Youssef Ayyad, Mircea Sofonea
Abstract:
We consider two mathematical models which describe the
contact between an elastic-visco-plastic body and an obstacle,
the so-called foundation. In both models the contact is
frictionless and the process is assumed to be dynamic.
In the first model the contact is described with a normal
compliance condition and, in the second one, is described
with a normal damped response condition.
We derive a variational formulation of the models which is
in the form of a system coupling an integro-differential
equation with a second order variational equation for the
displacement and the stress fields.
Then we prove the unique weak solvability of the models.
The proofs are based on arguments on nonlinear evolution
equations with monotone operators and fixed point.
Finally, we study the dependence of the solution with respect
to a perturbation of the contact conditions and prove a
convergence result.
Submitted March 12, 2007. Published April 17, 2007.
Math Subject Classifications: 74M15, 74H20, 74H25, 49J40.
Key Words: Elastic-visco-plastic material; dynamic process;
frictionless contact; normal compliance;
normal damped response; variational formulation;
weak solution.
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Youssef Ayyad Laboratoire de Mathématiques et Physique pour les Systémes, University of Perpignan 52 avenue Paul Alduy 66860 Perpignan, France email: youssef.ayyad@univ-perp.fr |
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Mircea Sofonea Laboratoire de Mathématiques et Physique pour les Systémes, University of Perpignan 52 avenue Paul Alduy 66860 Perpignan, France email: sofonea@univ-perp.fr |
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