Three field finite elements for the elastoplastic analysis of 2D continua

A three field variational framework is used to formulate a new class of mixed finite elements for the elastoplastic analysis of 2D problems. The proposed finite elements are based on the independent interpolation of the stress, displacement and plastic multiplier fields. In particular new and richer interpolating patterns are proposed for the plastic multiplier in order to go beyond the oversimplifying constant assumption used in Bilotta and Casciaro (2007) [1]. As will be shown, this last choice is useful to simplify the return mapping algorithm but adversely affect the accuracy of the finite element. More articulated interpolations transform the return mapping process into a convex nonlinear optimization problem with few variables and constraints, a problem that can be efficiently solved using optimization algorithms, without penalizing overall computational efficiency. Several kinds of interpolations are proposed and compared with respect to accuracy and efficiency by performing a series of numerical tests on plane stress/strain problems modeled on the basis of the von Mises and Drucker–Prager yield functions. The reliability and good performance of the proposed elements are evident.