THE RATIONAL SPIRIT IN MODERN CONTINUUM MECHANICS The Rational Spirit in Modern Continuum Mechanics Essays and Papers Dedicated to the Memory of Clifford Ambrose Truesdell III Edited by CHI-SING MAN University of Kentucky, Lexington, U.S.A. and ROGER L. FOSDICK University of Minnesota, Minneapolis, U.S.A. Reprinted from Journal of Elasticity: The Physical and Mathematical Science of Solids, Vols. 70, 71, 72 (2003) KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBook ISBN: 1-4020-2308-1 Print ISBN: 1-4020-1828-2 ©2005 Springer Science + Business Media, Inc. Print ©2004 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Springer's eBookstore at: http://ebooks.kluweronline.com and the Springer Global Website Online at: http://www.springeronline.com Portrait by Joseph Sheppard Table of Contents Portrait by Joseph Sheppard v Foreword by Chi-Sing Man and Roger Fosdick xi Published Works of Clifford Ambrose Truesdell III xiii Serials Edited by Clifford Ambrose Truesdell III xli Eulogium by Roger Fosdick xliii Photograph: Bloomington, Indiana, 1959 xlv BERNARD D. COLEMAN / Memories of Clifford Truesdell 1–13 ENRICO GIUSTI / Clifford Truesdell (1919–2000), Historian of Mathematics 15–22 WALTER NOLL / The Genesis of Truesdell’s Nonlinear Field Theories of Mechanics 23–30 JAMES SERRIN / An Appreciation of Clifford Truesdell 31–38 D. SPEISER / Clifford A. Truesdell’s Contributions to the Euler and the Bernoulli Edition 39–53 Photograph: Baltimore, Maryland, 1978 STUART S. ANTMAN / Invariant Dissipative Mechanisms for the Spatial Motion of Rods Suggested by Artificial Viscosity 55–64 MILLARD F. BEATTY / An Average-Stretch Full-Network Model for Rubber Elasticity 65–86 MICHELE BUONSANTI and GIANNI ROYER-CARFAGNI / From 3-D Non- linear Elasticity Theory to 1-D Bars with Nonconvex Energy 87–100 GIOVANNI BURATTI, YONGZHONG HUO and INGO MÜLLER / Eshelby Tensor as a Tensor of Free Enthalpy 101–112 SANDRO CAPARRINI and FRANCO PASTRONE / E. Frola (1906–1962): An Attempt Towards an Axiomatic Theory of Elasticity 113–125 GIANFRANCO CAPRIZ and PAOLO MARIA MARIANO / Symmetries and Hamiltonian Formalism for Complex Materials 127–140 DONALD E. CARLSON, ELIOT FRIED and DANIEL A. TORTORELLI / Geometrically-based Consequences of Internal Constraints 141–149 vii viii YI-CHAO CHEN / Second Variation Condition and Quadratic Integral In- equalities with Higher Order Derivatives 151–167 ELENA CHERKAEV and ANDREJ CHERKAEV / Principal Compliance and Robust Optimal Design 169–196 JOHNC . CRISCIONE / Rivlin’s Representation Formula is Ill-Conceived for the Determination of Response Functions via Biaxial Testing 197–215 CESARE DAVINI and ROBERTO PARONI / Generalized Hessian and Ex- ternal Approximations in Variational Problems of Second Order 217–242 F. DELL’ISOLA, G. SCIARRA and R.C. BATRA / Static Deformations of a Linear Elastic Porous Body Filled with an Inviscid Fluid 243–264 GIANPIETRO DEL PIERO / A Class of Fit Regions and a Universe of Shapes for Continuum Mechanics 265–285 LUCA DESERI and DAVID R. OWEN / Toward a Field Theory for Elastic Bodies Undergoing Disarrangements 287–326 MARCELO EPSTEIN and IOAN BUCATARU / Continuous Distributions of Dislocations in Bodies with Microstructure 327–344 MARCELO EPSTEIN and MAREK ELZANOWSKI˙ / A Model of the Evolu- tion of a Two-dimensional Defective Structure 345–355 J.L. ERICKSEN / On the Theory of Rotation Twins in Crystal Multilattices 357–373 MAURO FABRIZIO and MURROUGH GOLDEN / Minimum Free Energies for Materials with Finite Memory 375–397 ROGER FOSDICK and LEV TRUSKINOVSKY / About Clapeyron’s The- orem in Linear Elasticity 399–426 M. FOSS, W. HRUSA and V.J. MIZEL / The Lavrentiev Phenomenon in Non- linear Elasticity 427–435 GIOVANNI P. GALDI / Steady Flow of a Navier–Stokes Fluid around a Ro- tating Obstacle 437–467 TIMOTHY J. HEALEY and ERROL L. MONTES-PIZARRO / Global Bifurc- ation in Nonlinear Elasticity with an Application to Barrelling States of Cylindrical Columns 469–494 MOJIA HUANG and CHI-SING MAN / Constitutive Relation of Elastic Poly- crystal with Quadratic Texture Dependence 495–524 MASARU IKEHATA and GEN NAKAMURA / Reconstruction Formula for Identifying Cracks 525–538 R.J. KNOPS and PIERO VILLAGGIO / An Approximate Treatment of Blunt Body Impact 539–554 I-SHIH LIU / On the Transformation Property of the Deformation Gradient under a Change of Frame 555–562 ix KONSTANTIN A. LURIE / Some New Advances in the Theory of Dynamic Materials 563–573 GERARD A. MAUGIN / Pseudo-plasticity and Pseudo-inhomogeneity Effects in Materials Mechanics 575–597 A. IAN MURDOCH / On the Microscopic Interpretation of Stress and Couple Stress 599–625 PABLO V. NEGRÓN-MARRERO / The Hanging Rope of Minimum Elonga- tion for a Nonlinear Stress–Strain Relation 627–649 MARIO PITTERI / On Certain Weak Phase Transformations in Multilattices 651–671 PAOLO PODIO-GUIDUGLI / A New Quasilinear Model for Plate Buckling 673–698 G. RODNAY and R. SEGEV / Cauchy’s Flux Theorem in Light of Geometric