Homogeneous elastic deformation ($\mathbf{x}=F(t)\mathbf{X}+\mathbf{c}(t)$)

An elastic deformation map whose deformation gradient is independent of position at each time. Its spatial material acceleration is $\mathbf{a}=\ddot{F}{F}^{-1}(\mathbf{x}-\mathbf{c})+\ddot{\mathbf{c}}$. Incompressibility requires $\det F=1$.