Large deformation frictional contact mechanics: continuum formulation and augmented Lagrangian treatment Original Research Article

A complete methodology for the formulation and solution of unilateral contact problem with non-associated, threshold friction between solids undergoing large deformations is presented. The approach includes a continuum contact mechanics model combined with an augmented Lagrangian method for treating the contact and friction inequality constraints. The main developments are a precise statement of the incremental contact minimization problem, the exact computations of the first and second variations of the normal gap and the tangential slip velocity and an extension of the augmented Lagrangian formulation for frictional contact problems from the discrete to the continuum framework. The corresponding saddle-point functional first variation (mixed virtual work) and second variation (exact linearization) are given. The development are illustrated by numerical simulations of frictional contact problems between rigid, elastic and elastoplastic bodies. A new severe benchmark for large slip frictional contact elements is also proposed.