A mortar-based frictional contact formulation for large deformations using Lagrange multipliers

In this work a Lagrange multiplier method is proposed to solve 2D Coulomb frictional contact problems in the context of large deformations. As the proposed formulation is based on the mortar method, the constraints are imposed in a weak integral sense along the contact surface. In order to compute the contact integrals, we use a numerical integration based on the definition of the kinematical variables (gap, slip and their variations) at the quadrature points. The linearization of non-linear equations (virtual work and contact constraints) is developed in order to apply a Newton’s method. The examples show that the numerical integration still preserves the optimal rate of convergence of the finite element solution.