Numerical solution of the quasistatic contact problem with the Tresca friction in elastic-viscoplastic materials by the element-free Galerkin method

Abstract

The element-free Galerkin method is presented for a quasistatic contact problem with the Tresca friction in elastic-viscoplastic materials. The elastic-viscoplastic constitutive model is considered in the problem and the clamped boundary conditions are imposed by the penalty method. The error estimates of the element-free Galerkin method are also obtained, which indicate that the convergence order depends on the nodal spacing, the time step, the largest degree of basis functions in the moving least-squares approximation and the penalty factor. Numerical examples demonstrate that the element-free Galerkin method provides an efficient numerical solution of the quasistatic contact problem with the Tresca friction in elastic-viscoplastic materials.