“…For example, electrical conductivity, yield strength and other properties during the heating may vary by several times. Furthermore, inelastic flow at high temperature is accompanied by changes in microstructure, such that hardening, softening, recovery and damage processes should be taken into account within a constitutive model with internal state variables [23,[30][31][32] or by application of enhanced continuum theories with higher order gradients and phase field variables [7,28]. Therefore there is a practical need for the mathematical formulation of problems of non-isothermal elasto-plastic deformation of bodies under the influence of external electromagnetic fields, taking into account the mutual influence of fields of different nature in a wide ranges of temperature, and taking into account the nonlinearity of electromagnetic, thermal and mechanical properties of materials.…”