Mixed finite elements for the elastoplastic analysis of 2D continua

The paper aims to formulate assumed stress finite elements for the analysis of elastoplastic structures. The interpolations of the displacement and stress fields, typical of the elastic version of the mixed elements, is enriched with the FEM representation of the plastic strain field. The formulation of the elastoplastic problem of the element is then established, consistently, with respect to its variational basis based on the weak enforcement of the compatibility condition. Its correlation with the Haar–Karman principle leads to a minimization problem of a quadratic functional subjected to a linearized form of the plastic admissibility constraints.