Abstract
Consider an incompressible, hyperelastic material occupying the unit ball B⊂ℝn in its reference state. Suppose that the deformation u:B→ℝn is specified on the boundary by $$\mathbf{u}({\mathbf{x}})=\lambda{\mathbf{x}}\quad\mbox{for}\ {\mathbf{x}}\in \partial B,$$ where λ>1 is a given constant.In this paper, isoperimetric arguments are used to prove that the radial deformation, producing a spherical cavity, is the energy minimiser in a general class of isochoric mappings that are discontinuous at the centre of the ball and produce a (possibly non-symmetric) cavity in the deformed body. This result has implications for the study of cavitation in certain polymers.
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