Time-stepping method for frictional contact of anisotropic viscoelastic solids

Abstract

By the time-stepping method proposed in this paper, the basic equations for linear anisotropic viscoelasticity with small strains and quasi-static condition can be separated into two parts. One is an elastic system of the initial state, and the other is an elastic-like system related to the follow-up time step. Based upon this result, all the viscoelastic problems can be handled by two sets of elastic systems. Boundary element method and its associated constraint relations are then formulated for these two different elastic systems, which lead to a system of linear equations for each time step. To solve these systems of equations, in addition to the known boundary conditions for the non-contact portion, we need to pre-assume contact region and contact mode for each node pair as well as the possible slip direction, which should be checked later by contact criteria. Therefore, we further design an iteration procedure via time-stepping to solve the contact problems of anisotropic viscoelastic solids. The stability, accuracy, and generality of our proposed method are then demonstrated through three representative numerical examples. In these examples, the effects of time step size, material properties, friction coefficient, horizontal force as well as the presence of holes are all studied and discussed.