Applied Elasticity & Plasticity 1. Basic Equations Of
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Mechanics of Materials Plasticity
Provided for non-commercial research and educational use. Not for reproduction, distribution or commercial use. This article was originally published in the Reference Module in Materials Science and Materials Engineering, published by Elsevier, and the attached copy is provided by Elsevier for the author’s benefit and for the benefit of the author’s institution, for non-commercial research and educational use including without limitation use in instruction at your institution, sending it to specific colleagues who you know, and providing a copy to your institution’s administrator. All other uses, reproduction and distribution, including without limitation commercial reprints, selling or licensing copies or access, or posting on open internet sites, your personal or institution’s website or repository, are prohibited. For exceptions, permission may be sought for such use through Elsevier’s permissions site at: http://www.elsevier.com/locate/permissionusematerial Lubarda V.A., Mechanics of Materials: Plasticity. In: Saleem Hashmi (editor-in-chief), Reference Module in Materials Science and Materials Engineering. Oxford: Elsevier; 2016. pp. 1-24. ISBN: 978-0-12-803581-8 Copyright © 2016 Elsevier Inc. unless otherwise stated. All rights reserved. Author's personal copy Mechanics of Materials: Plasticity$ VA Lubarda, University of California, San Diego, CA, USA r 2016 Elsevier Inc. All rights reserved. 1 Yield Surface 1 1.1 Yield Surface in Strain Space 2 1.2 Yield Surface in Stress Space 2 2 Plasticity Postulates, Normality and Convexity -
Identification of Rock Mass Properties in Elasto-Plasticity D
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Archive Ouverte en Sciences de l'Information et de la Communication Identification of rock mass properties in elasto-plasticity D. Deng, D. Nguyen Minh To cite this version: D. Deng, D. Nguyen Minh. Identification of rock mass properties in elasto-plasticity. Computers and Geotechnics, Elsevier, 2003, 30, pp.27-40. 10.1016/S0266-352X(02)00033-2. hal-00111371 HAL Id: hal-00111371 https://hal.archives-ouvertes.fr/hal-00111371 Submitted on 26 Sep 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Identification of rock mass properties in elasto-plasticity Desheng Deng*, Duc Nguyen-Minh Laboratoire de Me´canique des Solides, E´cole Polytechnique, 91128 Palaiseau, France Abstract A simple and effective back analysis method has been proposed on the basis of a new cri-terion of identification, the minimization of error on the virtual work principle. This method works for both linear elastic and nonlinear elasto-plastic problems. The elasto-plastic rock mass properties for different criteria of plasticity can be well identified based on field measurements. -
Crystal Plasticity Model with Back Stress Evolution. Wei Huang Louisiana State University and Agricultural & Mechanical College
Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1996 Crystal Plasticity Model With Back Stress Evolution. Wei Huang Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Huang, Wei, "Crystal Plasticity Model With Back Stress Evolution." (1996). LSU Historical Dissertations and Theses. 6154. https://digitalcommons.lsu.edu/gradschool_disstheses/6154 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type o f computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. -
Tuning the Performance of Metallic Auxetic Metamaterials by Using Buckling and Plasticity
materials Article Tuning the Performance of Metallic Auxetic Metamaterials by Using Buckling and Plasticity Arash Ghaedizadeh 1, Jianhu Shen 1, Xin Ren 1,2 and Yi Min Xie 1,* Received: 28 November 2015; Accepted: 8 January 2016; Published: 18 January 2016 Academic Editor: Geminiano Mancusi 1 Centre for Innovative Structures and Materials, School of Engineering, RMIT University, GPO Box 2476, Melbourne 3001, Australia; [email protected] (A.G.); [email protected] (J.S.); [email protected] (X.R.) 2 Key Laboratory of Traffic Safety on Track, School of Traffic & Transportation Engineering, Central South University, Changsha 410075, China * Correspondence: [email protected]; Tel.: +61-3-9925-3655 Abstract: Metallic auxetic metamaterials are of great potential to be used in many applications because of their superior mechanical performance to elastomer-based auxetic materials. Due to the limited knowledge on this new type of materials under large plastic deformation, the implementation of such materials in practical applications remains elusive. In contrast to the elastomer-based metamaterials, metallic ones possess new features as a result of the nonlinear deformation of their metallic microstructures under large deformation. The loss of auxetic behavior in metallic metamaterials led us to carry out a numerical and experimental study to investigate the mechanism of the observed phenomenon. A general approach was proposed to tune the performance of auxetic metallic metamaterials undergoing large plastic deformation using buckling behavior and the plasticity of base material. Both experiments and finite element simulations were used to verify the effectiveness of the developed approach. By employing this approach, a 2D auxetic metamaterial was derived from a regular square lattice. -
