On large deformations of thin elasto-plastic shells: Implementation of a finite rotation model for quadrilateral shell element

A large-deformation model for thin shells composed of elasto-plastic material is presented in this work, Formulation of the shell model, equivalent to the two-dimensional Cosserat continuum, is developed from the three-dimensional continuum by employing standard assumptions on the distribution of the displacement held in the shell body, A model for thin shells is obtained by an approximation of terms describing the shell geometry. Finite rotations of the director field are described by a rotation vector formulation. An elasto-plastic constitutive model is developed based on the von Mises yield criterion and isotropic hardening. In this work, attention is restricted to problems where strains remain small allowing for all aspects of material identification and associated computational treatment, developed for small-strain elastoplastic models, to be transferred easily to the present elasto-plastic thin-shell model. A finite element formulation is based on the four-noded isoparametric element. A particular attention is devoted to the consistent linearization of the shell kinematics and elasto-plastic material model, in order to achieve quadratic rate of asymptotic convergence typical for the Newton-Raphson-based solution procedures. To illustrate the main objective of the present approach-namely the simulation of failures of thin elastoplastic shells typically associated with buckling-type instabilities and/or bending-dominated shell problems resulting in formation of plastic hinges-several numerical examples are presented, Numerical results are compared with the available experimental results and representative numerical simulations.

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