A basic thin shell triangle with only translational DOFs for large strain plasticity

Published in Int. Journal for Numerical Methods in Engineering Vol. 51 (1), pp. 57-83, 2001
doi: 10.1002/nme.147

Abstract

A simple finite element triangle for thin shell analysis is presented. It has only nine translational degrees of freedom and is based on a total Lagrangian formulation. Large strain plasticity is considered using a logarithmic strain–stress pair. A plane stress isotropic behaviour with an additive decomposition of elastic and plastic strains is assumed. A hyperelastic law is considered for the elastic part while for the plastic part a von Mises yield function with non‐linear isotropic hardening is adopted. The element is an extension of a previous similar rotation‐free triangle element based upon an updated Lagrangian formulation with hypoelastic constitutive law. The element termed BST (for basic shell triangle) has been implemented in an explicit (hydro‐) code adequate to simulate sheet‐stamping processes and in an implicit static/dynamic code. Several examples are shown to assess the performance of the present formulation.