Symplectic Elasticity Approach for Exact Bending Solutions of Rectangular Thin Plates
Copyright Warning Use of this thesis/dissertation/project is for the purpose of private study or scholarly research only. Users must comply with the Copyright Ordinance. Anyone who consults this thesis/dissertation/project is understood to recognise that its copyright rests with its author and that no part of it may be reproduced without the author’s prior written consent. SYMPLECTIC ELASTICITY APPROACH FOR EXACT BENDING SOLUTIONS OF RECTANGULAR THIN PLATES CUI SHUANG MASTER OF PHILOSOPHY CITY UNIVERSITY OF HONG KONG November 2007 CUI SHUANG RECTANGULAR TH FOR EXACT BENDING SOLUTIONS OF SYMPLECTIC ELASTICITY APPROACH IN PLATES MPhil 2007 CityU CITY UNIVERSITY OF HONG KONG 香港城市大學 SYMPLECTIC ELASTICITY APPROACH FOR EXACT BENDING SOLUTIONS OF RECTANGULAR THIN PLATES 辛彈性力學方法在矩形薄板的彎曲精確解 上的應用 Submitted to Department of Building and Construction 建築學系 in Partial Fulfillment of the Requirements for the Degree of Master of Philosophy 哲學碩士學位 by Cui Shuang 崔爽 November 2007 二零零七年十一月 i Abstract This thesis presents a bridging analysis for combining the modeling methodology of quantum mechanics/relativity with that of elasticity. Using the symplectic method that is commonly applied in quantum mechanics and relativity, a new symplectic elasticity approach is developed for deriving exact analytical solutions to some basic problems in solid mechanics and elasticity that have long been stumbling blocks in the history of elasticity. Specifically, the approach is applied to the bending problem of rectangular thin plates the exact solutions for which have been hitherto unavailable. The approach employs the Hamiltonian principle with Legendre’s transformation. Analytical bending solutions are obtained by eigenvalue analysis and the expansion of eigenfunctions. Here, bending analysis requires the solving of an eigenvalue equation, unlike the case of classical mechanics in which eigenvalue analysis is required only for vibration and buckling problems. -
On the Path-Dependence of the J-Integral Near a Stationary Crack in an Elastic-Plastic Material
On the Path-Dependence of the J-integral Near a Stationary Crack in an Elastic-Plastic Material Dorinamaria Carka and Chad M. Landis∗ The University of Texas at Austin, Department of Aerospace Engineering and Engineering Mechanics, 210 East 24th Street, C0600, Austin, TX 78712-0235 Abstract The path-dependence of the J-integral is investigated numerically, via the finite element method, for a range of loadings, Poisson's ratios, and hardening exponents within the context of J2-flow plasticity. Small-scale yielding assumptions are employed using Dirichlet-to-Neumann map boundary conditions on a circular boundary that encloses the plastic zone. This construct allows for a dense finite element mesh within the plastic zone and accurate far-field boundary conditions. Details of the crack tip field that have been computed previously by others, including the existence of an elastic sector in Mode I loading, are confirmed. The somewhat unexpected result is that J for a contour approaching zero radius around the crack tip is approximately 18% lower than the far-field value for Mode I loading for Poisson’s ratios characteristic of metals. In contrast, practically no path-dependence is found for Mode II. The applications of T or S stresses, whether applied proportionally with the K-field or prior to K, have only a modest effect on the path-dependence. Keywords: elasto-plastic fracture mechanics, small scale yielding, path-dependence of the J-integral, finite element methods 1. Introduction The J-integral as introduced by Eshelby [1,2] and Rice [3] is perhaps the most useful quantity for the analysis of the mechanical fields near crack tips in both linear elastic and non-linear elastic materials. -
On Generalized Cosserat-Type Theories of Plates and Shells: a Short Review and Bibliography Johannes Altenbach, Holm Altenbach, Victor Eremeyev
