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

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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Submitted on : Thursday, May 12, 2022 - 3:21:40 PM
Last modification on : Friday, August 5, 2022 - 2:41:30 PM

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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, Society for Industrial and Applied Mathematics, 2016, 48 (2), pp.861-883. ⟨10.1137/151005610⟩. ⟨hal-01346147⟩

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