2007/12/12 by Julien Dervaux, Martine Ben Amar · 5 citations
Biochemistry, Genetics and Molecular Biology · Engineering · #Advanced Materials and Mechanics #Cellular Mechanics and Interactions #Elasticity and Material Modeling #q-bio.TO
paper · pdf · doi:10.1103/physrevlett.101.068101
4 pages, 3 figures
arxiv created 2007/12/12 · openalex publication_date 2008/08/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.