Computational Methods for Plasticity - Theory and Applications





COMPUTATIONAL

METHODS FOR

PLASTICITY

THEORY AND APPLICATIONS

EA de Souza Neto

D Peri'c

DRJ Owen

Civil and Computational Engineering Centre, Swansea University


PREFACE

HE purpose of this text is to describe in detail numerical techniques used in small and

large strain finite element analysis of elastic and inelastic solids. Attention is focused

on the derivation and description of various constitutive models – based on phenomenological

hyperelasticity, elastoplasticity and elasto-viscoplasticity – together with the relevant

numerical procedures and the practical issues arising in their computer implementation

within a quasi-static finite element scheme. Many of the techniques discussed in the text are

incorporated in the FORTRAN program, named HYPLAS, which accompanies this book and

can be found at . This computer program has been specially

written to illustrate the practical implementation of such techniques. We make no pretence

that the text provides a complete account of the topics considered but rather, we see it as an

attempt to present a reasonable balance of theory and numerical procedures used in the finite

element simulation of the nonlinear mechanical behaviour of solids.

When we embarked on the project of writing this text, our initial idea was to produce

a rather concise book – based primarily on our own research experience – whose bulk

would consist of the description of numerical algorithms required for the finite element

implementation of small and large strain plasticity models. As the manuscript began to take

shape, it soon became clear that a book designed as such would be most appropriate to those

already involved in research on computational plasticity or closely related areas, being of

little use to those willing to learn computational methods in plasticity from a fundamental

level. A substantial amount of background reading from other sources would be required for

readers unfamiliar with topics such as basic elastoplasticity theory, tensor analysis, nonlinear

continuum mechanics – particularly nonlinear kinematics – finite hyperelasticity and general

dissipative constitutive theory of solids. Our initial plan was then gradually abandoned as

we chose to make the text more self-contained by incorporating a considerable amount of

basic theory. Also, while writing the manuscript, we decided to add more advanced (and very

exciting) topics such as damage mechanics, anisotropic plasticity and the treatment of finite

strain single crystal plasticity. Following this route, our task took at least three times as long

to complete and the book grew to about twice the size as originally planned. There remains

plenty of interesting material we would like to have included but cannot due to constraints

of time and space. We are certainly far more satisfied with the text now than with its early

versions, but we do not believe our final product to be optimal in any sense. We merely offer

it to fill a gap in the existing literature, hoping that the reader will benefit from it in some way.

The text is arranged in three main parts. Part One presents some basic material of relevance

to the subject matter of the book. It includes an overview of elementary tensor analysis,

continuum mechanics and thermodynamics, the finite element method in quasi-static nonlinear

solid mechanics and a brief description of the computer program HYPLAS.PartTwo



deals with small strain problems. It introduces the mathematical theory of infinitesimal

plasticity as well as the relevant numerical procedures for the implementation of plasticity

models within a finite element environment. Both rate-independent (elastoplastic) and ratedependent

(elasto-viscoplastic) theories are addressed and some advanced models, including

anisotropic plasticity and ductile damage are also covered. Finally, in Part Three we focus

on large strain problems. The theory of finite hyperelasticity is reviewed first together with

details of its finite element implementation. This is followed by an introduction to large strain

plasticity. Hyperelastic-based theories with multiplicative elastoplastic kinematics as well as

hypoelastic-based models are discussed, together with relevant numerical procedures for their

treatment. The discussion on finite plasticity and its finite element implementation culminates

with a description of techniques for single crystal plasticity. Finite element techniques for

large-strain near-incompressibility are also addressed.


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