= Isotropic elastic modulus relation
{title2=$E=3B(1-2\nu)=2G_s(1+\nu)$}
Under uniform compressive <pressure> $p$, isotropic <Hooke's law> gives each normal <strain> as $-p(1-2\nu)/E$. The volume strain is three times this, so the <bulk modulus> is $B=E/[3(1-2\nu)]$, where $E$ is <Young's modulus> and $\nu$ is <Poisson's ratio>. Positivity of $E$ and finite $B$ gives $\nu<1/2$. Positive <shear modulus> $G_s=E/[2(1+\nu)]$ adds the lower bound $\nu>-1$. Negative <Poisson's ratio> is allowed; the bulk relation alone does not supply the lower bound.
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