  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
behaviour 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 Foppl-von Karman type. As an
illustration, the circumferential growth of a free hyperelastic disk is
studied.
