An eight!node C 9 shell element for _nite elasticÐplastic deformations with anisotropies is developed[ It combines the advantages of an isoparametric description of geometry and deformation\ the application of tensors in Cartesian components\ and a real and e}ective plane stress description with three displacement and three director degrees!of!freedom at each node[ In Part I of the paper the shell theory including the kinematics\ the variational principle\ the application of Lagrange multipliers with their condensation on the element level and a comparative study of various assumed strain techniques were presented and the results of convergence tests given[
In this paper\ we consider the constitutive equations for large elastic and large plastic strains accounting for initial and induced anisotropies and the corresponding thermodynamics[ Then we investigate the return algorithm for _nite strains and the implementation of the element procedure including sti}ness matrix and residual force vector[ Finally\ we present the results of extended numerical applications and a comparison with FE solutions published in the literature\ as far as such are available[ Þ 0888 Elsevier Science Ltd[ All rights reserved[ Corresponding author[ Tel[] 99 38 123 69 95 914^fax] 99 38 123 69 83 043^e!mail] stumpfÝam[bi[ruhr!uni! bochum[de
1[04# are the total "usually called {material|#\ elastic and plastic spins[ The spin V of the rotation tensor Q is then obtained as V w-w e -w p [ "1[05# A detailed discussion of this kinematical concept and several numerical examples for elastic and plastic deformations with various magnitudes were given in Schieck and Stumpf "0884#[ Within this concept the elastic deformation rate d e is a linear function of the rate of the elastic stretch V e 9 and the plastic deformation rate d p is a linear function of the rate of the plastic stretch V p 9