Thermoviscoelastic contact analysis with friction by an incremental thermal relaxation procedure Original Research Article

An incremental relaxation finite element procedure which has been successfully established by the authors for the analysis of viscoelastic problems with contact and friction is extended to deal with thermoviscoelastic contact problems. The temperature-time equivalence hypothesis and the extended law are used to describe the temperature dependent behavior of thermoviscoelastic material. By the use of the concept of reduced time, a modified generalized Maxwell model is then devised to model the thermoviscoelastic constitutive equations. Based on this model and the incremental mechanical/thermal relaxation procedure, the total stress at instant tN−1 is only dependent on the previous stress level, the incremental strain and the incremental pseudo-temperature applied at instant t(N). The relaxation process and the thermal loading which is described by a step function can be modeled exactly and the tiny time increments are not necessary for the simulation of time history even near initial instant t(0). The difference between the elastic and viscoelastic contact behaviors with friction in both isothermal and thermal cases is observed.