Efficient and low memory strain-rate independent return mapping algorithm for general yield surfaces and stress states

Abstract Structural theories often consider constraints on the stresses, creating a partition into active and fixed components. Sophisticated nonlinear material models are usually described in 3D-continuum form. A reformulation of the material models is then necessary in order to enforce the constraint on the relevant stress components. In this paper, a new strain-rate independent return mapping algorithm is developed in order to deal with arbitrary partitions of the stresses considering general associative elasto-plastic material models. The developed algorithm works directly with the active stress and strain components, satisfying the constraints on the relevant stresses components at each integration point of each element and yielding optimal computational efficiency and memory costs. The tangent operator is obtain in closed-form, providing quadratic convergence to the local iterative process. A comparison of the proposed approach to a previously developed algorithm is made to highlight its properties.