A general criterion for solid instability and its application to creases

TL;DR

This paper introduces a universal force-perturbation criterion for predicting solid instability, including creases, without prior knowledge of the specific instability configuration, and extends it to anisotropic materials.

Contribution

It proposes a new element stiffness-based criterion that improves prediction accuracy and unifies various instability phenomena, including creases, necking, and shear bands.

Findings

The criterion predicts crease instability without prior configuration knowledge.

It can determine instability in strongly anisotropic materials.

The criterion encompasses known phenomena like necking and shear bands.

Abstract

A general force-perturbation-based criterion for solid instability is proposed, which can predict instability including crease without priori knowledge of instability configuration. The crease instability is analyzed in detail, we found that the occurrence of solid instability does not always correspond to the non-positive definiteness of global stiffness matrix. An element stiffness-based criterion based on material stiffness is proposed as a stronger criterion in order to fast determine the occurrence of instability. This criterion has been shown to degenerate into the criterion for judging instability of certain known phenomena, such as necking and shear band phenomena. Besides, instability in strongly anisotropic materials is also predicted by the element stiffness-based criterion.