Numerical simulation of an elastoplastic plate via mixed finite elements

A mixed interpolated formulation for the analysis of elastoplastic Reissner-Mindlin plates is presented. Special attention is given to the limit case of very small thickness that is well known to lead to inaccurate numerical solutions, unless ad-hoc remedies are taken into account to avoid locking (such as reduced or selective integration schemes). The finite element presented herein combines the higher-order approach with the mixed-interpolated formulation of linear elastic problems. This mixed element has been herein extended to the elastoplastic behavior, using a J2 approach with yield function depending on moments and shear stresses. A backward-Euler procedure is then used to map the elastic trial stresses back to the yield surface with the aid of a Newton-Raphson approach to solve the nonlinear system and without the calculation of the consistent tangent matrix. The element is shown to be very effective for the class of benchmark problems analyzed and does not present any locking or instability tendencies, as illustrated by various representative examples.