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Phys Rev Lett. 2008 Aug 8;101(6):068101. Epub 2008 Aug 5.

Morphogenesis of growing soft tissues.

Author information

1
Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France.

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 behavior 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 Föppl-von Kármán type. As an illustration, the circumferential growth of a free hyperelastic disk is studied.

PMID:
18764507
DOI:
10.1103/PhysRevLett.101.068101
[Indexed for MEDLINE]

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