A shell finite element for large strain elastoplasticity with anisotropies—: Part II: Constitutive equations and numerical applications

Abstract

An eight-node C 0 shell element for finite elastic–plastic 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 effective 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 finite strains and the implementation of the element procedure including stiffness 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.