= Radial elastic compatibility
{title2=$\frac{d}{dr}\operatorname{tr}\tau=0$}
In a homogeneous isotropic solid without <body force>, a radial <displacement field> satisfies $(\lambda+2\mu)(u'+2u/r)'=0$. For nonzero $\lambda+2\mu$, its <volumetric strain> is constant. Since <Hooke's law> gives $\operatorname{tr}\tau=(3\lambda+2\mu)(u'+2u/r)$, its <stress tensor> has constant <trace>. After <plasticity in continuum mechanics> has occurred, this conclusion applies to purely elastic increments during <elastic unloading>, and need not apply to the total <residual stress>.
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