Introduction of pseudo-stress for local residual and algebraic derivation of consistent tangent in elastoplasticity

In this article, an introduction of pseudo-stress for local residual and an algebraic derivation of consistent tangent are presented. The authors define a coupled problem of the equilibrium equation for the overall structure and the constrained equations for stress state at every material point, and the pseudo-stress and the derived consistent tangent can be implemented easily to finite element analysis. In the proposed block Newton method, the internal variables are also updated algebraically without any local iterative calculations. In addition, the authors demonstrate the performance of the proposed approach for both J 2 plasticity and J 2 plasticity under plane stress state.