Explicit dynamic analysis of sheet metal forming processes using linear prismatic and hexahedral solid‒shell elements

Abstract

This paper proposes two linear solid‒shell finite elements for the three-dimensional modeling of thin structures in the context of explicit dynamic analysis. These solid‒shell formulations, which are extensions of their quasi-static counterparts, consist of a six-node prismatic element, denoted SHB6-EXP, and an eight-node hexahedral element, denoted SHB8PS-EXP. Both elements are formulated based on a purely three-dimensional approach, with displacements as the only degrees of freedom. To prevent various locking phenomena, a reduced-integration scheme is used along with the assumed-strain method. The resulting formulations are computationally efficient, since only a single layer of elements with an arbitrary number of through-thickness integration points is required to model 3D thin structures. Both SHB6-EXP and SHB8PS-EXP elements have been implemented into the explicit dynamic code ABAQUS, using the VUEL user-element subroutine. The performance of these elements is first assessed through a set of selective and representative dynamic elasto-plastic benchmark tests, including impact-type problems. Then, attention is directed to the simulation of deep drawing processes involving complex non-linear loading paths, anisotropic plasticity and double-sided contact. The obtained numerical results demonstrate the good performance of the SHB-EXP elements in the modeling of 3D thin structures, with only a single element layer and few integration points in the thickness direction.