Advanced solid elements for sheet metal forming simulation

Abstract

The solid-shells are an attractive kind of element for the simulation of forming processes, due to the fact that any kind of generic 3D constitutive law can be employed without any additional hypothesis. The present work consists in the improvement of a triangular prism solid-shell originally developed by Flores [2, 3]. The solid-shell can be used in the analysis of thin/thick shell, undergoing large deformations. The element is formulated in total Lagrangian formulation, and employs the neighbour (adjacent) elements to perform a local patch to enrich the displacement field. In the original formulation a modified right Cauchy-Green deformation tensor (C¯) is obtained; in the present work a modified deformation gradient (F¯) is obtained, which allows to generalise the methodology and allows to employ the Pull-Back and Push-Forwards operations. The element is based in three modifications: (a) a classical assumed strain approach for transverse shear strains (b) an assumed strain approach for the in-plane components using information from neighbour elements and (c) an averaging of the volumetric strain over the element. The objective is to use this type of elements for the simulation of shells avoiding transverse shear locking, improving the membrane behaviour of the in-plane triangle and to handle quasi-incompressible materials or materials with isochoric plastic flow.