A Viscoplastic Contact Problem with Normal Compliance, Unilateral Constraint and Memory Term

A Viscoplastic Contact Problem with Normal Compliance, Unilateral Constraint and Memory Term We consider a mathematical model which describes the quasistatic contact between a viscoplastic body and a foundation. The material’s behavior is modelled with a rate-type constitutive law with internal state variable. The contact is frictionless and is modelled with normal compliance, unilateral constraint and memory term. We present the classical formulation of the problem, list the assumptions on the data and derive a variational formulation of the model. Then we prove its unique weak solvability. The proof is based on arguments of history-dependent quasivariational inequalities. We also study the dependence of the solution with respect to the data and prove a convergence result. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

A Viscoplastic Contact Problem with Normal Compliance, Unilateral Constraint and Memory Term

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Publisher
Springer US
Copyright
Copyright © 2014 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-013-9216-2
Publisher site
See Article on Publisher Site

Abstract

We consider a mathematical model which describes the quasistatic contact between a viscoplastic body and a foundation. The material’s behavior is modelled with a rate-type constitutive law with internal state variable. The contact is frictionless and is modelled with normal compliance, unilateral constraint and memory term. We present the classical formulation of the problem, list the assumptions on the data and derive a variational formulation of the model. Then we prove its unique weak solvability. The proof is based on arguments of history-dependent quasivariational inequalities. We also study the dependence of the solution with respect to the data and prove a convergence result.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Apr 1, 2014

References

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