Morphoelasticity: A theory of elastic growth

Alain Goriely, Derek Moulton

Research output: Chapter in Book/Report/Conference proceedingChapter

6 Scopus citations

Abstract

This chapter is concerned with the modelling of growth processes in the framework of continuum mechanics and nonlinear elasticity. It begins by considering growth and deformation in a one-dimensional setting, illustrating the key relationship between growth, the elastic response of the material, and the generation of residual stresses. The general three-dimensional theory of morphoelasticity is then developed from conservation of mass and momentum balance equations. In the formulation, the multiplicative decomposition of the deformation tensor, the standard approach in morphoelasticity, is derived in a new way. A discussion of continuous growth is also included. The chapter concludes by working through a sample problem of a growing cylindrical tube. A stability analysis is formulated, and the effect of growth on mucosal folding, a commonly seen instability in biological tubes, is demonstrated.
Original languageEnglish (US)
Title of host publicationNew Trends in the Physics and Mechanics of Biological Systems
PublisherOxford University Press (OUP)
Pages153-176
Number of pages24
ISBN (Print)9780199605835
DOIs
StatePublished - Oct 11 2011
Externally publishedYes

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