Electro-mechanically guided growth and patterns

TL;DR

This paper extends growth theory to include electro-elastic effects, modeling how electrical and mechanical stimuli influence pattern formation and stability in biological tissues and hydrogels, with applications to controlled growth and morphogenesis.

Contribution

It introduces a coupled electro-mechanical growth model for electro-elastic solids, analyzing pattern formation under external fields and providing insights into controlling morphologies.

Findings

High voltage enhances residual stress non-uniformity and buckling.

Low voltage delays wrinkling and creates complex shapes.

Axial stretching can stabilize or destabilize growth patterns.

Abstract

Several experiments have demonstrated the existence of an electro-mechanical effect in many biological tissues and hydrogels, and its actual influence on growth, migration, and pattern formation. Here, to model these interactions and capture some growth phenomena found in Nature, we extend volume growth theory to account for an electro-elasticity coupling. Based on the multiplicative decomposition, we present a general analysis of isotropic growth and pattern formation of electro-elastic solids under external mechanical and electrical fields. As an example, we treat the case of a tubular structure to illustrate an electro-mechanically guided growth affected by axial strain and radial voltage. Our numerical results show that a high voltage can enhance the non-uniformity of the residual stress distribution and induce extensional buckling, while a low voltage can delay the onset of wrinkling shapes and can also generate more complex morphologies. Within a controllable range, axial tensile stretching shows the ability to stabilise the tube and help form more complex 3D patterns, while compressive stretching promotes instability. Both the applied voltage and external axial strain have a significant impact on guiding growth and pattern formation. Our modelling provides a basic tool for analysing the growth of electro-elastic materials, which can be useful for designing a pattern prescription strategy or growth self-assembly in Engineering.