Symmetrization of Various Friction Models Based on an Augmented Lagrangian Approach

The standard implementation of the classical Coulomb frictionmodel together with the Newton iterative method for the finite element method leads to non-symmetric tangent matrices for sliding zones of contact surfaces. This fact is known in literature as consequence of the non-associativity of the friction law. Considering anisotropic models for friction, especially including coupling of adhesion and friction, leads to additional non-symmetries due to anisotropy. Since, non-symmetry of matrices is a non-desirable feature of most engineering problems, various proposals for symmetrization are known in computational mechanics. A further suggestion is made in this contribution. The covariant approach for both isotropic and anisotropic frictional contact problems leads to a very simple structure of the tangent matrices. This allows to obtain very robust tangent matrices within the symmetrized Augmented Lagrangian method. In the current contribution, the nested Uzawa algorithm is applied for symmetrization within the Augmented Lagrangian approach for an anisotropic friction model including adhesion and friction. The numerical examples show the good convergence behavior for various problems such as small and large sliding problems.

Key words: Anisotropic friction and adhesion, covariant description, Augmented Lagrangian method, symmetrization.