ed. W.T. Koiter), Vol. 1, North-Holland Publishing Co., (1976), 207-220. 62. J. R. Rice and D. A. Simons, “The Stabilization of Spreading Shear Faults by Coupled Deformation-Diffusion Effects in Fluid-Infiltrated Porous Materials”, Journal of Geophysical Research, 81, (1976), pp. 5322-5334. 63. J. R. Rice, “Elastic-Plastic Fracture Mechanics”, in The Mechanics of Fracture (ed. F. Erdogan), Applied Mechanics Division (AMD) Volume 19, American Society of Mechanical Engineers, New York, (1976), pp. 23-53. 64. J. R. Rice, “Mechanics Aspects of Stress Corrosion Cracking and Hydrogen Embrittlement”, in Stress Corrosion Cracking and Hydrogen Embrittlement of Iron Base Alloys_ (eds. R. W. Staehle et al.), National Association of Corrosion Engineers, Houston, (1977), pp. 11-15. 65. A. P. Kfouri and J. R. Rice, “Elastic/Plastic Separation Energy Rate for Crack Advance in Finite Growth Steps”, in Fracture 1977 (eds. D.M.R. Taplin et al.), Vol. 1, Solid Mechanics Division Publication, University of Waterloo, Canada, (1977), pp. 43-59. 66. R. J. Asaro and J. R. Rice, “Strain Localization in Ductile Single Crystals”, Journal of the Mechanics and Physics of Solids, 25, (1977), pp. 309-338. 67. J. R. Rice, “Pore Pressure Effects in Inelastic Constitutive Formulations for Fissured Rock Masses”, in Advances in Civil Engineering Through Engineering Mechanics (Proceedings of 2nd ASCE Engineering Mechanics Division Specialty Conference, Raleigh, N.C., 1977), American Society of Civil Engineers, New York, (1977), pp. 295-297. xxxii LIST OF PUBLICATIONS BY J. R. RICE

68. J. R. Rice, “Fracture Mechanics Model for Slip Surface Propagation in Soil and Rock Masses”, in Advances in Civil Engineering Through Engineering Mechanics (Proceedings of 2nd ASCE Engineering Mechanics Division Specialty Conference, Raleigh, N.C., 1977), American Society of Civil Engineers, New York, NY (1977), pp. 373-376. 69. J. R. Rice, J. W. Rudnicki and D. A. Simons, “Deformation of Spherical Cavities and Inclusions in Fluid-Infiltrated Elastic Materials”, International Journal of Solids and Structures, 14, (1978), pp. 289-303. 70. A. Needleman and J. R. Rice, “Limits to Ductility Set by Plastic Flow Localization”, in Mechanics of Sheet Metal Forming (Proceedings of General Motors Research Laboratories Symposium, October 1977, ed. D.P. Koistinen and N.-M. Wang), Plenum Press, (1978), pp. 237-267. 71. J. R. Rice, “Some Computational Problems in Elastic-Plastic Crack Mechanics”, in Numerical Methods in Fracture Mechanics (Proceedings of the First International Conference on Numerical Methods in Fracture Mechanics, Swansea, Wales, 1978; eds. A. R. Luxmoore and D. R. J. Owen), Department of Civil Engineering, University College of Swansea, Wales, (1978), pp. 434-449. 72. J. R. Rice, “Thermodynamics of the Quasi-Static Growth of Griffith Cracks”, Journal of the Mechanics and Physics of Solids, 26, (1978) pp. 61-78. 73. J. R. Rice and E. P. Sorensen, “Continuing Crack Tip Deformation and Fracture for Plane-Strain Crack Growth in Elastic-Plastic Solids”, Journal of the Mechanics and Physics of Solids, 26, (1978), pp. 163-186. 74. B. Budiansky and J. R. Rice, “On the Estimation of a Crack Fracture Parameter by Long-Wavelength Scattering”, Journal of Applied Mechanics, 45, (1978), pp. 453- 454. 75. V. N. Nikolaevskii and J. R. Rice, “Current Topics in Non-elastic Deformation of Geological Materials”, in High-Pressure Science and Technology: Sixth AIRAPT Conference, Volume 2: Applications and Mechanical Properties (ed. K.D. Timmerhaus and M.S. Barber), Plenum Press, New York, NY (1979), pp. 455- 464. 76. J. R. Rice, “Theory of Precursory Processes in the Inception of Earthquake Rupture”, in Proceedings of the Symposium on Physics of Earthquake Sources (at General Assembly of International Association of Seismology and Physics of the Earth’s Interior, Durham, England, August 1977), Gerlands Beitrage zur Geophysik, 88, (1979), pp. 91-127. 77. J. R. Rice and J. W. Rudnicki, “Earthquake Precursory Effects due to Pore Fluid Stabilization of a Weakening Fault Zone”, Journal of Geophysical Research, 84, (1979), pp. 2177-2193. 78. J. B. Walsh and J. R. Rice, “Local Changes in Gravity Resulting from Deformation”, Journal of Geophysical Research, 84, (1979) pp. 165-170. LIST OF PUBLICATIONS BY J. R. RICE xxxiii

