Analysis of nonlinear thermo-viscoelastic–viscoplastic contacts

This study introduces a numerical model for the analysis of contact problems of nonlinear thermo-viscoelastic–viscoplastic bodies, whose viscoelastic behavior belongs to a class of thermo-rheologically complex materials (TCM). The nonlinear viscoelastic behavior is expressed with an integral form of a creep function, whose properties change with stresses and temperatures, while the viscoplastic behavior follows the Perzyna model in the framework of associative viscoplasticity. To this end, a finite element model is derived based on uncoupled thermo-mechanical problems, which include both material and geometrical nonlinearities in the framework of the total Lagrangian description. An incremental-recursive form of the constitutive equations is derived. The Lagrange multiplier method is adopted to model the inequality contact constraints. The performance of the developed model is validated by analyzing three thermo-mechanical contact problems with different natures. Moreover, results show that the thermo-rheological behavior and the mechanical properties of the contacting bodies have distinct effects on the contact response of nonlinear thermo-viscoelastic–viscoplastic materials.