A numerical solution for contact problem with finite deformation in nonlinear Schapery viscoelastic solids

The present paper presents an incremental finite element model for the solution of the two dimensional quasi-static frictionless nonlinear viscoelastic contact problems with large deformations. The nonlinear viscoelasticity is simulated using the Schapery’s single-integral viscoelastic model with stress-dependent properties. The updated Lagrangian formulation is used to model the material and geometrical nonlinearity of the problem. To eliminate the need to store the entire strain histories, the constitutive equations are transformed into an incremental recursive form. The contact constraints are enforced by using the Lagrange multiplier method where the normal contact forces are treated as independent variables. The resulting nonlinear equilibrium equations are solved by the Newton–Raphson method in an incremental-iterative procedure. The capability of the developed numerical incremental-iterative solution procedure is demonstrated by analysing two different contact problems with different nature.