Antiplane Deformations for Anisotropic Multilayered Media by Using the Coordinate Transform Method

Green’s functions for anisotropic elastic multilayered media subjected to antiplane shear deformation are presented in this study. The antiplane shear deformation due to a concentrated shear force and screw dislocation in an arbitrary layer was investigated in detail. A linear coordinate transformation is introduced in this study to simplify the problem. The linear coordinate transformation reduces the anisotropic multilayered problem to an equivalent isotropic problem without complicating the geometry of the problem. Explicit analytical solutions were derived using the Fourier transform and the series expansion technique. The complete solutions for the multilayered problem consist only of the simplest solutions obtained from an infinite homogeneous medium with concentrated loadings. Numerical results for the full-field stress distribution in multilayered media subjected to a point body force are presented. These numerical results were compared with the solutions obtained by considering the multilayered medium as one layer with effective elastic constants determined from the averaged material constants of the multilayered medium. It is found that the shear stress $τyz$ of the homogeneous one layer solution is a very good approximation of the result for the multilayered medium; however, the shear stress $τxz$ in these two solutions has a large discrepancy due to the fact that $τxz$ is discontinuous at the interfaces of the multilayered medium. [S0021-8936(00)01703-7]