Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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 $ G$. It is shown that the maximum plastic work inequality together with the assumption that $ G$ 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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DOI: https://doi.org/10.1090/qam/1040234
Article copyright: © Copyright 1990 American Mathematical Society


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