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Plasticity Models and Nonlinear Semigroups

✍ Scribed by R.E Showalter; Peter Shi

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
337 KB
Volume
216
Category
Article
ISSN
0022-247X

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✦ Synopsis

The evolution of an elastic-plastic material is modeled as an initial boundary value problem consisting of the dynamic momentum equation coupled with a constitutive law for which the hysteretic dependence between stress and strain is described by a system of variational inequalities. This system is posed as an evolution equation in Hilbert space for which is proved the existence and uniqueness of three classes of solutions which are distinguished by their regularity. Weak solutions are obtained in a very general situation, strong solutions arise in the presence of kinematic work-hardening or viscosity, and the solution is even more regular under a stability assumption connecting the constraint set with the divergence operator.

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## Abstract In this paper we study the properties of a new one parameter family of nonlinear operators which is a generalization of __B__‐bounded linear semigroups. This family is constructed by means of a nonlinear operator __A__ and a linear operator __B__. We give also examples of problems which