A Lagrange multiplier method for the finite element solution of frictionless contact problems

This article proposes a novel Lagrange multiplier-based formulation for the finite element solution of the quasi-static two-body contact problem in the presence of finite motions and deformations. The main idea rests in the interpretation of the two-body contact as a composition of two simultaneous Signorini-like problems, which naturally yield geometrically unbiased approximations of the kinematics and kinetics of frictionless contact. A two-dimensional finite element is introduced that exactly satisfies the impenetrability constraint and allows for the direct computation of consistent pressure distributions on the interacting surfaces.