79. T.- J. Chuang, K. I. Kagawa, J. R. Rice and L. B. Sills, “Non-equilibrium Models for Diffusive Cavitation of Grain Interfaces”, Acta Metallurgica, Overview Paper No. 2, 27, (1979), pp. 265-284. 80. J. R. Rice, R. M. McMeeking, D. M. Parks and E. P. Sorensen, “Recent Finite Element Studies in Plasticity and Fracture Mechanics”, in Proceedings of the FENOMECH '78 Conference (Stuttgart, edited by K.S. Pister et al.), North- Holland Publ. Co., Vol. 2, (1979), pp. 411-442; also, Computer Methods in Applied Mechanics and Engineering, 17/18, (1979), pp. 411-442. 81. W. Kohn and J. R. Rice, “Scattering of Long Wavelength Elastic Waves form Localized Defects in Solids”, Journal of Applied Physics, 50, (1979), pp. 3346- 3353. 82. J. R. Rice, “The Mechanics of Quasi-static Crack Growth”, in Proceedings of the 8th U.S. National Congress of Applied Mechanics (at U.C.L.A., June 1978; ed. R. E. Kelly), Western Periodicals Co., North Hollywood, California, (1979), pp. 191- 216. 83. B. Budiansky and J. R. Rice, “An Integral Equation for Dynamic Elastic Response of an Isolated 3-D Crack”, Wave Motion, 1, (1979), pp. 187-192. 84. J. R. Rice, “Plastic Creep Flow Processes in Fracture at Elevated Temperature”, in Time-Dependent Fracture of Materials at Elevated Temperature (ed. S.M. Wolf), U.S. Department of Energy Report CONF 790236 UC-25 (June 1979), pp. 130-145. 85. B. Budiansky, D. C. Drucker, G. S. Kino and J. R. Rice, “The Pressure Sensitivity of a Clad Optical Fiber”, Applied Optics, 18, (1979), pp. 4085-4088. 86. B. Cotterell and J. R. Rice, “Slightly Curved or Kinked Cracks”, International Journal of Fracture, 16, (1980), pp. 155-169. 87. A. G. Evans, J. R. Rice and J. P. Hirth, “The Suppression of Cavity Formation in Ceramics: Prospects for Superplasticity”, Journal of the American Ceramic Society, 63, (1980), pp. 368-375. 88. J. R. Rice, “The Mechanics of Earthquake Rupture”, in Physics of the Earth’s Interior (Proc. International School of Physics ‘Enrico Fermi’, Course 78, 1979; (ed. A. M. Dziewonski and E. Boschi), Italian Physical Society and North-Holland Publ. Co., (1980), pp. 555-649. 89. J. R. Rice, “Discussion on ‘Outstanding Problems in Geodynamics: Mechanisms of Faulting"', in Physics of the Earth’s Interior (Proc. International School of Physics ‘Enrico Fermi’, Course 78, 1979; ed. A. M. Dziewonski and E. Boschi), Italian Physical Society and North-Holland Publ. Co., (1980) pp. 713-716. 90. J. R. Rice and J. W. Rudnicki, “A Note on Some Features of the Theory of Localization of Deformation”, International Journal of Solids and Structures, 16, (1980), pp. 597-605. 91. H. Riedel and J. R. Rice, “Tensile Cracks in Creeping Solids”, in Fracture Mechanics: Twelfth Conference (ed. P.C. Paris), Special Technical Publication 700, ASTM, Philadelphia, (1980), pp. 112-130. xxxiv LIST OF PUBLICATIONS BY J. R. RICE

92. J. R. Rice, W. J. Drugan and T. L. Sham, “Elastic-Plastic Analysis of Growing Cracks”, in Fracture Mechanics: Twelfth Conference (ed. P. C. Paris), Special Technical Publication 700, ASTM, Philadelphia, PA (1980), pp. 189-221. 93. A. Needleman and J. R. Rice, “Plastic Creep Flow Effects in the Diffusive Cavitation of Grain Boundaries”, Acta Metallurgica, Overview Paper No. 9, 28, (1980), pp. 1315-1332. 94. J. P. Hirth and J. R. Rice, “On the Thermodynamics of Adsorption at Interfaces as it Influences Decohesion”, Metallurgical Transactions, 11A, (1980), pp. 1501- 1511. 95. L. Hermann and J. R. Rice, “Comparison of Theory and Experiment for Elastic- Plastic Plane-Strain Crack Growth”, Metal Science, 14, (1980), pp. 285-291. 96. J. R. Rice, “Pore-Fluid Processes in the Mechanics of Earthquake Rupture”, in Solid Earth Geophysics and Geotechnology (ed. S. Nemat-Nasser), American Society of Mechanical Engineers, Appl. Mech. Div. Volume 42, New York, NY (1980), pp. 81-89. 97. J. R. Rice, “Elastic Wave Emission from Damage Processes”, Journal of Nondestructive Evaluation, 1, (1980), pp. 215-224. 98. J. R. Rice and T.- J. Chuang, “Energy Variations in Diffusive Cavity Growth”, Journal of the American Ceramic Society, 64, (1981), pp. 46-53. 99. J. R. Rice, “Creep Cavitation of Grain Interfaces”, in Three-Dimensional Constitutive Relations and Ductile Fracture (ed. S. Nemat-Nasser), North-Holland Publ. Co., (1981), pp. 173-184. 100. J. R. Rice, “Constraints on the Diffusive Cavitation of Isolated Grain Boundary Facets in Creeping Polycrystals”, Acta Metallurgica, 29, (1981), pp. 675-681. 101. F. K. Lehner, V. C. Li and J. R. Rice, “Stress Diffusion along Rupturing Plate Boundaries”, Journal of Geophysical Research, 86, (1981), pp. 6155-6169. 102. J. R. Rice, “Elastic-Plastic Crack Growth”, in Mechanics of Solids: The Rodney Hill 60th Anniversary Volume (ed. H.G. Hopkins and M.J. Sewell), Pergamon Press, Oxford and New York, (1982), pp. 539-562. 103. W. J. Drugan, J. R. Rice and T.-L. Sham, “Asymptotic Analysis of Growing Plane Strain Tensile Cracks in Elastic-Ideally Plastic Solids”, Journal of the Mechanics and Physics of Solids, 30, 1982, pp. 447-473; erratum, 31, (1983), p. 191. 104. J. R. Rice and A. L. Ruina, “Stability of Steady Frictional Slipping”, Journal of Applied Mechanics, 50, (1983), pp. 343-349. 105. J. Pan and J. R. Rice, “Rate Sensitivity of Plastic Flow and Implications for Yield Surface Vertices”, International Journal of Solids and Structures, 19, (1983), pp. 973-987. 106. V. C. Li and J. R. Rice, “Pre-seismic Rupture Progression and Great Earthquake Instabilities at Plate Boundaries”, Journal of Geophysical Research, 88, (1983), pp. 4231-4246. LIST OF PUBLICATIONS BY J. R. RICE xxxv

107. V. C. Li and J. R. Rice, "Precursory Surface Deformation in Great Plate Boundary Earthquake Sequences", Bulletin of the Seismological Society of America, 73, (1983), pp. 1415-1434 108. J. R. Rice and J.-c. Gu, "Earthquake Aftereffects and Triggered Seismic Phenomena", Pure and Applied Geophysics, 121, (1983), pp. 187-219. 109. J. R. Rice, "Constitutive Relations for Fault Slip and Earthquake Instabilities", Pure and Applied Geophysics, 121, (1983), pp. 443-475. 110. J. R. Rice, "On the Theory of Perfectly Plastic Anti-Plane Straining", Mechanics of Materials, 3, (1984), pp. 55-80. 111. W. J. Drugan and J. R. Rice, "Restrictions on Quasi-Statically Moving Surfaces of Strong Discontinuity in Elastic-Plastic Solids", in Mechanics of Material Behavior (the D.C. Drucker anniversary volume, ed. G.J. Dvorak and R.T. Shield), Elsevier, (1984), pp. 59-73. 112. J. R. Rice, "Shear Instability in Relation to the Constitutive Description of Fault Slip", in Rockbursts and Seismicity in Mines (ed. N.C. Gay and E.H. Wainwright), Symp. Ser. No. 6, S. African Inst. Mining and Metallurgy, Johannesburg, (1984), pp. 57-62. 113. J.-c. Gu, J. R. Rice, A. L. Ruina and S.T. Tse, "Slip Motion and Stability of a Single Degree of Freedom Elastic System with Rate and State Dependent Friction", Journal of the Mechanics and Physics of Solids, 32, (1984), pp. 167- 196. 114. J. R. Rice, "Comments on 'On the Stability of Shear Cracks and the Calculation of Compressive Strength' by J.K. Dienes", Journal of Geophysical Research, 89, (1984), pp. 2505-2507. 115. J. R. Rice, "Shear Localization, Faulting and Frictional Slip: Discusser’s Report", in Mechanics of Geomaterials (Proc. IUTAM W. Prager Symp., Sept. 1983, ed. Z.P. Bazant), J. Wiley and Sons Ltd., (1985), Chp. 11, pp. 211-216. 116. J. R. Rice, "Conserved Integrals and Energetic Forces", in Fundamentals of Deformation and Fracture (Eshelby Memorial Symposium), ed. B.A. Bilby, K.J. Miller and J.R. Willis, Cambridge Univ. Press, (1985) pp. 33-56. 117. P. M. Anderson and J. R. Rice, "Constrained Creep Cavitation of Grain Boundary Facets", Acta Metallurgica, 33, (1985), pp. 409-422. 118. J. R. Rice, "First Order Variation in Elastic Fields due to Variation in Location of a Planar Crack Front", Journal of Applied Mechanics, 52, (1985), pp. 571-579. 119. S. T. Tse, R. Dmowska and J. R. Rice, "Stressing of Locked Patches along a Creeping Fault", Bulletin of the Seismological Society of America, 75, (1985), pp. 709-736. 120. J. R. Rice and R. Nikolic, "Anti-plane Shear Cracks in Ideally Plastic Crystals", Journal of the Mechanics and Physics of Solids, 33, (1985), pp. 595-622. 121. J. R. Rice, "Three Dimensional Elastic Crack Tip Interactions with Transformation Strains and Dislocations", International Journal of Solids and Structures, 21, (1985), pp. 781-791. xxxvi LIST OF PUBLICATIONS BY J. R. RICE

