Swelling-Induced Cavitation of Elastic Spheres
Thomas J. Pence*
Hungyu Tsai
Department of Mechanical Engineering, Michigan State University, East
Lansing, MI 48824, USA
* To whom correspondence should be addressed.
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Abstract |
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Swelling, generally referring to volumetric change and typically due to mass
addition from some diffusive or transport mechanism, is central to a variety of physical
phenomena. Here we consider the role of swelling as it relates to the inflation of
hollow spheres and to cavity formation at the center of solid spheres. The swelling is
modeled in terms of a prescribed scalar field that gives the local free volume. The
finite deformation theory of incompressible hyperelasticity is generalized so as to
include the effect of this swelling field directly in the stored energy density. The
general framework is based on global energy minimization wherein the stored energy
density is minimized at the locally prescribed swollen state. On this basis it is found
that both inflation and cavitation can be caused solely by swelling. This result is
intuitive with respect to inflation where it follows from a simple uniform swelling
field. In contrast, to obtain swelling-induced cavitation we consider a non-uniform
swelling field and study how this field can cause a cavity to nucleate, grow, shrink and disappear.
Key Words:
Swelling, cavitation, elastic materials, bifurcation, energy minimization
