Coupled systems of anisotropic layers: A group formulation

A matrix formalism allows for the simple calculation of the anisotropic, homogeneous medium equivalent to a stationary distribution of thin layers in welded contact. Each layer itself may be an elastic anisotropic medium. The calculated medium is equivalent to the layered medium in the long wavelength limit. The physical properties of any constituent of the heterogeneous system can be shown to be transformable to an element of a commutative group. Adding group elements GA and GB (corresponding to thin layers of constituents A and B, respectively) gives the group element for the homogeneous medium equivalent to the interleaved layers of A and B. The group formulation, which is essentially a statement of conservation laws applicable to layered media, enables us to “decompose” an anisotropic medium into several constituent sets of layers by successive additions of inverse elements, i.e., subtractions. If, after each subtraction, the remaining group element corresponds to a stable anisotropic medium, a valid ...