An algorithm for the numerical realization of 3D contact problems with Coulomb friction

Scalable algorithm for solving 3D contact problems with friction

“…Finally we introduce full rank matrices N and T 1 , T 2 ∈ R mc×3nc projecting displacements at contact nodes to normal and tangential directions, respectively, and we denote B = B d , B g , N , T 1 , T 2 ∈ R m d +mg +3mc×3nc . For more details about this model problem, we refer to [5].…”

Mixed finite element approximation of 3D contact problems with given friction: Error analysis and numerical realization

“…we formally obtain the same situation as in 2D contact problems. The discretized version of (6.3) together with the augmented Lagrangian formulation has been used in (see [15]) for the numerical realization of 3D contact problems with friction, including Coulomb's model of friction. The previous numerical method has a drawback, too, namely the number of variables is now equal to N × q, where N is the number of squares and q = dim L H .…”

Mixed finite element analysis of semi-coercive unilateral contact problems with given friction

“…If a given friction (Tresca's model) has to be considered, a non-differentiable term appears in the inequality, making the approximate solution more complicated. A remedy can be a mixed variational formulation of the problem which employs Lagrange multipliers ( [8], [9], [10], [11], [12], [17], [2]). …”