Abstract
We consider two mathematical models which describe the frictionless process of contact between a rate-type viscoplastic body and a foundation. The contact is modelled with normal compliance and memory term such that penetration is not restricted in the first problem, but is restricted with unilateral constraint in the second one.
For each problem, we derive a variational formulation in terms of displacements, which is in a form of a history-dependent variational equation and a history-dependent variational inequality. Then we prove the unique weak solvability of each model. Next, we prove the convergence of the weak solution of the first problem and the weak solution of the second problem, as the stiffness coefficient of the foundation converges to infinity.
Finally, we provide numerical simulations which illustrate this convergence result.
Authors
Mikael Barboteu
(Laboratoire de Mathématiques et Physique, Université de Perpignan)
Flavius Patrulescu
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)
Ahmad Ramadan
(Laboratoire de Mathématiques et Physique, Université de Perpignan)
Mircea Sofonea
(Laboratoire de Mathématiques et Physique, Université de Perpignan)
Keywords
viscoplastic material; frictionless contact; normal compliance; unilateral constraint; memory term; history-dependent variational inequality; weak solution; numerical simulations
Cite this paper as:
M. Barboteu, F. Pătrulescu, A. Ramadan, M. Sofonea, History-dependent contact models for viscoplastic materials, IMA J. Appl. Math., 79 (2014) no. 6, pp. 1180-1200.
About this paper
Publisher Name
Oxford University Press, Oxford
Print ISSN
0272-4960
Online ISSN
1464-3634
MR
3286321
ZBL
1307.74055
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