Arc-Length Method for Frictional Contact Problems by using Mathematical Program with Complementarity Constraints

A new formulation as well as a new solution technique is proposed for an equilibrium path-following method in two-dimensional quasi-static frictional contact problems. We consider the classical Coulomb friction law as well as geometrical nonlinearity explicitly. Based on a criterion of maximum dissipation of energy, we propose a formulation as a mathematical program with complementarity constraints (MPEC) in order to avoid unloading solutions in which most contact candidate nodes become stuck. A regularization scheme for the MPEC is proposed, which can be solved by using the conventional nonlinear programming approach. The equilibrium paths of various structures are computed in cases such that there exist some limit points and/or infinite number of successive bifurcation points.