Modeling of nonlinear viscoelastic contact problems with large deformations

Contact problems are one of the most important engineering problems. These problems become much more tedious when one of the contacting bodies behaves nonlinear viscoelasticity and large deformations. This paper presents an incremental-iterative finite element model for the analysis of two dimensional quasistatic frictionless contact problems. Nonlinear viscoelastic behavior and large deformations are considered. The Schapery’s single-integral creep model with stress-dependent properties is used for nonlinear viscoelasticity. The constitutive equations are transformed into an incremental form resulting in a recursive relationship. Thereby, the need to store the entire strain histories is eliminated, except that from the previous time increment. The updated Lagrangian formulation is used to model the material and geometrical nonlinearities. Also, the Lagrange multiplier method is adopted to enforce the contact constraints. The converged solution is obtained using the Newton–Raphson iterative technique. The developed model has been verified with the previously published works and found a good agreement with them. To demonstrate the efficient capability of the developed computational model, three contact problems with different nature are analyzed.