122. J. R. Rice (Editor), Solid Mechanics Research Trends and Opportunities (Report of the Committee on Solid Mechanics Research Directions of the Applied Mechanics Division, American Society of Mechanical Engineers), Applied Mechanics Reviews, 38, (1985), pp. 1247-1308; published simultaneously as AMD-Vol. 70, ASME Book No. I00198. 123. J. R. Rice, "Fracture Mechanics", in Solid Mechanics Research Trends and Opportunities, ed. J. R. Rice, Applied Mechanics Reviews, 38, (1985), pp. 1271- 1275; published simultaneously in AMD-Vol. 70, ASME Book No. I00198. 124. J. R. Rice and S. T. Tse, "Dynamic Motion of a Single Degree of Freedom System following a Rate and State Dependent Friction Law", Journal of Geophysical Research, 91, (1986), pp. 521-530. 125. R. Dmowska and J. R. Rice, "Fracture Theory and Its Seismological Applications", in Continuum Theories in Solid Earth Physics (Vol. 3 of series "Physics and Evolution of the Earth's Interior"; ed. R. Teisseyre), Elsevier and Polish Scientific Publishers, (1986), pp. 187-255. 126. H. Gao and J. R. Rice, "Shear Stress Intensity Factors for a Planar Crack with Slightly Curved Front", Journal of Applied Mechanics, 53, (1986), pp. 774-778. 127. S. T. Tse and J. R. Rice, "Crustal Earthquake Instability in Relation to the Depth Variation of Frictional Slip Properties", Journal of Geophysical Research, 91, (1986), pp. 9452-9472. 128. P. M. Anderson and J. R. Rice, "Dislocation Emission from Cracks in Crystals or Along Crystal Interfaces", Scripta Metallurgica, 20, (1986), pp. 1467-1472. 129. J.-S. Wang, P.M. Anderson and J. R. Rice, "Micromechanics of the Embrittlement of Crystal Interfaces", in Mechanical Behavior of Materials - V (Proceedings of the 5th International Conference, Beijing, 1987; ed. M.G. Yan, S.H. Zhang and Z.M. Zheng), Pergamon Press, (1987), pp. 191-198. 130. J. R. Rice, "Mechanics of Brittle Cracking of Crystal Lattices and Interfaces", in Chemistry and Physics of Fracture (proceedings of a 1986 NATO Advanced Research Workshop; edited by R.M. Latanision and R.H. Jones), Martinus Nijhoff Publishers, Dordrecht, (1987), pp. 22-43. 131. P. M. Anderson and J. R. Rice, "The Stress Field and Energy of a Three- Dimensional Dislocation Loop at a Crack Tip", Journal of the Mechanics and Physics of Solids, 35, (1987), pp. 743-769. 132. H. Gao and J. R. Rice, "Somewhat Circular Tensile Cracks", International Journal of Fracture, 33, (1987), 155-174. 133. J. R. Rice, "Two General Integrals of Singular Crack Tip Deformation Fields", Journal of Elasticity, 20, (1988), pp. 131-142. 134. H. Gao and J. R. Rice, "Nearly Circular Connections of Elastic Half Spaces", Journal of Applied Mechanics, 54, (1987) pp. 627-634. 135. R. Hill and J. R. Rice, "Discussion of 'A Rate-Independent Constitutive Theory for Finite Inelastic Deformation' by M.M. Carroll", Journal of Applied Mechanics, 54, (1987), pp. 745-747. LIST OF PUBLICATIONS BY J. R. RICE xxxvii

