Anisotropic elastic materials that uncouple antiplane and inplane displacements but not antiplane and inplane stresses, and vice versa

When an anisotropic linear elastic material is subjected to a two-dimension al deformation, the antiplane displacement us and the inplane displacements u(1), u(2) are in general coupled. For certain materials such as monoclini c materials with the symmetry plane at x(3) = 0, the antiplane displacement and the inplane displacements are uncoupled. For these materials, the anti plane stresses sigma (31), sigma (32) and the inplane stresses sigma (11), sigma (12), sigma (22) are also uncoupled. We show that there are materials more general than monoclinic materials with the symmetry plane at x(3) = 0 for which, when the antiplane and inplane displacements are uncoupled, the antiplane and inplane stresses remain coupled. Conversely, when the antipl ane and inplane stresses are uncoupled, the antiplane and inplane displacem ents remain coupled. Examples are presented for which the solutions are ide ntical to the solutions for an isotropic elastic material with additional d isplacements or stresses that do not exist in isotropic elasticity solution s.