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IMA Journal of Applied Mathematics Advance Access originally published online on December 17, 2004
IMA Journal of Applied Mathematics 2005 70(1):173-189; doi:10.1093/imamat/hxh049
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IMA Journal of Applied Mathematics Vol. 70 No. 1 © Institute of Mathematics and its Applications 2005; all rights reserved.

Swelling-induced microchannel formation in nonlinear elasticity*

Thomas J. Pence and Hungyu Tsai

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA

We study the effect of swelling on the axisymmetric deformation of a circular cylinder. A continuum description of swelling is established on the basis of a specific generalization of nonlinear elasticity for incompressible materials. This theory is used to analyse microchannel formation and channel growth. We show that certain kinds of material constitutive laws in conjunction with certain types of variable swelling fields are capable of inducing this formation and growth process without the aid of an externally applied traction. The solutions are presented as a bifurcation from the standard solution that involves no channel formation. The channel formation solution is found to be energetically preferable to the standard solution.

Keywords: hyperelasticity; microchannel; swelling volume transition.

* Dedicated to Ray W. Ogden on the occasion of his 60th birthday


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