Spherically symmetric deformation
= Spherically symmetric deformation
{title2=$\mathbf x=f(R)\mathbf X/R$}
A radial <deformation map> preserving each particle's direction from a common centre. In an <orthonormal basis> of <spherical coordinates>, its <deformation gradient> has <principal stretches> $f'(R),f(R)/R,f(R)/R$. Thus <incompressibility> gives $f'(R)f(R)^2=R^2$, and integration gives $f(R)^3=R^3+C$.