Nonlinear Micromorphic Continuum Mechanics and Finite Strain Elastoplasticity

Abstract

Abstract : The report presents the detailed formulation of nonlinear micromorphic continuum kinematics and balance equations (balance of mass; microinertia; linear, angular, and first moment of momentum; energy; and the Clausius-Duhem inequality). The theory is extended to elastoplasticity assuming a multiplicative decomposition of the deformation gradient and microdeformation tensor. A general three-level (macro, micro, and microgradient) micromorphic finite strain elastoplasticity theory results, with simpler forms presented for linear isotropic elasticity, J2 flow associative plasticity, and nonassociative Drucker-Prager pressure-sensitive plasticity. Assuming small elastic deformations for the class of materials of interest, bound particulate materials (ceramics, metal matrix composites, energetic materials, infrastructure materials, and geologic materials), the constitutive equations formulated in the intermediate configuration are mapped to the current configuration, and a new elastic Truesdell objective higher order stress rate is defined. A semi-implicit time integration scheme is presented for the Drucker-Prager model mapped to the current configuration. A strategy to couple the micromorphic continuum finite element implementation to a direct numerical simulation of the grain-scale response of a bound particulate material is outlined that will lead to a concurrent multiscale computational method for simulating dynamic failure in bound particulate materials.