Elasticity of multilayers: Properties of the propagator matrix and some applications

The elasticity of generalized plane strain is written in terms of a first-order matrix differential equation in six variables (the components of the displacement and the stress function vector). The approach holds for general elastic anisotropy and provides a unified analytical description of elastic fields in layered, stratified, or graded media. The theory is formulated in terms of a propagator matrix. An analysis of its general properties is presented. In particular, the decomposition of this matrix into two parts with different behavior at too in Fourier space is explicitly found. This allows one to obtain analytically the Green's functions for a series of boundary-value problems in anisotropic inhomogeneous media of infinite extent.