An internal variable theory of elastoplasticity based on the maximum plastic work inequality

Authors:
R. A. Eve, B. D. Reddy and R. T. Rockafellar

Journal:
Quart. Appl. Math. **48** (1990), 59-83

MSC:
Primary 73E99; Secondary 73B30, 73E50

DOI:
https://doi.org/10.1090/qam/1040234

MathSciNet review:
MR1040234

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Abstract | References | Similar Articles | Additional Information

Abstract: The methods of convex analysis are used to explore in greater depth the nature of the evolution equation in internal variable formulations of elastoplasticity. The evolution equation is considered in a form in which the thermodynamic force belongs to a set defined by a multi-valued map . It is shown that the maximum plastic work inequality together with the assumption that is maximal responsive (a term defined in Sec. 4), is necessary and sufficient to give a theory equivalent to that proposed by Moreau. Further consequences are investigated or elucidated, including the relationship between the yield function and the dissipation function; these functions are polars of each other. Examples are given to illustrate the theory.

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Additional Information

DOI:
https://doi.org/10.1090/qam/1040234

Article copyright:
© Copyright 1990
American Mathematical Society