A quasistatic analysis for thermoviscoelastic contact problems

Thermomechanical contact of viscoelastic bodies is a non-linear time- and temperature-dependent problem. Consideration of temperature as an independent variable destroys the convolution integral form of the viscoelasticity constitutive relations. This paper presents a computational procedure capable of predicting the quasistatic response of uncoupled, thermoviscoelastic, frictionless contact problems. The contact problem as a convex programming model is solved throughout an incremental procedure. The Wiechert model is adopted to simulate the linear behaviour of viscoelastic materials. The temperature dependency of viscoelasticity is accounted for by applying the time-temperature superposition principle, in which the William, Landel, and Ferry relationship is adopted to determine the shift factor. Thus, the constitutive equations are transformed to be a function of the reduced time as the only independent variable, maintaining the convolution integral form. Therefore, the complications that arise during the direct integration of these equations, especially with contact problems, are avoided. Two different illustrative examples are included to demonstrate the applicability of the proposed procedure.