A dual decomposition of the closest point projection in incremental elasto‐plasticity using a mixed shell finite element. (13th September 2022) - Liguori, Francesco S.; Madeo, Antonio; Garcea, Giovanni
Abstract: 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.