Plane-stress constrained multiplicative hyperelasto-plasticity with nonlinear kinematic hardening. Consistent theory based on elastic corrector rates and algorithmic implementation

Abstract

Small-strain plane-stress projected formulations are typically employed in 2D, plate and thin membrane problems because of their efficiency. However, at large strains, equivalent algorithms have been precluded by the difficulties of kinematics, specially using the multiplicative decomposition and nonlinear kinematic hardening. In this paper, we present a plane-stress constrained formulation for large strain multiplicative hyperelasto-plasticity based on the novel framework which uses elastic strain corrector rates. The proposed plane-stress projected model is consistent with the principle of maximum dissipation as in the 3D/plane-strain case, and it is valid for any stored energy function (e.g. for soft materials). Hyperelasticity-based nonlinear kinematic hardening at large strains, which preserves Masing's rules if desired, is also included in the formulation. The consistent tangent moduli tensor for the plane stress subspace is also derived to provide the asymptotic second order convergence of Newton algorithms during global equilibrium iterations. Some numerical examples are presented in order to evaluate both the congruency with the equivalent 3D formulation and the numerical performance of the proposed plane-stress projected algorithm.