A Variational-Hemivariational Inequality in Contact Mechanics

Mircea Sofonea (1) , Weimin Han (2) , Mikaël Barboteu (1)

1 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations
2 University of Iowa [Iowa City]

This chapter deals with a new mathematical model for the frictional contact between an elastic body and a rigid foundation covered by a deformable layer made of soft material. We study the model in the form of a variational-hemivariational inequality for the displacement field. We review a unique solvability result of the problem under certain assumptions on the data. Then we turn to the numerical solution of the problem, based on the finite element method. We derive an optimal order error estimate for the linear finite element solution. Finally, we present numerical simulation results in the study of a two-dimentional academic example. The theoretically predicted optimal convergence order is observed numerically. Moreover, we provide mechanical interpretations of the numerical results for our contact model.

Domaines: Mathématiques [math]

Mircea Sofonea, Weimin Han, Mikaël Barboteu. A Variational-Hemivariational Inequality in Contact Mechanics. Mathematical Modelling in Solid Mechanics, 69, Springer, pp.251-264, 2017, ⟨10.1007/978-981-10-3764-1_16⟩. ⟨hal-01628000⟩