136. V. C. Li and J. R. Rice, "Crustal Deformation in Great California Earthquake Cycles", Journal of Geophysical Research, 92, (1987), pp. 11,533-11,551. 137. J. R. Rice, "Tensile Crack Tip Fields in Elastic-Ideally Plastic Crystals", Mechanics of Materials, 6, (1987), pp. 317-335. 138. J. W. Hutchinson, M. E. Mear and J. R. Rice, "Crack Paralleling an Interface Between Dissimilar Materials", Journal of Applied Mechanics, 54, (1987), pp. 828- 832. 139. J. R. Rice and M. Saeedvafa, "Crack Tip Singular Fields in Ductile Crystals with Taylor Power-Law Hardening, I: Anti-Plane Shear", Journal of the Mechanics and Physics of Solids, 36, (1988), pp. 189-214. 140. J. R. Rice, "Elastic Fracture Mechanics Concepts for Interfacial Cracks", Journal of Applied Mechanics, 55, (1988), pp. 98-103. 141. R. Dmowska, J. R. Rice, L.C. Lovison and D. Josell, "Stress Transfer and Seismic Phenomena in Coupled Subduction Zones During the Earthquake Cycle", Journal of Geophysical Research, 93, (1988), pp. 7869-7884. 142. J. R. Rice, "Crack Fronts Trapped by Arrays of Obstacles: Solutions Based on Linear Perturbation Theory", in Analytical, Numerical and Experimental Aspects of Three Dimensional Fracture Processes (eds. A. J. Rosakis, K. Ravi-Chandar and Y. Rajapakse), ASME Applied Mechanics Division Volume 91, American Society of Mechanical Engineers, New York, (1988), pp. 175-184. 143. J. Yu and J. R. Rice, "Dislocation Pinning Effect of Grain Boundary Segregated Solutes at a Crack Tip", in Interfacial Structure, Properties and Design (eds. M.H. Yoo, W.A.T. Clark and C.L. Briant), Materials Research Society Proc. Vol. 122, (1988), pp. 361-366. 144. R. Nikolic and J. R. Rice, "Dynamic Growth of Anti-Plane Shear Cracks in Ideally Plastic Crystals", Mechanics of Materials, 7, (1988), pp. 163-173. 145. J. R. Rice, "Weight Function Theory for Three-Dimensional Elastic Crack Analysis", in Fracture Mechanics: Perspectives and Directions (Twentieth Symposium), Special Technical Publication 1020, eds. R. P. Wei and R. P. Gangloff, ASTM, Philadelphia, (1989), pp. 29-57. 146. H. Gao and J. R. Rice, "Application of 3D Weight Functions - II. The Stress Field and Energy of a Shear Dislocation Loop at a Crack Tip", Journal of the Mechanics and Physics of Solids, 37, (1989), pp. 155-174. 147. J. R. Rice and J.-S. Wang, "Embrittlement of Interfaces by Solute Segregation", Materials Science and Engineering, A107, (1989), pp. 23-40. 148. M. Saeedvafa and J. R. Rice, "Crack Tip Singular Fields in Ductile Crystals with Taylor Power-Law Hardening, II: Plane Strain", Journal of the Mechanics and Physics of Solids, 37, (1989), pp. 673-691. 149. H. Gao and J. R. Rice, "A First Order Perturbation Analysis of Crack Trapping by Arrays of Obstacles", Journal of Applied Mechanics, 56, (1989), pp. 828-836. 150. J. R. Rice, D. E. Hawk and R. J. Asaro, "Crack Tip Fields in Ductile Crystals", International Journal of Fracture, 42, (1990), pp. 301-321. xxxviii LIST OF PUBLICATIONS BY J. R. RICE

