Analytical Solutions of Model Problems for Large-Deformation Micromorphic Approach to Gradient Plasticity

Abstract

The objective of this work is to present analytical solutions for several 2D model problems to demonstrate the unique plastic fields generated by the implementation of micromorphic approach for gradient plasticity. The approach is presented for finite deformations and several macroscopic and nonstandard microscopic boundary conditions are applied to a gliding plate to illustrate the capability to predict the size effects and inhomogeneous plastic fields promoted by the gradient terms. The constitutive behavior of the material undergoing plastic deformation is analyzed for softening, hardening and perfect plastic response and corresponding solutions are provided. The analytical solutions are also shown to match with the numerical results obtained by implementing a user element subroutine (UEL) to the commercial finite element software Abaqus/Standard.