Chapter 11 - Anisotropic Elasticity

Abstract

It has long been recognized that the behavior of many materials depends upon the orientation of the sample taken from the body under study. The term anisotropic is generally used to describe such behaviors. Early investigators were motivated by the response of naturally occurring anisotropic materials such as wood and crystalline substances. The advent and extensive use of engineered composites has now brought forward many new types of fiber and particle-reinforced materials with such behavior. Therefore, knowledge of stress distributions in anisotropic materials is very important for proper use of these new high-performance materials in structural applications. Our previous development of the linear elastic stress–strain relations in Section 4.2 began with the general case of inhomogeneous and anisotropic behavior. However, this generality was quickly eliminated, and only the homogeneous isotropic case was subsequently developed in detail. We now wish to go back and further investigate the anisotropic case and develop applications for particular elasticity problems including torsion and plane problems. We will explore various material symmetries including monoclinic, orthotropic, and transversely isotropic materials in detail.