An extension of 3-D procedure to large strain analysis of shells

Abstract

A numerical stress integration procedure for general 3-D large strain problems in inelasticity, based on the total formulation and the governing parameter method (GPM), is extended to shell analysis. The multiplicative decomposition of the deformation gradient is adopted with the evaluation of the deformation gradient practically in the same way as in a general 3-D material deformation. The calculated trial elastic logarithmic strains are transformed to the local shell Cartesian coordinate system and the stress integration is performed according to the GPM developed for small strain conditions. The consistent tangent matrix is calculated as in case of small strain deformation and then transformed to the global coordinate system. A specific step in the proposed procedure is the updating of the left elastic Green–Lagrangian deformation tensor. Namely, after the stresses are computed, the principal elastic strains and the principal vectors corresponding to the stresses at the end of time step are determined. In this way the shell conditions are taken into account appropriately for the next step. Some details are given for the stress integration in case of thermoplastic and creep material model. Numerical examples include bulging of plate (plastic, thermoplastic, and creep models for metal) and necking of a thin sheet. Comparison of solutions with those available in the literature, and with solutions using other type of finite elements, demonstrates applicability, efficiency and accuracy of the proposed procedure.