On the Small and Finite Deformation Thermo-elasto-viscoplasticity Theory for Strain Localization Problems: Algorithmic and Computational Aspects

ABSTRACT. This work is focused on the numerical implementation of thermo-viscoplastic constitutive equations in small and finite strain contexts using FEM. A length scale parameter is introduced implicitly through viscosity in order to address strain localization in the (initial) boundary value problems. The mathematical structure of the infinitesimal viscoplasticity theory is concise and similar to that of the finite strain theory. These characteristics make the numerical implementation of this theory easy. The proposed numerical algorithms are implemented in such a way that the extension from the standard small strain FEM code to the finite strain analysis is straightforward. An extension to the viscoplastic range of the classical radial return algorithm for plasticity is developed. Numerical examples prove the excellent performance of the present framework in describing the strain localization problem.