University of MaraghehSahand Communications in Mathematical Analysis2322-580718420211201Boundary Value Problems in Thermo Viscoplasticity193024617810.22130/scma.2021.127385.797ENIlyasBoukarouraDepartment of Mathematics, Faculty of Science, Applied Mathematics Laboratory, Ferhat Abbas- Setif 1 University, Setif, AlgeriaSeddikDjabiDepartment of Mathematics, Faculty of Science, Applied Mathematics Laboratory, Ferhat Abbas- Setif 1 University, Setif, Algeria0000-0002-0619-7399SamiaKhelladiDepartment of Mathematics, Faculty of Science, Fundamental and Numerical Mathematics Laboratory, Ferhat Abbas- Setif 1 University, Setif, AlgeriaJournal Article20200510In 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.https://scma.maragheh.ac.ir/article_246178_f12cdb82487b0b2d05c87715398f0e46.pdf