Variational analysis for some frictional contact problems

Covariant description for frictional contact problems

Evolutionary Variational Inequalities Arising in Quasistatic Frictional Contact Problems for Elastic Materials

We consider a class of evolutionary variational inequalities arising in quasistatic frictional contact problems for linear elastic materials. We indicate sufficient conditions in order to have the existence, the uniqueness and the Lipschitz continuous dependence of the solution with respect to the data, respectively. The existence of the solution is obtained using a time-discretization method, ...

Solving Frictional Contact Problems with Multigrid Efficiency

The construction of fast and reliable solvers for contact problems with friction is even nowadays a challenging task. It is well known that contact problems with Coulomb friction have the weak form of a quasi-variational inequality [KO88, HHNL88, NJH80]. For small coefficients of friction, a solution can be obtained by means of a fixed point iteration in the boundary stresses [NJH80]. This fixe...

A Class of Variational-Hemivariational Inequalities with Applications to Frictional Contact Problems

A class of variational-hemivariational inequalities is studied in this paper. An inequality in the class involves two nonlinear operators and two nondifferentiable functionals, of which at least one is convex. An existence and uniqueness result is proved for a solution of the inequality. Continuous dependence of the solution on the data is shown. Convergence is established rigorously for finite...

On Solving Frictional Contact Problems Part Iii: Unilateral Contact

In this paper, we study mixed variational nite element methods for the unilateral problems arising in contact mechanics.The presented discrete spaces can handle the case of non matching meshes in the contact area. We rst state the static problem and then extend it to the frictional contact case, and end with the dynamic frictional problem.