Recent developments in anisotropic elasticity

Anisotropic elasticity has been an active research subject for the last thi rty years due to its applications to composite materials. There are essenti ally two formalisms for two-dimensional deformations of a general anisotrop ic elastic material. The Lekhnitskii formalism [Lekhnitskii, S.G., 1950. Th eory 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 math ematics and physics community. The Stroh formalism (Stroh, A.N., 1958. Disl ocations and cracks in anisotropic elasticity. Phil. Mag. 3, 625-646,) is m athematically elegant and technically powerful. It began to be noticed by t he engineering community in recent years, specially among the younger resea rchers. A comprehensive treatment of both formalisms and applications of th e 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 a pplications of anisotropic elasticity. We present here new results that hav e appeared since 1996. Only linear anisotropic elasticity is considered her e, for nonlinear elasticity, the reader is referred to the book by Antman ( Antman, S.S., 1995. Nonlinear Problems in Elasticity. Springer-Verlag, New York). (C) 1999 Published by Elsevier Science Ltd. All rights reserved.