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Journal Articles SIAM Journal on Mathematical Analysis Year : 2016

The Rothe Method for Variational-Hemivariational Inequalities with Applications to Contact Mechanics

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Abstract

We consider a new class of first order evolutionary variational-hemivariational inequalities for which we prove an existence and uniqueness result. The proof is based on a time-discretization method, also known as the Rothe method. It consists of considering a discrete version of each inequality in the class, proving its unique solvability, and recovering the solution of the continuous problem as the time step converges to zero. Then we introduce a quasi-static frictionless problem for Kelvin--Voigt viscoelastic materials in which the contact is modeled with a nonmonotone normal compliance condition and a unilateral constraint. We prove the variational formulation of the problem cast in the abstract setting of variational-hemivariational inequalities, with a convenient choice of spaces and operators. Further, we apply our abstract result in order to prove the unique weak solvability of the problem.
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Dates and versions

hal-01346147 , version 1 (12-05-2022)

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Attribution - NonCommercial - CC BY 4.0

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Krzysztof Bartosz, Mircea Sofonea. The Rothe Method for Variational-Hemivariational Inequalities with Applications to Contact Mechanics. SIAM Journal on Mathematical Analysis, 2016, 48 (2), pp.861-883. ⟨10.1137/151005610⟩. ⟨hal-01346147⟩
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