On the comparison of two solid-shell formulations based on in-plane reduced and full integration schemes in linear and non-linear applications

Abstract

In the present paper, a detailed description of the formulation of the new SSH3D solid-shell element is presented. This formulation is compared with the previously proposed RESS solid-shell element [1,2]. Both elements were recently implemented within the LAGAMINE in-house research finite element code. These solid-shell elements possess eight nodes with only displacement nodal degrees of freedom (DOF). In order to overcome various locking pathologies, the SSH3D formulation employs the well known Enhanced Assumed Strain (EAS) concept originally introduced by Simo and Rifai [3] and based on the Hu-Veubeke-Washizu variational principle combined with the Assumed Natural Strain (ANS) technique based on the work of Dvorkin and Bathe [4]. For the RESS solid-shell element, on the other hand, only the EAS technique is used with a Reduced Integration (RI) Scheme. A particular characteristic of these elements is their special integration schemes, with an arbitrary number of integration points along the thickness direction, dedicated to analyze problems involving non-linear through-thickness distribution (i.e. metal forming applications) without requiring many element layers. The formulation of the SSH3D element is also particular, with regard to the solid-shell elements proposed in the literature, in the sense that it is characterized by an in-plane full integration and a large variety in terms of (i) enhancing parameters, (ii) the ANS version choice and (iii) the number of integration points through the thickness direction. The choice for these three parameters should be adapted to each problem so as to obtain accurate results and to keep the calculation time low. Numerous numerical examples are performed to investigate the performance of these elements. These examples illustrate the reliability and the efficiency of the proposed formulations in various cases including linear and non-linear problems. SSH3D element is more robust thanks to the various options proposed and its full in-plane integration scheme, while RESS element in more efficient from a computational point of view.

Damage prediction in single point incremental forming using an extended Gurson model

“…Due to the important stress and strain gradients found in the sheet during SPIF and the use of a 3D material model, the Reduced Enhanced Solid Shell (RESS) element (Alves de Sousa et al, 2005Sousa et al, , 2006Ben Bettaieb et al, 2015) is used because of its good balance between accuracy and CPU time. This element is based on the solidshell element concept, which basically lies between a four-noded shell element and a eight-noded solid element.…”

Thermal Analysis of Concrete Blocks and Stack-Bond Prisms under Different Boundary Conditions

“…Fournode tetrahedral elements and full integration were used in all models. Full integration is commonly preferred for the development of tridimensional finite elements to address numerical instabilities and convergence problems by providing the exact integrals for the elements' stiffness matrix [39][40][41]. Some analyses were conducted to obtain viable and useful FEM models in terms of accuracy and computational time.…”

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

“…These values do not allow to draw definitive conclusions due to the large number of aspects involved in the simulations, but they show that the present solid-shell element is a competitive alternative to shell elements for metal forming problems. In a recent paper Bettaieb et al [40] tested and compared two solidshell formulation with in-plane reduced and full integration. The tests included sheet metal forming and springback analysis.…”