A Frictional Dynamic Thermal Contact Problem with Normal Compliance and Damage

Oanh Chau (), Adrien Petrov (), Arnaud Heibig () and Manuel Monteiro Marques ()
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Oanh Chau: PIMENT EA4518
Adrien Petrov: CNRS, INSA of Lyon, Institut Camille Jordan UMR 5208
Arnaud Heibig: CNRS, INSA of Lyon, Institut Camille Jordan UMR 5208
Manuel Monteiro Marques: Faculty of Science

A chapter in Nonlinear Analysis and Global Optimization, 2021, pp 71-107 from Springer

Abstract: Abstract We study a class of non-clamped dynamical problems for visco-elastic materials, the contact condition is modeled by a normal compliance, with friction, damage and heat exchange. The weak formulation leads to a general system defined by a second-order quasi-variational evolution inequality on the displacement field coupled with a nonlinear evolutional inequality on temperature field and a parabolic variational inequality on the damage field. We present and establish an existence and uniqueness result of different fields, by using general results on evolution variational inequalities, with monotone operators and fixed point methods. Then, we present a fully discrete numerical scheme of approximation and derive an error estimate. Finally, various numerical computations are developed.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-61732-5_4

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DOI: 10.1007/978-3-030-61732-5_4

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