Mixed finite element formulation in large deformation frictional contact problem

This paper presents a mixed variational framework and numerical examples to treat a bidimensional friction contact problem in large deformation. Two different contact algorithms with friction are developed using the 2D finite element code PLAST2. The first contact algorithm is the classical node-on-segment, and the second one corresponds to an extension of the mortar element method to a unilateral contact problem with friction. In this last method, the discretized normal and tangential stresses on the contact surface are expressed by using either continuous piecewise linear or piecewise constant Lagrange multipliers in the saddle-point formulation. The two algorithms based on Lagrange multipliers method are developed and compared for linear and quadratic elements.