GENERALIZED DUNDURS CONSTANTS FOR ANISOTROPIC BIMATERIALS

It is well known that when a homogeneous isotropic elastic medium is under a plane strain deformation due to prescribed tractions at the boundary, the stress is independent of elastic constants. In the case of a bimaterial that consists of two dissimilar isotropic materials bonded together along their interface, the stress depends on two composite elastic constants known as Dundurs constants. For anisotropic elastic materials, plane strain deformations are possible for monoclinic materials with the symmetry plane at x(3) = 0. For these materials, the plane strain solution is in terms of two complex variables z(1) = x(1) + p(1)x(2) and z(2) = x(1) + p(2)x(2), where p(1) and p(2) are complex eigenvalues depending on elastic constants. If the boundary conditions are prescribed in terms of tractions, it is shown that the stress is independent of elastic constants except p(1) and p(2). In the case of a bimaterial that consists of two dissimilar monoclinic materials bonded together along their interface, the stress depends on two composite elastic constants alpha and beta (in addition to p(1) and p(2) in both materials). They reduce to Dundurs constants in the isotropic limit. The result remains valid when the interface is not perfectly bonded. We also show that every plane strain solution to a given anisotropic material or bimaterial is applicable to a wider class of anisotropic materials and bimaterials. In particular, every plane strain solution to an isotropic material or bimaterial is applicable to a class of anisotropic materials or bimaterials that may possess no material symmetry. Finally, we show how the results obtained here can be modified for plane stress deformations.