= Homogeneous deformation
{title2=$y(X)=FX+b$}
A homogeneous <deformation> has the same <deformation gradient> at every material point. On a connected reference domain it is an affine map $y(X)=FX+b$ with constant matrix $F$ and translation $b$. Orientation preservation requires $\det F>0$. Its stretches and local volume ratio are spatially constant. A homogeneous deformation describes the kinematics; a <homogeneous hyperelastic material> instead describes spatial independence of a constitutive law.
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