Journal of Engineering Mathematics 46: 69–86, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands. Numerical simulation of an elastoplastic plate via mixed finite elements LUCIA DELLA CROCE 1 , PAOLO VENINI 2 and ROBERTO NASCIMBENE 2 1 Department of Mathematics, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy (E-mail: luciadc@dimat.unipv.it) 2 Department of Structural Mechanics, University of Pavia, Via Ferrata 1, 27100, 11 Pavia, Italy (E-mails: paolo.venin@unipv.it, roberto.nascimbene@unipv.it) Received 8 April 2002; accepted in revised form 7 September 2002 Abstract. 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 elasto-plastic behavior, using a J 2 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. Key words: elasto-plastic analysis, mixed finite element, Reissner-Mindlin plate 1. Introduction A tremendous effort has been recently put in the development of numerical methods for the analysis of nonlinear solids and materials. New concepts such as multiscale analysis [1], fractals [2], localization [3, 4], size effects [5, 6] and multifield theories [7, 8], just to mention a few, have been investigated giving rise to entirely new branches of the mechanics of solids. Textbooks that are nowadays classical, such as [9–13], deal with several aspects of material nonlinearity, focussing in particular on continuum plasticity even at large strains. Conversely, considerably less attention has been paid to nonlinear material behavior at the structural level. Although a wide range of works concerning linear elastic plates are available in the scientific literature [14–17], on the contrary not many contributions are available in the recent literature concerning the analysis of elastoplastic Reissner-Mindlin plates at the thin limit that are herein dealt with [18, 19]. Among them, a pioneering contribution seems to be [20] that has developed a shell element whose behavior in the inelastic limit plate case resembles closely the well-known four-noded element by Bathe and Dvorkin [21]. Further contributions come from [22, 23] that have put forth a step-marching methodology for thick elastoplastic plates whereby stress updates and consistency are imposed simultaneously via a linearized coupled system of equations. Attention is paid in [23] to the definition of a consis- tent tangent matrix that is crucial in order to preserve the expected convergence order [10]. In [24] a four-node element with assumed shear strains and incompatible bending modes is