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 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 mathematical program with complementarity constraints (MPEC) formulation 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. Keywords: contact problem, Coulomb's friction; arc-length method, mathematical program with complementarity constraints (MPEC), maximum dissipation + Department of Urban and Environmental Engineering, Kyoto University e-mail: kanno@archi.kyoto-u.ac.jp # Instituto Superior Tecnico, Dep. Eng. Civil and ICIST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal e-mail: jmartins@civil.ist.utl.pt 1