Non-iterative stress integration method for anisotropic materials

Abstract

A non-iterative stress update method is proposed to accelerate finite element simulations while retaining the numerical robustness and accuracy in rate-independent plasticity. The stress tensor is directly integrated on the basis of the elastoplastic constitutive law without a recursive root-finding process such as the Newton-Raphson method. The iterative return mapping process for stress integration is avoided by first introducing an equation that guarantees the positive-definite nature of the effective plastic strain increment. Furthermore, the uncertainty of the yield condition fulfillment in a non-iterative stress update method is completely resolved by employing a stress projection technique. The numerical robustness, accuracy, and computational efficiency are comprehensively assessed through a wide range of strain increments in both implicit and explicit finite element analyses. Consequently, the computation time is remarkably reduced by more or less 50% with high fidelity in a variety of finite element simulation examples.