Micromorphic theory and its finite element formulation

In this work, the kinematics and basic laws of microcontinuum field theories, including micromorphic theory and micropolar theory, are introduced. Then, constitutive equations for micromorphic thermo-visco-elastic solids, heat conducting fluids, and thermal plasticity are rigorously derived. The concept of material force, which may also be named as Eshelby mechanics, is briefly introduced. The balance law of pseudo-momentum, including the detailed expression of the material forces, for the mathematical theory of micromorphic plasticity is rigorously derived. Finally, a set of finite element equations for the coupling of finite displacement, micromotion, and temperature fields is rigorously formulated.