Robust implementation of contact under friction and large sliding with the eXtended finite element method

Abstract

An X-FEM formulation is proposed for the case of large sliding frictional interfaces. A continuous augmented lagrangian framework is adopted for contact and friction. We provide an algorithm for the selection of an appropriate discrete space for the lagrange multipliers, accounting for the transition between contact and free zones, and also between sliding and adherent zones. A 3D numerical test is realized with Code_Aster free software for the compression of a cylinder cut along a radial section and shows the ability of the model to capture such transitions.

Experimental and numerical analysis of fretting crack formation based on 3D X-FEM frictional contact fatigue crack model

“…It is well known that the existence and unicity of the solution of a discrete mixed formulation require a continuous definition of the Lagrange multiplier space in accordance with the displacement space, satisfying the LBB inf-sup condition. Comments and details regarding this question within X-FEM models with contact and friction can be found in [31][32][33]21,34,20,19]. Additional remarks will be exposed in the next sections regarding the unilateral or frictional contact problems.…”

“…The linear system (23) being solved, the local traction T i+1 is computed according to (21). The local and the global steps are repeated until the convergence is achieved.…”

“…X-FEM has been applied to 3D crack growth combined with level set techniques for the crack shape description [10][11][12][13] with possible multi-scale effects [14]. The implementation within the X-FEM framework of contact with or without friction has been further performed in 2D [15][16][17][18][19] and in 3D [20][21][22]. The accurate modeling of tribological fatigue dealing with non-proportional multi-axial loading and severe stress gradients in the cracked area has been further performed [23][24][25][26].…”