Recent developments in anisotropic elasticity

Abstract

Anisotropic elasticity has been an active research subject for the last thirty years due to its applications to composite materials. There are essentially two formalisms for two-dimensional deformations of a general anisotropic elastic material. The Lekhnitskii formalism [Lekhnitskii, S.G., 1950. Theory of Elasticity of an Anisotropic Elastic Body. Gostekhizdat, Moscow (in Russian)] has been the favorite among the engineering community, while the newer Stroh formalism is well-known in the material sciences, applied mathematics and physics community. The Stroh formalism (Stroh, A.N., 1958. Dislocations and cracks in anisotropic elasticity. Phil. Mag. 3, 625–646.) is mathematically elegant and technically powerful. It began to be noticed by the engineering community in recent years, specially among the younger researchers. A comprehensive treatment of both formalisms and applications of the theory have been presented in a book by Ting. Since the appearance of the book in 1996, there have been several new developments in the theory and applications of anisotropic elasticity. We present here new results that have appeared since 1996. Only linear anisotropic elasticity is considered here; for nonlinear elasticity, the reader is referred to the book by Antman (Antman, S.S., 1995. Nonlinear Problems in Elasticity. Springer–Verlag, New York).