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A Frictional Dynamic Thermal Contact Problem with Normal Compliance and Damage

In: Nonlinear Analysis and Global Optimization

Author

Listed:
  • 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)

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.

Suggested Citation

  • Oanh Chau & Adrien Petrov & Arnaud Heibig & Manuel Monteiro Marques, 2021. "A Frictional Dynamic Thermal Contact Problem with Normal Compliance and Damage," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Nonlinear Analysis and Global Optimization, pages 71-107, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-61732-5_4
    DOI: 10.1007/978-3-030-61732-5_4
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