ON LARGE DEFORMATIONS OF THIN ELASTOPLASTIC SHELLS - IMPLEMENTATION OF A FINITE ROTATION MODEL FOR QUADRILATERAL SHELL ELEMENT

A large-deformation model for thin shells composed of elasto-plastic m aterial is presented in this work, Formulation of the shell model, equ ivalent to the two-dimensional Cosserat continuum, is developed from t he three-dimensional continuum by employing standard assumptions on th e distribution of the displacement held in the shell body, A model for thin shells is obtained by an approximation of terms describing the s hell geometry. Finite rotations of the director field are described by a rotation vector formulation. An elasto-plastic constitutive model i s developed based on the von Mises yield criterion and isotropic harde ning. In this work, attention is restricted to problems where strains remain small allowing for all aspects of material identification and a ssociated computational treatment, developed for small-strain elastopl astic models, to be transferred easily to the present elasto-plastic t hin-shell model. A finite element formulation is based on the four-nod ed isoparametric element. A particular attention is devoted to the con sistent linearization of the shell kinematics and elasto-plastic mater ial model, in order to achieve quadratic rate of asymptotic convergenc e typical for the Newton-Raphson-based solution procedures. To illustr ate the main objective of the present approach-namely the simulation o f failures of thin elastoplastic shells typically associated with buck ling-type instabilities and/or bending-dominated shell problems result ing in formation of plastic hinges-several numerical examples are pres ented, Numerical results are compared with the available experimental results and representative numerical simulations.