This study presents a numerical finite element model to analyze the response of frictional thermo-viscoelastic contact systems, which experience material and geometrical nonlinearities. Thermo-rheologically complex behavior of the contacting bodies is assumed. The nonlinear viscoelastic constitutive model is expressed by an integral form of a creep function, whose elastic and time-dependent properties vary with stresses and temperatures. Adopting the assumption that the hydrostatic and deviatoric responses are uncoupled, the constitutive equation is expressed in an incremental form, with the hereditary integral updated at the end of each time increment by recursive computation. The Lagrange multiplier approach is applied to incorporate the inequality contact constraints, while friction effect along the contact interface is modeled using a local nonlinear friction law. The material and geometrical nonlinearities are modeled in the framework of the total Lagrangian formulation. The developed nonlinear viscoelastic model is verified using the available benchmarks. The applicability of the developed model is demonstrated by solving two thermo-viscoelastic frictional contact problems with different contact natures. Results show a distinct effect of the thermo-rheological behavior on viscoelastic contact status.
Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems