Contact problems with nonmonotone friction: discretization and numerical realization

Abstract

The paper deals with the formulation, approximation and numerical realization of a constrained hemivariational inequality describing the behavior of two elastic bodies in mutual contact, taking into account a nonmonotone friction law on a contact surface. The original hemivariational inequality is transformed into a problem of finding substationary points of a nonconvex, locally Lipschitz continuous function representing the discrete total potential energy functional. The resulting discrete problem is solved by using a nonsmooth variant of the Newton method. Numerical results of a model example are shown.

Approximation of thermoelasticity contact problem with nonmonotone friction

“…If τ : Ω → R 2×2 s is the stress tensor in Ω, where R 2×2 s is the space of symmetric matrices of order 2, then S : Γ → R 2 , where S = τn is the stress vector on Γ. Furthermore, S N = (τn) · n and S T = (τn) · t stand for the normal, respectively tangential, components of S on Γ [13] .…”

Semicoercive Variational Inequalities: From Existence to Numerical Solution of Nonmonotone Contact Problems

“…It is devoted to the numerical solution of nonmonotone semicoercive contact problems in solid mechanics modelled by hemivariational inequalities, a class of variational inequalities (VIs) introduced and studied by Panagiotopoulos [3], see also [4,5,6]. Here we treat unilateral contact problems with nonmonotone friction [7], which occur with adhesion and delamination in the delicate situation, where the body is not fixed along some boundary part, but is only subjected to surface tractions and body forces. Thus there is a loss of coercivity leading to so-called semicoercive or noncoercive variational problems [8,9].…”