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.
%0 Journal Article
%1 bieber2023artificial
%A Bieber, Simon
%A Auricchio, Ferdinando
%A Reali, Alessandro
%A Bischoff, Manfred
%D 2023
%J International Journal for Numerical Methods in Engineering
%K ibb
%R 10.1002/nme.7224
%T Artificial instabilities of finite elements for nonlinear elasticity: Analysis and remedies
%X 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.
@article{bieber2023artificial,
abstract = {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.},
added-at = {2023-03-20T16:42:37.000+0000},
author = {Bieber, Simon and Auricchio, Ferdinando and Reali, Alessandro and Bischoff, Manfred},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2020536b4460f96f3d33e27b3c4c2b2ad/ibb-publication},
doi = {10.1002/nme.7224},
interhash = {af15b4949c53f383f8bb6da4f2b7e36f},
intrahash = {020536b4460f96f3d33e27b3c4c2b2ad},
journal = {International Journal for Numerical Methods in Engineering},
keywords = {ibb},
timestamp = {2023-03-20T16:43:32.000+0000},
title = {Artificial instabilities of finite elements for nonlinear elasticity: Analysis and remedies},
year = 2023
}
