= Constant-shear bulk-modulus inclusion
{title2=$\operatorname{tr}\varepsilon=\frac{3\kappa^0+4\mu}{3\kappa(x)+4\mu}\operatorname{tr}\varepsilon^0$}
When only the <bulk modulus> differs from an isotropic matrix, the <elastic polarization> is spherical: $\tau=(\kappa-\kappa^0)\operatorname{tr}(\varepsilon)I$. The double trace of the <isotropic elastic strain Green kernel> makes the trace equation local, giving the displayed formula. Individual <strain> components still depend on a nonlocal potential of the spherical polarization, so the complete <infinitesimal strain tensor> is not generally a local multiple of its reference value.
Back to article page
