= Elastic cavitation
{title2=$P_{\mathrm{crit}}=-\int_1^\infty h'(\lambda)/(\lambda^3-1)\,d\lambda$}
The opening of an internal cavity under tensile loading in a solid. For <spherically symmetric deformation> of an <isotropic> <hyperelastic material> with <incompressibility>, and an empty cavity without <surface tension>, radial <static elastic equilibrium> gives the displayed critical signed external <pressure>, where $h(\lambda)=W(\lambda^{-2},\lambda,\lambda)$ and positive $P$ denotes compression. Indeed, the <principal stress formula for incompressible hyperelasticity> gives $dt_r/d\lambda=h'(\lambda)/(1-\lambda^3)$. Integration between the free inner surface and the outer surface, followed by the vanishing-initial-hole and vanishing-current-cavity limits, gives the formula. For a <neo-Hookean solid> with <shear modulus> $\mu>0$, the tensile magnitude is $-P_{\mathrm{crit}}=5\mu/2$.
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