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Morphogenesis of Growing Soft Tissues

Julien Dervaux and Martine Ben Amar
Phys. Rev. Lett. 101, 068101 – Published 5 August 2008
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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.

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  • Received 12 December 2007

DOI:https://doi.org/10.1103/PhysRevLett.101.068101

©2008 American Physical Society

Authors & Affiliations

Julien Dervaux and Martine Ben Amar

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

See Also

Elizabethan Geometry

Don Monroe
Phys. Rev. Focus 22, 12 (2008)

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Issue

Vol. 101, Iss. 6 — 8 August 2008

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