Simulation of nonlinear benchmarks and sheet metal forming processes using linear and quadratic solid–shell elements combined with advanced anisotropic behavior models

LEM3, UMR CNRS 7239 - Arts et Métiers ParisTech, 4, rue Augustin Fresnel, 57078 Metz Cedex 03, France

^a Corresponding author: peng.wang@ensam.eu

Abstract

A family of prismatic and hexahedral solid‒shell (SHB) elements with their linear and quadratic versions is presented in this paper to model thin 3D structures. Based on reduced integration and special treatments to eliminate locking effects and to control spurious zero-energy modes, the SHB solid‒shell elements are capable of modeling most thin 3D structural problems with only a single element layer, while describing accurately the various through-thickness phenomena. In this paper, the SHB elements are combined with fully 3D behavior models, including orthotropic elastic behavior for composite materials and anisotropic plastic behavior for metallic materials, which allows describing the strain/stress state in the thickness direction, in contrast to traditional shell elements. All SHB elements are implemented into ABAQUS using both standard/quasi-static and explicit/dynamic solvers. Several benchmark tests have been conducted, in order to first assess the performance of the SHB elements in quasi-static and dynamic analyses. Then, deep drawing of a hemispherical cup is performed to demonstrate the capabilities of the SHB elements in handling various types of nonlinearities (large displacements and rotations, anisotropic plasticity, and contact). Compared to classical ABAQUS solid and shell elements, the results given by the SHB elements show good agreement with the reference solutions.