Numerical Analysis of a Contact Problem with Wear

This paper represents a sequel to the previous one, where numerical solution of a quasistatic contact problem is considered for an elastic body in frictional contact with a moving foundation. The model takes into account wear of the contact surface of the body caused by the friction. Some preliminary error analysis for a fully discrete approximation of the contact problem was provided in the previous paper. In this paper, we consider a more general fully discrete numerical scheme for the contact problem, derive optimal order error bounds and present computer simulation results showing that the numerical convergence orders match the theoretical predictions.Comment: 13 pages, 6 figure

Time-dependent variational inequalities for viscoelastic contact problems

AbstractWe consider a class of abstract evolutionary variational inequalities arising in the study of contact problems for viscoelastic materials. We prove an existence and uniqueness result, using standard arguments of time-dependent elliptic variational inequalities and Banach's fixed point theorem. We then consider numerical approximations of the problem. We use the finite element method to discretize the spatial domain and we introduce spatially semi-discrete and fully discrete schemes. For both schemes, we show the existence of a unique solution, and derive error estimates. Finally, we apply the abstract results to the analysis and numerical approximations of a viscoelastic contact problem with normal compliance and friction

On the Finite Element Method for Mixed Variational Inequalities Arising in Elastoplasticity

We analyze the finite-element method for a class of mixed variational inequalities of the second kind, which arises in elastoplastic problems. An abstract variational inequality, of which the elastoplastic problems are special cases, has been previously introduced and analyzed [B. D. Reddy, Nonlinear Anal., 19 (1992), pp. 1071-1089], and existence and uniqueness results for this problem have been given there. In this contribution the same approach is taken ; that is, finite-element approximations of the abstract variational inequality are analyzed, and the results are then discussed in further detail in the context of the concrete problems. Results on convergence are presented, as are error estimates. Regularization methods are commonly employed in variational inequalities of this kind, in both theoretical and computational investigations. We derive a posteriori error estimates which enable us to determine whether the solution of a regularized problem can be taken as a sufficiently accurate approximation of the solution of the original problem