An internal variable theory of elastoplasticity based on the maximum plastic work inequality
RA Eve, BD Reddy, RT Rockafellar - Quarterly of Applied Mathematics, 1990 - ams.org
RA Eve, BD Reddy, RT Rockafellar
Quarterly of Applied Mathematics, 1990•ams.orgThe 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 …
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 …
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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