Constitutive relations of micromorphic thermoplasticity

The constitutive theory of micromorphic thermoplasticity has been formulated in Lagrangian form. The generalized Lagrangian strains, strain rates, temperature, temperature rate and temperature gradients are considered as the independent constitutive variables. Internal variables, including generalized Lagrangian plastic strains, are incorporated. The axioms of objectivity and equipresence are strictly followed. The entropy inequality has been fully utilized to guide the derivations of the constitutive relations. No restrictive assumption has been made to the magnitude of any independent constitutive variables. Finite element formulations for micromorphic thermoplasticity are developed based on the balance laws and the constitutive theory.