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Dynamic viscoelastic unilateral constrained contact problems with thermal effects

Author

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  • Guo, Furi
  • Wang, JinRong
  • Han, Jiangfeng

Abstract

A new model that describes a dynamic frictional contact between a viscoelastic body and an obstacle is investigated in this paper. We consider a nonlinear viscoelastic constitutive law which involves a convex subdifferential inclusion term and thermal effects. The contact condition is modeled with unilateral constraint condition for a version of normal velocity. The boundary conditions that describe the contact, friction and heat flux are govern by the generalized Clarke multivalued subdifferential. We derive a coupled system of two nonlinear first order evolution inclusions problems, which consists of a parabolic variational-hemivariational inequality for the displacement and a hemivariational inequality of parabolic type for the temperature. Then, the unique weak solvability of the contact problem is obtained by virtue of a fixed point theorem and the surjectivity result of multivalued maps. Finally, we deliver a continuous dependence result on a coupled system when the data are subjected to perturbations.

Suggested Citation

  • Guo, Furi & Wang, JinRong & Han, Jiangfeng, 2022. "Dynamic viscoelastic unilateral constrained contact problems with thermal effects," Applied Mathematics and Computation, Elsevier, vol. 424(C).
    • Handle: RePEc:eee:apmaco:v:424:y:2022:i:c:s0096300322001205
    DOI: 10.1016/j.amc.2022.127034
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    References listed on IDEAS

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    1. Stanisław Migórski & Shengda Zeng, 2018. "A class of differential hemivariational inequalities in Banach spaces," Journal of Global Optimization, Springer, vol. 72(4), pages 761-779, December.
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