Boundary element method for contact between multiple rigid punches and anisotropic viscoelastic foundation

In this paper both of the elastic-viscoelastic correspondence principle and time stepping method, which can convert viscoelasticity to elasticity, are employed to the boundary element method (BEM) to solve the contact problems between multiple rigid punches and anisotropic viscoelastic foundation. The one based upon the correspondence principle has the restriction on time-invariant boundaries, and hence can only be applied to the cases of complete indentation whose contact region as well as contact status are time-independent. The other based upon the time stepping method is processed step-by-step in time domain, and its boundary conditions may vary in each time step, and hence can be applied to both complete and incomplete indentations. Both methods are valid for the frictionless or frictional contact surface, the punches can be in equilibrium status or in quasi-static sliding condition, and the number of punches and the punch profiles are arbitrary. Benefited by the elastic system used for BEM, both methods hold the feature that no meshes are required on the rigid punches and holes/cracks. Through the iteration procedure and numerical examples presented in this study, we see that the one based upon time-stepping method is much more general and efficient than the other one.