151. J. R. Rice, "Summary of Studies on Crack Tip Fields in Ductile Crystals", in Yielding, Damage, and Failure of Anisotropic Solids (ed. J. P. Boehler), Mechanical Engineering Publications (London), (1990), pp. 49-52. 152. P. M. Anderson, J.-S. Wang and J. R. Rice, "Thermodynamic and Mechanical Models of Interfacial Embrittlement", in Innovations in Ultrahigh-Strength Steel Technology (eds. G. B. Olson, M. Azrin and E. S. Wright), Sagamore Army Materials Research Conference Proceedings, Volume 34, (1990), pp. 619-649. 153. J. R. Rice, Z. Suo and J.-S. Wang, "Mechanics and Thermodynamics of Brittle Interfacial Failure in Bimaterial Systems", in Metal-Ceramic Interfaces (eds. M. Rühle, A. G. Evans, M. F. Ashby and J. P. Hirth), Acta-Scripta Metallurgica Proceedings Series, Volume 4, Pergamon Press, (1990), pp. 269-294. 154. Y. Sun, J. R. Rice and L. Truskinovsky, "Dislocation Nucleation Versus Cleavage in Ni3Al and Ni", in High-Temperature Ordered Intermetallic Alloys (eds. L. A. Johnson, D. T. Pope and J. O. Stiegler), Materials Research Society Proc. Vol. 213, (1991) pp. 243-248. 155. G. E. Beltz and J. R. Rice, "Dislocation Nucleation Versus Cleavage Decohesion at Crack Tips", in Modeling the Deformation of Crystalline Solids (eds. T. C. Lowe, A. D. Rollett, P. S. Follansbee and G. S. Daehn), The Minerals, Metals and Materials Society (TMS), Warrendale, Penna., (1991), pp. 457-480. 156. H. Gao, J. R. Rice and J. Lee, "Penetration of a Quasistatically Slipping Crack into a Seismogenic Zone of Heterogeneous Fracture Resistance", Journal of Geophysical Research, 96, (1991), 21535-21548 157. J. R. Rice, "Fault Stress States, Pore Pressure Distributions, and the Weakness of the San Andreas Fault", in Fault Mechanics and Transport Properties in Rocks (eds. B. Evans and T.-F. Wong), Academic Press, (1992), pp. 475-503. 158. J. R. Rice, "Dislocation Nucleation from a Crack Tip: An Analysis Based on the Peierls Concept", Journal of the Mechanics and Physics of Solids, 40, (1992), pp. 239-271. 159. G. E. Beltz and J. R. Rice, "Dislocation Nucleation at Metal/Ceramic Interfaces", Acta Metallurgica et Materiala, 40, Supplement, (1992), pp. s321-s331. 160. J. R. Rice, G. E. Beltz and Y. Sun, "Peierls Framework for Analysis of Dislocation Nucleation from a Crack Tip", in Topics in Fracture and Fatigue (ed. A. S. Argon), Springer Verlag, (1992), Chapter 1, pp. 1-58. 161. M. Saeedvafa and J. R. Rice, "Crack Tip Fields in a Material with Three Independent Slip Systems: NiAl Single Crystal", Modelling and Simulation in Materials Science and Engineering, 1, (1992), pp. 53-71. 162. Y. Ben-Zion, J. R. Rice and R. Dmowska, "Interaction of the San Andreas Fault Creeping Segment with Adjacent Great Rupture Zones, and Earthquake Recurrence at Parkfield, Journal of Geophysical Research, 98, (1993), pp. 2135- 2144. LIST OF PUBLICATIONS BY J. R. RICE xxxix

163. J. R. Rice, "Mechanics of Solids", section of the article on "Mechanics", in Encyclopaedia Britannica (1993 printing of the 15th edition), volume 23, pp. 734- 747 and 773, (1993). 164. J. R. Rice, "Spatio-temporal Complexity of Slip on a Fault", Journal of Geophysical Research, 98, (1993), pp. 9885-9907. 165. Y. Sun, G. E. Beltz and J. R. Rice, "Estimates from Atomic Models of Tension- Shear Coupling in Dislocation Nucleation from a Crack Tip", Materials Science and Engineering A, 170, (1993), pp. 67-85. 166. Y. Ben-Zion and J. R. Rice, "Earthquake Failure Sequences Along a Cellular Fault Zone in a 3D Elastic Solid Containing Asperity and Non-Asperity Regions", Journal of Geophysical Research, 98, (1993), pp. 14,109-14,131. 167. J. R. Rice and G. E. Beltz, "The Activation Energy for Dislocation Nucleation at a Crack", Journal of the Mechanics and Physics of Solids, 42, (1994), pp. 333-360. 168. J. R. Rice, Y. Ben-Zion and K.-S. Kim, "Three-Dimensional Perturbation Solution for a Dynamic Planar Crack Moving Unsteadily in a Model Elastic Solid", Journal of the Mechanics and Physics of Solids, 42, (1994), pp. 813-843. 169. G. Perrin and J. R. Rice, "Disordering of a Dynamic Planar Crack Front in a Model Elastic Medium of Randomly Variable Toughness", Journal of the Mechanics and Physics of Solids, 42, (1994), pp. 1047-1064. 170. Y. Ben-Zion and J. R. Rice, "Quasi-Static Simulations of Earthquakes and Slip Complexity along a 2D Fault in a 3D Elastic Solid", in The Mechanical Involvement of Fluids in Faulting, Proceedings of June 1993 National Earthquake Hazards Reduction Program Workshop LXIII, USGS Open-File Report 94-228, Menlo Park, CA, (1994), pp. 406-435. 171. Y. Ben-Zion and J. R. Rice, "Slip Patterns and Earthquake Populations along Different Classes of Faults in Elastic Solids", Journal of Geophysical Research, 100, (1995), pp. 12959-12983. 172. G. Perrin, J. R. Rice and G. Zheng, "Self-healing Slip Pulse on a Frictional Surface", Journal of the Mechanics and Physics of Solids, 43, (1995), pp. 1461- 1495. 173. P. H. Geubelle and J. R. Rice, "A Spectral Method for Three-Dimensional Elastodynamic Fracture Problems", Journal of the Mechanics and Physics of Solids, 43, (1995), pp. 1791-1824. 174. J. R. Rice, "Text of Timoshenko Medal Speech", in Applied Mechanics Newsletter (ed. B. Moran), American Society of Mechanical Engineers, (Spring 1995), pp. 2- 3. 175. P. Segall and J. R. Rice, "Dilatancy, Compaction, and Slip Instability of a Fluid Infiltrated Fault", Journal of Geophysical Research, 100, (1995), pp. 22155-22171. 176. J. R. Rice and Y. Ben-Zion, "Slip Complexity in Earthquake Fault Models", Proceedings of the National Academy of Sciences USA, 93, (1996), pp. 3811- 3818. xl LIST OF PUBLICATIONS BY J. R. RICE

