Return mapping algorithm in principal space for general isotropic elastoplasticity involving multi-surface plasticity and combined isotropic-kinematic hardening within finite deformation framework

The compatibility with complicated elastoplasticity and efficiency of the constitutive integration algorithm both significantly influence the performance of finite element analysis for engineering practical problems. In this work, a numerical integration algorithm in principal space is proposed for general isotropic elastoplastic constitutive models that involve multi-surface plasticity with corners in the yield surface and combined isotropic-kinematic hardening law as well as nonlinear elasticity within the framework of finite deformation. For the multi-surface plasticity, a strategy, which uses the mid-direction of two plastic flow directions at a corner as the border of critical regions, is proposed to predict the yield functions activated in the return mapping iterations, making the prediction procedure simpler. By making use of the relative stress, the combined isotropic-kinematic hardening law is incorporated into the numerical integration algorithm in principal space. The consistent tangent operator is also derived. Besides, the fully implicit return mapping algorithm based on representation theorem is employed. The expressions of the first and second derivatives of yield/potential function, which are frequently evaluated in the algorithm, maintain a simple form and reduce the computational cost. Solution of finite element practical problems demonstrates that compatibility and efficiency of the constitutive integration algorithm are improved while accuracy is retained.