Geodesic
Analysis of two dynamic frictionless contact problems for elastic-viscoplastic materials
Electronic Journal of Differential Equations, Tome 2007 (2007).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 74M15, 74H20, 74H25, 49J40
Keywords: elastic-visco-plastic material, dynamic process, frictionless contact, normal compliance, normal damped response, variational formulation, weak solution 
@article{EJDE_2007__2007__a263,
     author = {Ayyad, Youssef and Sofonea, Mircea},
     title = {Analysis of two dynamic frictionless contact problems for elastic-viscoplastic materials},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a263/}
}
TY  - JOUR
AU  - Ayyad, Youssef
AU  - Sofonea, Mircea
TI  - Analysis of two dynamic frictionless contact problems for elastic-viscoplastic materials
JO  - Electronic Journal of Differential Equations
PY  - 2007
VL  - 2007
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a263/
LA  - en
ID  - EJDE_2007__2007__a263
ER  - 
%0 Journal Article
%A Ayyad, Youssef
%A Sofonea, Mircea
%T Analysis of two dynamic frictionless contact problems for elastic-viscoplastic materials
%J Electronic Journal of Differential Equations
%D 2007
%V 2007
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a263/
%G en
%F EJDE_2007__2007__a263
Ayyad, Youssef; Sofonea, Mircea. Analysis of two dynamic frictionless contact problems for elastic-viscoplastic materials. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a263/