177. R. Dmowska, G. Zheng and J. R. Rice, "Seismicity and Deformation at Convergent Margins due to Heterogeneous Coupling", Journal of Geophysical Research, 101, (1996), pp. 3015-3029. 178. M. A. J. Taylor, G. Zheng, J. R. Rice, W. D. Stuart and R. Dmowska, "Cyclic Stressing and Seismicity at Strongly Coupled Subduction Zones", Journal of Geophysical Research, 101, (1996), pp. 8363-8381. 179. G. Zheng, R. Dmowska and J. R. Rice, "Modeling Earthquake Cycles in the Shumagins Subduction Segment, Alaska, with Seismic and Geodetic Constraints", Journal of Geophysical Research, 101, (1996), pp. 8383-8392. 180. G. E. Beltz, J. R. Rice, C. F. Shih and L. Xia, "A Self-Consistent Model for Cleavage in the Presence of Plastic Flow", Acta Materiala, 44, (1996), pp. 3943- 3954. 181. M. F. Linker and J. R. Rice, "Models of Postseismic Deformation and Stress Transfer Associated with the Loma Prieta Earthquake", in U. S. Geological Survey Professional Paper 1550-D: The Loma Prieta, California, Earthquake of October 17, 1989 - Aftershocks and Postseismic Effects, (1997), pp. D253-D275. 182. A. Cochard and J. R. Rice, "A Spectral Method for Numerical Elastodynamic Fracture Analysis without Spatial Replication of the Rupture Event", Journal of the Mechanics and Physics of Solids, 45, (1997), pp. 1393-1418. 183. Y. Ben-Zion and J. R. Rice, "Dynamic Simulations of Slip on a Smooth Fault in an Elastic Solid", Journal of Geophysical Research, 102, (1997), pp. 17771-17784. 184. J. W. Morrissey and J. R. Rice, "Crack Front Waves", Journal of the Mechanics and Physics of Solids, 46, (1998), pp. 467-487. 185. M. A. J. Taylor, R. Dmowska and J. R. Rice, "Upper-plate Stressing and Seismicity in the Subduction Earthquake Cycle", Journal of Geophysical Research, 103, (1998), pp. 24523-24542. 186. G. Zheng and J. R. Rice, "Conditions under which Velocity-Weakening Friction allows a Self-healing versus a Cracklike Mode of Rupture", Bulletin of the Seismological Society of America, 88, (1998), pp. 1466-1483. 187. K. Ranjith and J. R. Rice, "Stability of Quasi-static Slip in a Single Degree of Freedom Elastic System with Rate and State Dependent Friction", Journal of the Mechanics and Physics of Solids, 47, (1999), pp. 1207-1218. 188. J. R. Rice, "Foundations of Solid Mechanics", in Mechanics and Materials: Fundamentals and Linkages (eds. M. A. Meyers, R. W. Armstrong, and H. Kirchner), Chapter 3, Wiley, in press, (1999). 189. J. W. Morrissey and J. R. Rice, "Perturbative Simulations of Crack Front Waves", Journal of the Mechanics and Physics of Solids, in press. List of Contributors

Professor Peter M. Anderson, Department of Materials Science and Engineering, The Ohio State University, 2041 College Road, Columbus, OH 43210-1179 U. S. A.

