2.1 Basic Equations

Consider a single layer of fiber-reinforced composite material as shown in Fig. 2.1. In this layer, the 1-2-3 orthogonal coordinate system is used where the directions are taken as follows:

1. The 1-axis is aligned with the fiber direction.

2. The 2-axis is in the plane of the layer and perpendicular to the fibers.

3. The 3-axis is perpendicular to the plane of the layer and thus also perpendicular to the fibers.

Figure 2.1: A lamina illustrating the principle material coordinate system

The 1-direction is also called the fiber direction, while the 2- and 3-directions are called the matrix directions or the transverse directions. This 1-2-3 coordinate system is called the principal material coordinate system. The stresses and strains in the layer (also called a lamina) will be referred to the principal material coordinate system.

At this level of analysis, the strain or stress of an individual fiber or an element of matrix is not considered. The effect of the fiber reinforcement is smeared over the volume of the material. We assume that the two-material fiber-matrix system is replaced by a single homogeneous material. Obviously, this single material does not have the same properties in all directions. Such material with different properties in three mutually perpendicular directions is called an orthotropic material. Therefore, the layer (lamina) is considered to be orthotropic.

The stresses on a small infinitesimal element taken from the layer are illustrated in Fig. 2.2. There are three normal stresses ? ₁,