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Spontaneous Cavitation in Growing Elastic Membranes

¹ Program in Applied Mathematics, University of Arizona, AZ 85721, USA
² Program in Applied Mathematics and Department of Mathematics, University of Arizona, AZ 85721, USA

^* To whom correspondence should be addressed.

	Abstract

One of the possible effects of volumetric growth in elastic materials is the creation of residual stresses. These stresses are known to change many of the classical properties of the material and have been studied extensively in the context of volumetric growth in biomechanics. Here we consider the problem of elastic cavitation in a growing compressible elastic membrane. Growth is taken to be homogeneous but anisotropic, and the membrane is assumed to remain axisymmetric during growth and deformation. We prove that neo-Hookean membranes cannot cavitate, but for Varga elastic materials we find conditions under which the material exhibits spontaneous cavitation in the absence of external loads, in marked distinction from the cavitation problem without growth.

Key Words: elasticity, growth, cavitation

First published on September 17, 2008
Mathematics and Mechanics of Solids 2008, doi:10.1177/1081286508092010


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