An Augmented Lagrange Method to Solve Large Deformation Three-Dimensional Contact Problems

In this work an implementation of the mortar method is proposed to solve 3D contact problems in the context of large deformations. The contact constraints and non-linear equilibrium equations are derived from the augmented Lagrange method which is a C-1 continuous functional. Newton's method is used to solve the non-linear system. As the proposed formulation is based on the mortar method, the constraints are imposed in a weak integral sense. Although we use a numerical quadrature to compute the integral, we show that the optimal convergence rate of the finite element solution is still preserved.