Integration Theory 699–719 U. SARAVANAN and K.R. RAJAGOPAL / A Comparison of the Response of Isotropic Inhomogeneous Elastic Cylindrical and Spherical Shells and Their Homogenized Counterparts 721–749 M. ŠILHAVÝ / On SO(n)-Invariant Rank 1 Convex Functions 751–762 K. WILMANSKI´ / On Thermodynamics of Nonlinear Poroelastic Materials 763–777 WAN-LEE YIN / Anisotropic Elasticity and Multi-Material Singularities 779–808 Foreword Through his voluminous and influential writings, editorial activities, organiza- tional leadership, intellectual acumen, and strong sense of history, Clifford Am- brose Truesdell III (1919–2000) was the main architect for the renaissance of ra- tional continuum mechanics since the middle of the twentieth century. The present collection of 42 essays and research papers pays tribute to this man of mathematics, science, and natural philosophy as well as to his legacy. The first five essays by B.D. Coleman, E. Giusti, W. Noll, J. Serrin, and D. Speiser were texts of addresses given by their authors at the Meeting in memory of Clifford Truesdell, which was held in Pisa in November 2000. In these essays the reader will find personal reminiscences of Clifford Truesdell the man and of some of his activities as scientist, author, editor, historian of exact sciences, and principal founding member of the Society for Natural Philosophy. The bulk of the collection comprises 37 research papers which bear witness to the Truesdellian legacy. These papers cover a wide range of topics; what ties them together is the rational spirit. Clifford Truesdell, in his address upon receipt of a Birkhoff Prize in 1978, put the essence of modern continuum mechanics succinctly as “conceptual analysis, analysis not in the sense of the technical term but in the root meaning: logical criticism, dissection, and creative scrutiny.” It is in celebra- tion of this spirit and this essence that these research papers are dedicated to the memory of their bearer, driving force, and main promoter for half a century. Most of these papers were presented at the Symposium on Recent Advances and New Directions in Mechanics, Continuum Thermodynamics, and Kinetic Theory – In Memory of Clifford A. Truesdell III, held in Blacksburg, Virginia, in June 2002; parts of two papers were delivered at the meeting Remembering Clifford Truesdell, held in Turin in November 2002; and the rest was written especially for the present collection. The portrait, a photo of which serves as the frontispiece of this collection, adorns the Clifford A. Truesdell III Room of History of Science in the library of the Scuola Normale Superiore (Pisa, Italy), which was inaugurated in October 2003 and permanently houses Clifford Truesdell’s previously private collection of books, papers, and correspondence. We are grateful to Mrs. Charlotte Truesdell for helping us secure a digital file of this photo and for providing us with the list of published works of Clifford Truesdell. CHI-SING MAN ROGER FOSDICK University of Kentucky University of Minnesota Lexington Minneapolis xi Published Works of Clifford Ambrose Truesdell III The year of publication is omitted from the entry unless it differs from the year under which the entry is listed. Letters following a number indicate subsidiary separate publications, as follows: P Preliminary report or preprint, A Abstract, separately published or only published version, C Condensed or extracted version, L Lecture concerning part or all of the contents of main entry, R Reprint, entire, RE Reprint of an extract, T Translation, entire, TC Translation, condensed, TE Translation of an extract. The list excludes some 600 reviews published between 1949 and 1971 in Math- ematical Reviews, Applied Mechanics Reviews, Zentralblatt für Mathematik, In- dustrial Laboratories, and Mathematics of Computation but includes reviews pub- lished in other journals. 1943 1. (Co-author P. NEMÉNYI) A stress function for the membrane theory of shells of revolution, Proceedings of the National Academy of Sciences (U.S.A.) 29, 159–162. Other publication in 1943: No. 3A1. 1944 2. ALONZO CHURCH, Introduction to Mathematical Logic, Part I, Notes by C.A. TRUESDELL, Annals of Mathematics Studies No. 13, Princeton, Uni- versity Press, vi + 118 pp. Note by the editors: This list and the list on p. 29 are slightly edited versions of those that we received from Mrs. C. Truesdell, to whom we are heartily grateful. In our editorial work we have added a few entries, updated several items, and made a small number of other minor corrections. To G.P. Galdi, K. Hutter, R.G. Muncaster, F. Pastrone, and D. Speiser, we are beholden for their help in tracking down article titles and numbers of journal volumes. In what follows, explanatory remarks set off by square brackets were made by Clifford Truesdell himself. xiii xiv PUBLISHED WORKS OF C.A. TRUESDELL 1945 3. The membrane theory of shells of revolution, Transactions of the American Mathematical Society 58, 96–166.