Professor A. G. Atkins, Department of Engineering, University of Reading, Reading, BG6 6AY, UK

Professor Leslie Bank-Sills, The Dreszer Fracture Mechanics Laboratory, Department of Solid Mechanics, Materials and Structures, The Fleischman Faculty of Engineering, Tel Aviv University, 69978 Ramat Aviv, Israel

Dr. B Blug, Fraunhofer-Institut für Werkstoffmechanik,Wöhlerstr. 11,79108 Freiburg, Germany

Dr. Vinodkumar Boniface, The Dreszer Fracture Mechanics Laboratory, Department of Solid Mechanics, Materials and Structures, The Fleischman Faculty of Engineering, Tel Aviv University, 69978 Ramat Aviv, Israel

Professor Allan F. Bower, Division of Engineering, Brown University, Providence, RI 02912, U.S.A.

Dr. B. Chen,. Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61801

Dr. Z. Chen, Institute of Materials Research and Engineering, 3 Research Link, Singapore 117602

Dr. W. Y. Chien, Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109, USA

Dr.J. W. Cho, Technical Center, Deawoo Heavy Industries Co, Inchun, Korea

Dr. T.-J. Chuang, Ceramics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899-8521, U. S. A.

Dr. Brian Cotterell, Institute of Materials Research and Engineering, 3 Research Link, Singapore 117602 x1ii LIST OF CONTRIBUTORS

Professor Walter W.Drugan, Department of Engineering Physics, University of Wisconsin, Madison, 1500 Engineering Drive, Madison, WI 53706

Professor Glenn E. Beltz, Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, CA 93106-5070, USA

Professor Huajian Gao, Division of Mechanics and Computation, Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-4040

Mr. Anja Haug, Materials Department, University of California, Santa Barbara, California 93106 USA

Professor Young Huang, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61801

Mr. H.-M. Huang, Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109, USA

Professor Mark Kachanov, Department of Mechanical Engineering, Tufts University, Medford, MA 02155

Dr. E. Karapetian, Department of Mechanical Engineering, Tufts University, Medford, MA 02155, U.S.A.

Dr.Patrick A Klein, Sandia National Laboratories, Mail Stop 9161,P.O. Box 0969, Livermore, CA 94551

Professor Shiro Kubo, Department of Mechanical Engineering and Systems, Graduate School of Engineering, Osaka University, 2-1, Yamadaoka, Suita, Osaka 565-0871 Japan

Dr. L. L. Fischer, Department of Mechanical and Environmental Engineering, University of California,Santa Barbara, CA 93106-5070, USA

Dr. L. E. Levine, Maaterials Science and Engineering Lab., National Institute of Standards and Technology, Gaithersburg, MD 20899

Professor Victor C. Li, Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI, 48109-2125

Mr. W. Lu, Mechanical and Aerospace Engineering Department and Materials Institute, Princeton University, Princeton, NJ 08544 LIST OF CONTRIBUTORS xliii

Dr. S. R. MacEwen, Alcan International Ltd., P.O. Box 8400, Kinston, Ontario, K7L 5L9, Canada

Professor Robert M. McMeeking, Department of Mechanical and Environmental Engineering, University of Californi, Santa Barbara, California 93106, USA

Professor Sinisa Dj. Mesarovic, Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22903 U. S. A.

Professor Joe Pan, Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109, USA

Dr. Hermann Riedel, Fraunhofer-Institut für Werkstoffmechanik,Wöhlerstr. 11,79108 Freiburg, Germany

Professor Asher A. Rubinstein, Department of Mechanical Engineering, Tulane University, New Orleans, LA 70118, U. S. A.

Professor J. W .Rudnicki, Department of Civil Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3109

Dr. I. Sevostianov, Department of Mechanical Engineering, Tufts University, Medford, MA 02155

Dr. Y. Shim, Center for Simulational Physics, University of Georgia, Athens, GA 30602

Professor Z. Suo, Mechanical and Aerospace Engineering Department, and Materials Institute, Princeton University, Princeton, NJ 08544

Dr. S. C. Tang, Ford Research Lab., P.O. Box 2053, MD3135/SRL, Dearborn, MI 48121, U.S.A.

Mr. Zhibo Tang, Division of Engineering, Brown University, Providence, RI 02912

Dr. Robb M. Thomson, Maaterials Science and Engineering Lab., National Institute of Standards and Technology, Gaithersburg, MD 20899

Dr. Jian-Sheng Wang, Northwestern University, Evanston, IL 60201, USA

Dr. P. D. Wu, Alcan International Ltd., P.O. Box 8400, Kinston, Ontario, K7L 5L9, Canada

Dr. Z. C. Xia, Ford Research Lab., P.O. Box 2053, MD3135/SRL, Dearborn, MI 48121 x1iv LIST OF CONTRIBUTORS

Dr. Xiao J. Xin, Department of Mechanical and Nuclear Engineering, Kansas State University, 338 Rathbone Hall, Manhattan, KS 66506-5205 U. S. A.

Professor Jin Yu, Department of Materials Science and Engineering,Korea Advanced Institute of Science and Technology, P.O. Box 201, Chongryang. Seoul, Korea