Renormalised solutions in thermo-visco-plasticity for a Norton-Hoff type model. Part I: the truncated case

We prove existence of global in time strong solutions to the truncated thermo- visco-plasticity with an inelastic constitutive function of Norton-Hoff type. This result is a starting point to obtain renoramlised solutions for the considered model without truncations. The method of our proof is based on Yosida approximation of the maximal monotone term and a passage to the limit.