= Cavitation criterion for power-law strain energy
{title2=$0<\alpha<3/2$}
For <strain energy density> $W=\mu[(\lambda_r^2+\lambda_\theta^2+\lambda_\phi^2)^\alpha-3^\alpha]/2$ with $\mu>0$ and $\alpha>0$, the critical loading for <elastic cavitation> is finite exactly in the displayed range. To prove this, put $S=\lambda^{-4}+2\lambda^2$ in the reduced <strain energy density>. The critical-pressure integrand is $2\mu\alpha S^{\alpha-1}(\lambda^{-2}+\lambda^{-5})$. It is finite at $\lambda=1$ and asymptotic to $\mu\alpha2^\alpha\lambda^{2\alpha-4}$ at infinity. The <comparison test> for the resulting <improper integral> gives $2\alpha-4<-1$.
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