Anisotropic elastic materials that uncouple all three displacement components, and existence of one-displacement Green's function

It was shown in an earlier paper that, under a two-dimensional deformation, there are anisotropic elastic materials for which the antiplane displaceme nt u(3) and the inplane displacements u(1), u(2) are uncoupled but the anti plane stresses sigma (31), sigma (32) and the inplane stresses sigma (11), sigma (12), sigma (22) remain coupled. The conditions for this to be possib le were derived, but they have a complicated expression. In this paper new and simpler conditions are obtained, and a general anisotropic elastic mate rial that satisfies the conditions is presented. For this material, and for certain monoclinic materials with the symmetry plane at x(3) = 0, we show that the unnormalized Stroh eigenvectors a(k) for k = 1,2, 3 are all real. The matrix A = [a(1), a(2), a(3)] is a unit matrix when the material has a symmetry plane at x(2) = 0. Thus any one of the u(1), u(2), u(3) can be the only nonzero displacement, and the solution is a one-displacement field. A pplication to the Green's function due to a line of concentrated force f an d a line dislocation with Burgers vector v in the infinite space, the half- space with a rigid boundary, and the infinite space with an elliptic rigid inclusion shows that one can indeed have a one-displacement field u(1), u(2 ) or u(3) One can also have a two-displacement field polarized on a plane o ther than the (x(1), x(2))-plane. The material that uncouples u(1), u(2), u (3) is not as restrictive as one might have thought. It can be triclinic, m onoclinic, orthotropic, tetragonal, transversely isotropic, or cubic. Howev er, it cannot be isotropic.