Every week, we select a recently published Open Access article to feature. This week’s article is from the International Journal for Numerical Methods in Engineering and presents a discussion on the stability properties of Enhanced Assumed Strain finite element formulations.

The article’s abstract is given below, with the full article available to read here.

Bieber, S, Auricchio, F, Reali, A, Bischoff, M. Artificial instabilities of finite elements for nonlinear elasticity: Analysis and remedies. Int J Numer Methods Eng. 2023; 1– 38. doi: 10.1002/nme.7224

Within the framework of plane strain nonlinear elasticity, we present a discussion on the stability properties of various Enhanced Assumed Strain (EAS) finite element formulations with respect to physical and artificial (hourglassing) instabilities. By means of a linearized buckling analysis we analyze the influence of element formulations on the geometric stiffness and provide new mechanical insights into the hourglassing phenomenon. Based on these findings, a simple strategy to avoid hourglassing for compression problems is proposed. It is based on a modification of the discrete Green-Lagrange strain, simple to implement and generally applicable. The stabilization concept is tested for various popular element formulations (namely EAS elements and the assumed stress element by Pian and Sumihara). A further aspect of the present contribution is a discussion on proper benchmarking of finite elements in the context of hourglassing. We propose a simple bifurcation problem for which analytical solutions are readily available in the literature. It is tailored for an in-depth stability analysis of finite elements and allows a reliable assessment of its stability properties.