Encasement as a morphogenetic mechanism: The case of bending

TL;DR

This paper investigates how encasement of a growing elastic body within a different elastic coat can cause shape instabilities, exemplified by a cylinder transitioning to a bent shape due to growth-induced inhomogeneities.

Contribution

It introduces a novel mechanism where encasement influences morphogenesis through mechanical instabilities in elastic bodies.

Findings

Encasement can induce bending in elastic cylinders during growth.

Growth-induced inhomogeneities affect the shape stability of elastic bodies.

The study provides a simple model illustrating shape transition due to encasement.

Abstract

We study how the encasement of a growing elastic bulk within a possibly differently growing elastic coat may induce mechanical instabilities in the equilibrium shape of the combined body. The inhomogeneities induced in an incompressible bulk during growth are also discussed. These effects are illustrated through a simple example in which a growing elastic cylinder may undergo a shape transition towards a bent configuration.