A simple reduced integration hexahedral solid-shell element for large strains

Abstract

In this paper a hexahedral solid-shell element with in-plane reduced integration is developed. The element is intended to the analysis of thin/thick elastic-plastic shells with moderate to large strains. Developed within the framework of a total Lagrangian formulation, the element uses as strain measure the logarithm of the right stretch tensor (U) obtained from a modified right Cauchy-Green tensor (C). The modifications, in order to remove transverse shear, Poisson and volumetric locking, are three: (a) a classical assumed mixed shear strain approximation for C13 and C23 (b) an assumed strain approximation for the in-plane components Cαβ and (c) an enhanced assumed strain for the through the thickness normal component C33 (one additional degree of freedom). The first five components of C are interpolated to the integration points from values at the center of the top and bottom faces. An arbitrary number of integration points is used in the transverse direction and a stabilization scheme is used to avoid spurious modes due to the in-plane sub integration. Several examples are presented that show the locking-free behavior and the very good performance of the presented element for the analysis of shells with geometric and material nonlinearities, including quasi-incompressible elastic and elastic-plastic with incompressible plastic flow models.