Material force in micromorphic plasticity

Micromorphic theory envisions a material body as a continuous collection of deformable particles with finite size and inner structure. It is considered as the most successful top-down formulation of a two-level continuum model, in which the deformation is expressed as a sum of macroscopic continuous deformation and internal microscopic deformation of the inner structure. In this work, we revisit the original micromorphic theory and further construct a mathematical theory of micromorphic plasticity with generalized strain-based return mapping algorithm. The concept of material forces, which may also be referred as Eshelbian mechanics, was first derived for micromorphic thermo-visco-elastic solid, and, now in this work, it is extended to the micromorphic plasticity. The balance law of pseudo-momentum is formulated. The detailed expressions of Eshelby stress tensor, pseudo-momentum, and material forces are derived. Following this formulation, the failure mechanisms of micromorphic thermo-visco-elastoplastic materials can be further investigated.