Macromechanics of Lamina 
From control surfaces of modern aircrafts, to hulls and keels of yachts, to racing car bodies, to tennis rackets, fishing rods, golf shafts and heads, laminated fiber reinforced composite is one of the the most widely used composites in industry. Unless otherwise noted, the following assumptions are made in our discussion of the macromechanics of laminated composites.

StressStrain Relations for Principal Directions 
Before discussing the mechanics of laminated composites, we need to understand the mechanical behavior of a single layer  lamina. Since each lamina is a thin layer, one can treat a lamina as a plane stress problem. This simplification immediately reduces the 6×6 stiffness matrix to a 3×3 one. Since each lamina is constructed by unidirectional fibers bonded by a metal or polymer matrix, it can be considered as an orthotropic material. Thus, the stressstrain relations on the principal axes can be expressed by the compliance matrix [S] such that [] = [S][]
or by the stiffness matrix [C] such that [] = [C][]
Please note that the engineering shear strain is used in the stressstrain relations, and, the notation S for the compliance matrix and C for the stiffness matrix are not misprints. Please consult this page for more information. For both stiffness and compliant matrices are symmetric, i.e., only four of , , , , and are independent material properties. Again, the shear modulus G_{12} corresponds to the engineering shear strain which is twice the tensor shear strain . Please note that there can be many fibers across the thickness of a lamina and these fibers may not be arranged uniformly in most industrial practice. However, the combination of the matrix and the fibers forms an orthotropic and homogeneous material from a marcomechanics standpoint. Some literature therefore schematically illustrates a lamina with only one layer of uniformly distributed fibers as shown below. 