Energy Minimising Properties of the Radial Cavitation Solution in Incompressible Nonlinear Elasticity
نویسندگان
چکیده
Consider an incompressible hyperelastic material, occupying the unit ball B ⊂ R in its reference state. Suppose that the displacement is specified on the boundary, that is, u(x) = λx for x ∈ ∂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 deformations 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. Mathematics Subject Classifications (2000): 74G65, 74B20, 49K20, 35J50.
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