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On the small and finite deformation thermo-elasto-viscoplasticity theory for strain localization problems

This work is focused on the numerical implementation of thermo-elasto viscoplastic constitutive equations in small and finite strain contexts using the FEM. A length-scale parameter is introduced implicitly through viscosity in order to address strain localization and material instability in the (initial) boundary value problems. According to the second law of thermodynamics a dissipation inequality described in the rotated material coordinate system is developed by Voyiadjis et al. (2004), which was used along with the principle of maximum dissipation to formulate a viscoinelastic model. In order to check the effectiveness of the present framework a set of numerical examples under strict deformation conditions are presented. These numerical examples prove the excellent performance of the present framework in describing the strain localization problem and in obtaining mesh-independent results.