6.1 Basic Equations

The engineering properties or elastic constants were introduced in Chap. 2 with respect to the lamina 1-2-3 coordinate system. Their evaluation was presented in Chap. 3 based also on the 1-2-3 coordinate system. We can also define elastic constants with respect to the x- y- z global coordinate system. The elastic constants in the x- y- z coordinate system can be derived directly from their definitions, just as they were derived in Chap. 3 for the 1-2-3 coordinate system.

The elastic constants based on the x- y- z global coordinate system are given as follows [1]:

(6.1)

(6.2)

(6.3)

(6.4)

(6.5)

It is useful to define several other material properties for fiber-reinforced composite materials that can be used to categorize response [1]. These properties have as their basis the fact that an element of fiber-reinforced composite material with its fiber oriented at some arbitrary angle exhibits a shear strain when subjected to a normal stress, and it also exhibits an extensional strain when subjected to a shear stress.

Poisson's ratio is defined as the ratio of extensional strains, given that the element is subjected only to a simple normal stress. By analogy, the coefficient of mutual influence of the second kind is defined as the ratio of a shear strain to an extensional strain, given that the element is subjected to only a single normal stress. The coefficient of mutual influence of the first kind is...