Abstract
It is shown that there are anisotropic elastic materials that are capable of a non-uniform three-dimensional deformation with only one displacement component. For wave propagation, the equation of motion can be cast in the form of the differential equation for acoustic waves. For elastostatics, the equation of equilibrium reduces to Laplace’s equation. The material can be monoclinic, orthotropic, tetragonal, hexagonal or cubic. There are also anisotropic elastic materials that uncouple all three displacement components. The governing equation for each of the uncoupled displacement can be cast in the form of the differential equation for acoustic waves in the case of dynamic or Laplace’s equation in the case of static. The material can be orthotropic, tetragonal, hexagonal or cubic.
Highlights
For a two‐dimensional deformation in which the displacement u depends on x1 and x2 only, it is shown in [1] that there are anisotropic elastic materials that can have only one displacement component other than the anti‐plane displacement u3
The purpose of this paper is to show that there are anisotropic materials that can have one displacement component that depends on x1, x2 and x3
The equation of motion for u3 can be cast in the form of the differential equation for acoustic waves
Summary
For a two‐dimensional deformation in which the displacement u depends on x1 and x2 only, it is shown in [1] that there are anisotropic elastic materials that can have only one displacement component other than the anti‐plane displacement u3. There are anisotropic elastic materials for which all three displacement components are uncoupled. The purpose of this paper is to show that there are anisotropic materials that can have one displacement component that depends on x1, x2 and x3. Without loss of generality we take u3 as the one component displacement. The equation of motion for u3 can be cast in the form of the differential equation for acoustic waves.
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