Plasticity - Mathematical Theory and Numerical Analysis Interdisciplinary Applied Mathematics









Weimin Han B. Daya Reddy

Plasticity

Mathematical Theory and

Numerical Analysis

With 34 Illustrations



Preface

The basis for the modern theory of elastoplasticity was laid in the nineteenthcentury,

by Tresca, St. Venant, L

´

evy, and Bauschinger. Further

major advances followed in the early part of this century, the chief contributors

during this period being Prandtl, von Mises, and Reuss. This

early phase in the history of elastoplasticity was characterized by the introduction

and development of the concepts of irreversible behavior, yield

criteria, hardening and perfect plasticity, and of rate or incremental constitutive

equations for the plastic strain.

Greater clarity in the mathematical framework for elastoplasticity theory

came with the contributions of Prager, Drucker, and Hill, during the

period just after the Second World War. Convexity of yield surfaces, and

all its ramifications, was a central theme in this phase of the development

of the theory.

The mathematical community, meanwhile, witnessed a burst of progress

in the theory of partial differential equations and variational inequalities

from the early 1960s onwards. The timing of this set of developments was

particularly fortuitous for plasticity, given the fairly mature state of the

subject, and the realization that the natural framework for the study of

initial boundary value problems in elastoplasticity was that of variational

inequalities. This confluence of subjects emanating from mechanics and

mathematics resulted in yet further theoretical developments, the outstanding

examples being the articles by Moreau, and the monographs

by Duvaut and J.-L. Lions, and Temam. In this manner the stage was

set for comprehensive investigations of the well-posedness of problems in

elastoplasticity,









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