Elastoplastic Nonlocal Micromorphic Formulations With Damage Gradient

It is well known that the use of inelastic constitutive equations accounting for induced softening leads to pathological space (mesh) and time discretization dependency of the numerical solution of the Initial and Boundary value Problem (IBVP). To solve this drawback a thermodynamically-consistent formulation incorporating first gradient of micromorphic damage in the framework of micromorphic continuum is proposed. In this formulation the damage field is strongly coupled with mixed isotropic and kinematic nonlinear hardening together with micromorphic damage variables. A new finite element with one additional degree of freedom for the micromorphic damage field is developed and implemented into ABAQUS/EXPLICIT using the user’s subroutines VUEL and VUMAT. For the validation purpose, 3D uniaxial tension example of metallic sheet is performed using the proposed micromorphic fully coupled elastoplastic constitutive equations.