2. Anisotropic Elastic Solids

Properties of composite materials and their constituents often depend on both position and direction in a fixed system of coordinates. In the terminology of solid mechanics, such materials are heterogeneous and anisotropic. This chapter is concerned with the directional dependence, defined by certain material symmetry elements, and reflected in eight distinct forms of the stiffness and compliance matrices of elastic solids. Such materials include, for example, reinforcing fibers, particles and their coatings, or fibrous composites and laminates represented on the macroscale by homogenized solids with equivalent or effective elastic moduli. Identification of the positions of zero-valued coefficients, and of any connections between nonzero coefficients in those matrices is of particular interest. Different classes of crystals exhibit a much larger range of symmetries, derived from spatial arrangement of their lattices. Broader expositions of these topics can be found in several books, such as Love (1944), Lekhnitskii (1950), Green and Atkins (1960), Nye (1957, 1985), Hearmon (1961), Ting (1996), and Cowin and Doty (2007).