On finite strain micromorphic elastoplasticity

Abstract

In the micromorphic continuum theory of Eringen, it was proposed that microstructure of materials could be represented in a continuum framework using a micro-deformation tensor governing micro-element deformation, in addition to the deformation gradient governing macro-element deformation. The paper formulates finite strain micromorphic elastoplasticity based on micromorphic continuum mechanics in the sense of Eringen. Multiplicative decomposition into elastic and plastic parts of the deformation gradient and micro-deformation are assumed, and the Clausius–Duhem inequality is formulated in the intermediate configuration B ¯ to analyze what stresses, elastic deformation measures, and plastic deformation rates are used/defined in the constitutive equations. The resulting forms of plastic and internal state variable evolution equations can be viewed as phenomenological at their various scales (i.e., micro-continuum and macro-continuum). The phenomenology of inelastic mechanical material response at the various scales can be different, but for demonstration purposes, J 2 flow plasticity is assumed for each of three levels of plastic evolution equations identified, with different stress, internal state variables, and material parameters. All evolution equations and a semi-implicit time integration scheme are formulated in the intermediate configuration for future coupled Lagrangian finite element implementation. A simpler two-dimensional model for anti-plane shear kinematics is formulated to demonstrate more clearly how such model equations simplify for future finite element implementation.