Anisotropic Elastic Materials That Uncouple Antiplane and Inplane Displacements but not Antiplane and Inplane Stresses, and Vice Versa

Abstract

When an anisotropic linear elastic material is subjected to a two-dimensional deformation, the antiplane displacement U3 and the inplane displacements ul, U2 are in general coupled. For certain materials such as monoclinic materials with the symmetry plane at X3 = 0, the antiplane displacement and the inplane displacements are uncoupled. For these materials, the antiplane stresses 031, 032 and the inplane stresses all, 012, 022 are also uncoupled. We show that there are materials more general than monoclinic materials with the symmetry plane at X3 = 0 for which, when the antiplane and inplane displacements are uncoupled, the antiplane and inplane stresses remain coupled. Conversely, when the antiplane and inplane stresses are uncoupled, the antiplane and inplane displacements remain coupled. Examples are presented for which the solutions are identical to the solutions for an isotropic elastic material with additional displacements or stresses that do not exist in isotropic elasticity solutions.