On generalized Cosserat-type theories of plates and shells: a short review and bibliography Johannes Altenbach, Holm Altenbach, Victor Eremeyev To cite this version: Johannes Altenbach, Holm Altenbach, Victor Eremeyev. On generalized Cosserat-type theories of plates and shells: a short review and bibliography. Archive of Applied Mechanics, Springer Verlag, 2010, 80 (1), pp.73-92. hal-00827365 HAL Id: hal-00827365 https://hal.archives-ouvertes.fr/hal-00827365 Submitted on 29 May 2013 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. 74 J. Altenbach et al. and rotations (and by analogy of forces and couples or force and moment stresses) is stated, see, e.g., [307]. Historically the first scientist, who obtained similar results, was L. Euler. Discussing one of Langrange’s papers he established that the foundations of Mechanics are based on two principles: the principle of momentum and the principle of moment of momentum. Both principles results in the Eulerian laws of motion [307]. In [214] is given the following comment: the independence of the principle of moment of momentum, which is a generalization of the static equilibrium of the moments, was established by Jacob Bernoulli (1686) one year before Newton’s laws (1687). -
Introduction to FINITE STRAIN THEORY for CONTINUUM ELASTO
RED BOX RULES ARE FOR PROOF STAGE ONLY. DELETE BEFORE FINAL PRINTING. WILEY SERIES IN COMPUTATIONAL MECHANICS HASHIGUCHI WILEY SERIES IN COMPUTATIONAL MECHANICS YAMAKAWA Introduction to for to Introduction FINITE STRAIN THEORY for CONTINUUM ELASTO-PLASTICITY CONTINUUM ELASTO-PLASTICITY KOICHI HASHIGUCHI, Kyushu University, Japan Introduction to YUKI YAMAKAWA, Tohoku University, Japan Elasto-plastic deformation is frequently observed in machines and structures, hence its prediction is an important consideration at the design stage. Elasto-plasticity theories will FINITE STRAIN THEORY be increasingly required in the future in response to the development of new and improved industrial technologies. Although various books for elasto-plasticity have been published to date, they focus on infi nitesimal elasto-plastic deformation theory. However, modern computational THEORY STRAIN FINITE for CONTINUUM techniques employ an advanced approach to solve problems in this fi eld and much research has taken place in recent years into fi nite strain elasto-plasticity. This book describes this approach and aims to improve mechanical design techniques in mechanical, civil, structural and aeronautical engineering through the accurate analysis of fi nite elasto-plastic deformation. ELASTO-PLASTICITY Introduction to Finite Strain Theory for Continuum Elasto-Plasticity presents introductory explanations that can be easily understood by readers with only a basic knowledge of elasto-plasticity, showing physical backgrounds of concepts in detail and derivation processes -
FE-Modeling of Bolted Joints in Structures Master Thesis in Solid Mechanics Alexandra Korolija
Department of Management and Engineering Master of Science in Mechanical Engineering LIU-IEI-TEK-A—12/014446-SE FE-modeling of bolted joints in structures Master Thesis in Solid Mechanics Alexandra Korolija Linköping 2012 Supervisor: Zlatan Kapidzic Saab Aeronautics Supervisor: Sören Sjöström IEI, Linköping University Examiner: Kjell Simonsson IEI, Linköping University Division of Solid Mechanics Department of Mechanical Engineering Linköping University 581 83 Linköping, Sweden Datum Date 2012-09-04 Avdelning, Institution Division, Department Div of Solid Mechanics Dept of Mechanical Engineering SE-581 83 LINKÖPING Språk Rapporttyp Serietitel och serienummer Language Report category Title of series, Engelska / English ISRN nummer Antal sidor Examensarbete LIU-IEI-TEK-A—12/014446-SE 56 Titel FE modeling of bolted joints in structures Title Författare Alexandra Korolija Author Sammanfattning Abstract This paper presents the development of a finite element method for modeling fastener joints in aircraft structures. By using connector element in commercial software Abaqus, the finite element method can handle multi-bolt joints and secondary bending. The plates in the joints are modeled with shell elements or solid elements. First, a pre-study with linear elastic analyses is performed. The study is focused on the influence of using different connector element stiffness predicted by semi-empirical flexibility equations from the aircraft industry. The influence of using a surface coupling tool is also investigated, and proved to work well for solid models and not so well for shell models, according to a comparison with a benchmark model. Second, also in the pre-study, an elasto-plastic analysis and a damage analysis are performed. -
Elastic Plastic Fracture Mechanics Elastic Plastic Fracture Mechanics Presented by Calvin M
