A tutorial on the stability and bifurcation analysis of the electromechanical behaviour of soft materials

TL;DR

This tutorial introduces stability and bifurcation analysis for soft electromechanical materials, emphasizing understanding complex phenomena like surface instabilities and large deformations for applications and biological processes.

Contribution

It provides a beginner-friendly, comprehensive guide to stability and bifurcation analysis in soft electromechanical materials, integrating electrostatics and large deformation modeling.

Findings

Clarifies the role of instabilities in applications and biology

Provides simple examples for understanding complex analysis

Enables readers to engage with advanced research literature

Abstract

Soft materials, such as liquids, polymers, foams, gels, colloids, granular materials, and most soft biological materials, play an important role in our daily lives. From a mechanical viewpoint, soft materials can easily achieve large deformations due to their low elastic moduli; meanwhile, surface instabilities, including wrinkles, creases, folds, and ridges, among others, are often observed. In particular, soft dielectrics subject to electrical stimuli can achieve significantly large deformations that are often accompanied by instabilities. While instabilities are often thought to cause failures in the engineering context and carry a negative connotation, they can also be harnessed for various applications such as surface patterning, giant actuation strain, and energy harvesting. In the biological world, instability and bifurcation phenomena often precede important events such as endocytosis, cell fusion, among others. Stability and bifurcation analysis (especially for soft materials) is challenging and often presents a formidable barrier to entry in this important field. A multidisciplinary audience may lack the background in one or more areas that are needed to carry out the requisite modeling or even understand papers in the literature. Furthermore, combining electrostatics together with large deformations brings its own challenges. In this article, we provide a tutorial on the basics of stability and bifurcation analysis in the context of soft electromechanical materials. The aim of the article is to use simple examples and ``gently" lead a reader, unfamiliar with either stability analysis or electrostatics of deformable media, to develop the ability to understand the pertinent literature that already exists and position them to embark on state-of-the-art research on this topic.