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New Trends in the Physics and Mechanics of Biological SystemsLecture Notes of the Les Houches Summer School: Volume 92, July 2009$
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Martine Ben Amar, Alain Goriely, Martin Michael Müller, and Leticia Cugliandolo

Print publication date: 2011

Print ISBN-13: 9780199605835

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199605835.001.0001

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Morphoelasticity: A theory of elastic growth

Morphoelasticity: A theory of elastic growth

Chapter:
(p.153) 6 Morphoelasticity: A theory of elastic growth
Source:
New Trends in the Physics and Mechanics of Biological Systems
Author(s):

Alain Goriely

Derek Moulton

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199605835.003.0006

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.

Keywords:   differential growth, elasticity, residual stress, multiplicative decomposition, incremental growth, stability, mucosal folding

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