Smoothing Newton method for solving two- and three-dimensional frictional contact problems

Abstract

Two- and three-dimensional frictional contact problems are uniformly formulated as a system of non-differentiable equations based on variational inequality theory. Through constructing a simple continuously differentiable approximation function to the non-differentiable one, the smoothing Newton method is directly implemented as an exact method. Both the global convergence and the local quadratic convergent rate of the method are guaranteed. None of the additional variables and linear approximations on Coulomb friction law is introduced and hence the formulation exactly describes the frictional contact phenomenon in both two- and three-dimensional cases. Numerical experiments suggest that the method is very efficient and promising.