Qualitative analysis of solutions to discrete static contact problems with Coulomb friction

Abstract

We analyze properties of solutions to discrete contact problems with Coulomb friction which are parametrized by the coefficient of friction F. Using a generalized variant of the implicit-function theorem we establish conditions under which there exists a local Lipschitz continuous branch of solutions around a reference point.

Finally, a piecewise smooth continuation algorithm which allows to follow such branches of solutions is proposed.

Keywords

• Contact problem
• Coulomb friction
• Mixed finite element formulation
• Local Lipschitz continuous branches of solutions
• Piecewise smooth continuation methods