Boundary Value Problems in Thermo Viscoplasticity

In this work, we study two uncoupled quasistatic problems for thermo viscoplastic materials. In the model of the equation of generalised thermo viscoplasticity, both the elastic and the plastic rate of deformation depend on a parameter $theta $ which may be interpreted as the absolute temperature. The boundary conditions considered here as displacement-traction conditions as well as unilateral contact conditions. We establish a variational formulation for the model and we prove the existence of a unique weak solution to the problem, reducing the isotherm problem to an ordinary differential equation in a Hilbert space.