ELASTICITY OF MULTILAYERS .1. BASIC EQUATIONS AND SOLUTIONS

Multilayer structures, such as oxide or protective layers on a substrate, sandwich structures in electronics or magnetics, layered composites or simply thin foils, are of technological importance. Mechanically they are characterized by a variation of elastic constants with respect to the direction normal to the layer interfaces. These layered structures, if they are of finite extent, may be loaded externally, or, if of infinite extent, can be subject to line defects (dislocations or forces) and transformation (or thermal) strains. In this paper (part I) we develop the foundations of the anisotropic theory of elasticity under generalized plane strain for unidirectional heterogeneity and give the fundamental solution for line defects and transformation strains. Part II discusses sandwich structures and finite configurations.