Anisotropic elastic materials capable of a three-dimensional deformation (static or dynamic) with only one displacement component and uncoupling of all three displacement components

► We show that, for some anisotropic elastic materials, the following are possible. ► A three dimensional deformation, static or dynamic, with one displacement component is possible. ► All three displacements can be uncoupled. ► The equation of motion can be cast in the form of the differential equation for acoustic waves. ► For elastostatics, the equation of equilibrium can be written in the form of Laplace's equation.