Solving Frictional Contact Problems within the Bipotential Framework

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...

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.

On Solving Frictional Contact Problems Part I: Abstract Framework and the Static Case. submitted to IJNAM as Mixed FEM of Higher Order for Contact Problems with Friction

Keywords hp-FEM · contact problems This paper presents mixed variational formulation and its discretization with finite elements of higher-order for Signorini's problem with Tresca's friction. To guarantee the unique existence of the discrete saddle point of the mixed method, a discrete inf-sup condition is proven. Moreover, a solution scheme based on the dual formulation of the mixed method is...

Covariant description for frictional contact problems

On the Two-step Iterative Method of Solving Frictional Contact Problems in Elasticity

Unilateral contact problems in elasticity (Duvaut and Lions, 1976) have been extensively studied in the last two decades (Andersson and Klarbring, 2001; Angelov and Liolios, 2004; Cǎpǎtinǎ and Cocu, 1991; Cocu, 1984; Demkowicz and Oden, 1982; Duvaut and Lions, 1976; Hlavaček et al., 1988; Kikuchi and Oden, 1988; Klarbring et al., 1989; Lee and Oden, 1993a,1993b; Ne čas et al., 1980; Oden and Ca...