Fracture Mechanics Elastic Plastic Fracture Mechanics Elastic Plastic Fracture Mechanics Presented by Calvin M. Stewart, PhD MECH 5390-6390 Fall 2020 Outline • Introduction to Non-Linear Materials • J-Integral • Energy Approach • As a Contour Integral • HRR-Fields • COD • J Dominance Introduction to Non-Linear Materials Introduction to Non-Linear Materials • Thus far we have restricted our fractured solids to nominally elastic behavior. • However, structural materials often cannot be characterized via LEFM. Non-Linear Behavior of Materials • Two other material responses are that the engineer may encounter are Non-Linear Elastic and Elastic-Plastic Introduction to Non-Linear Materials • Loading Behavior of the two materials is identical but the unloading path for the elastic plastic material allows for non-unique stress- strain solutions. For Elastic-Plastic materials, a generic “Constitutive Model” specifies the relationship between stress and strain as follows n tot =+ Ramberg-Osgood 0 0 0 0 Reference (or Flow/Yield) Stress (MPa) Dimensionaless Constant (unitless) 0 Reference (or Flow/Yield) Strain (unitless) n Strain Hardening Exponent (unitless) Introduction to Non-Linear Materials • Ramberg-Osgood Constitutive Model n increasing Ramberg-Osgood −n K = 00 Strain Hardening Coefficient, K = 0 0 E n tot K,,,,0 n=+ E Usually available for a variety of materials 0 0 0 Introduction to Non-Linear Materials • Within the context of EPFM two general ways of trying to solve fracture problems can be identified: 1. A search for characterizing parameters (cf. K, G, R in LEFM). 2. Attempts to describe the elastic-plastic deformation field in detail, in order to find a criterion for local failure. -
Crystal Plasticity Based Modelling of Surface Roughness and Localized
Crystal Plasticity Based Modelling of Surface Roughness and Localized Deformation During Bending in Aluminum Polycrystals by Jonathan Rossiter A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Mechanical Engineering Waterloo, Ontario, Canada, 2015 © Jonathan Rossiter 2015 Author’s Declaration I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Abstract This research focuses on numerical modeling of formability and instabilities in aluminum with a focus on the bending loading condition. A three-dimensional (3D) finite element analysis based on rate-dependent crystal plasticity theory has been employed to investigate non-uniform deformation in aluminum alloys during bending. The model can incorporate electron backscatter diffraction (EBSD) maps into finite element analyses. The numerical analysis not only accounts for crystallographic texture (and its evolution) but also accounts for 3D grain morphologies, because a 3D microstructure (constructed from two-dimensional EBSD data) can be employed in the simulations. The first part of the research concentrates on the effect of individual aluminum grain orientations on the developed surface roughness during bending. The standard orientations found within aluminum are combined in a systematic way to investigate their interactions and sensitivity to loading direction. The end objective of the study is to identify orientations that promote more pronounced surface roughness so that future material processes can be developed to reduce the occurrence of these orientations and improve the bending response of the material. -
Bending Analysis of Simply Supported and Clamped Circular Plate P
SSRG International Journal of Civil Engineering (SSRG-IJCE) Volume 2 Issue 5–May 2015 Bending Analysis of Simply Supported and Clamped Circular Plate P. S. Gujar 1, K. B. Ladhane 2 1Department of Civil Engineering, Pravara Rural Engineering College, Loni,Ahmednagar-413713(University of Pune), Maharashtra, India. 2Associate Professor, Department of Civil Engineering, Pravara Rural Engineering College, Loni,Ahmednagar- 413713(University of Pune), Maharashtra, India. ABSTRACT : The aim of study is static bending appropriate plate theory. The stresses in the plate can analysis of an isotropic circular plate using be calculated from these deflections. Once the analytical method i.e. Classical Plate Theory and stresses are known, failure theories can be used to Finite Element software ANSYS. Circular plate determine whether a plate will fail under a given analysis is done in cylindrical coordinate system by load [1]. using Classical Plate Theory. The axisymmetric Vanam et al.[2] done static analysis of an bending of circular plate is considered in the present isotropic rectangular plate using finite element study. The diameter of circular plate, material analysis (FEA).The aim of study was static bending properties like modulus of elasticity (E), poissons analysis of an isotropic rectangular plate with ratio (µ) and intensity of loading is assumed at the various boundary conditions and various types of initial stage of research work. Both simply supported load applications. In this study finite element and clamped boundary conditions subjected to analysis has been carried out for an isotropic uniformly distributed load and center concentrated / rectangular plate by considering the master element point load have been considered in the present as a four noded quadrilateral element.