The Stroh Formalism for Anisotropic Elasticity with Applications to Composite Materials

Abstract

Abstract : Anisotropic elasticity has been an active research topic since the need of high strength, light weight composites in aerospace industry became apparent. The oldest theory of two dimensional anisotropic elasticity is due to Lekhnitskii. The Lekhnitskii theory is not only outdated, it is inefficient. A new theory, originally due to Stroh and further developed by others, is very powerful. We have extended the Stroh formalism by presenting new identities and sum rules. Using these identities and sum rules, some heretofore unsolved problems are solved and solutions which are available but are in a complex form are converted into a real form. With the solutions in a real form, many new physically interesting phenomena have been discovered. Some of these findings, such as the invariant properties of rotations about the x3 axis, would be useful in design of composite materials.