Morphogenesis of growing soft tissues

TL;DR

This paper develops a finite elasticity-based model for the growth of soft tissues, deriving equations for thin elastic objects under growth and illustrating with a hyperelastic disk example.

Contribution

It introduces a multiplicative decomposition of deformation gradient for modeling tissue growth within finite elasticity theory.

Findings

Derived Foppl-von Karman type equations for growing tissues

Analyzed circumferential growth in a hyperelastic disk

Provided a framework for modeling tissue morphogenesis

Abstract

Recently, much attention has been given to a noteworthy property of some soft tissues: their ability to grow. Many attempts have been made to model this behaviour in biology, chemistry and physics. Using the theory of finite elasticity, Rodriguez has postulated a multiplicative decomposition of the geometric deformation gradient into a growth-induced part and an elastic one needed to ensure compatibility of the body. In order to fully explore the consequences of this hypothesis, the equations describing thin elastic objects under finite growth are derived. Under appropriate scaling assumptions for the growth rates, the proposed model is of the Foppl-von Karman type. As an illustration, the circumferential growth of a free hyperelastic disk is studied.