Homogeneous deformation ($y(X)=FX+b$)

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.