A dual decomposition of the closest point projection in incremental elasto‐plasticity using a mixed shell finite element

Mixed assumed stress finite elements (FEs) have shown good advantages over traditional displacement-based formulations in various contexts. However, their use in incremental elasto-plasticity is limited by the need for return mapping schemes which preserve the assumed stress interpolation. For elastic-perfectly plastic materials and small deformation problems, the integration of the constitutive equation furnishes a closest point projection (CPP) involving all the element stress parameters. In this work, a dual decomposition strategy is adopted to split this problem into a series of CPPs at the integration points level and in a nonlinear system of equations over the element, in order to simplify its solution. The strategy is tested with a four nodes mixed shell FE, named MISS-4, characterized by an equilibrated stress interpolation which improves the accuracy. Two decomposition strategies are tested to express the plastic admissibility either in terms of stress resultants or point-wise Cauchy stresses. The recovered elasto-plastic solution preserves all the advantages of MISS-4, namely it is accurate for coarse meshes in recovering the equilibrium path and evaluating the limit load showing a quadratic rate of convergence, as demonstrated by the numerical results.