Elastic strain Green operator (source code)

= Elastic strain Green operator
{title2=$\varepsilon=E-\Gamma\tau$}

For a homogeneous comparison <elastic stiffness tensor> $C^0$, the <elastic strain Green operator> maps an <elastic polarization> to minus the induced <infinitesimal strain tensor>. In a bounded domain the induced <displacement field> has zero boundary data; in an infinite medium it is the decaying perturbation. The defining <static elastic equilibrium> equation is $\nabla\cdot(C^0\operatorname{sym}\nabla u+\tau)=0$. The bounded-domain operator is self-adjoint, annihilates constant <elastic polarizations>, has zero mean output, and satisfies $\Gamma C^0\Gamma=\Gamma$.