Artificial instabilities of finite elements for nonlinear elasticity: Analysis and remedies

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