Cyclic plastic behavior analysis based on the micromorphic mixed hardening plasticity model

In this paper, a small strain micromorphic elasto-plastic model with isotropic/kinematic hardening is presented for modeling the size effect and Bauschinger effect in material with microstructure. A nonlinear kinematic hardening model is embedded into the micromorphic framework by employing a backstress, a micro-backstress and a micro-couple-backstress in a physical way. The material intrinsic length scale is introduced in the constitutive law, leading to the presence of higher order stress. The present model is further implemented into a 2D plane strain finite element frame with a fully implicit stress integration scheme. The generalized consistent tangent modulus is derived to achieve the parabolic convergence of the global nodal force equilibrium equation. Two numerical examples, including a thin film and a plate with underlying structures subjected to cyclic loading, are analyzed to verify the theoretical developments and numerical formulations. Plastic behaviors in micromorphic continuum, such as size effect, Bauschinger effect, ratcheting effect and plastic shakedown phenomenon, are investigated.