On an implicit solution scheme for frictional contact of deformable bodies

Based on an augmented Lagrangian approach and the finite element method, an implicit formulation for frictional contact between deformable bodies is proposed. The methodology yields a mixed system of non-linear equations where the finite element nodal unknowns associated to each deformable member in contact are coupled consistently by Lagrangian multipliers. The resulting system of equations is solved simultaneously for frictional contact forces and displacement increments by a generalised-Newton method. The performance of the method is demonstrated by 3D simulations which include frictional contact of deformable bodies in the case of elasto-plastic material behaviour.