ABSTRACT
In this chapter, constitutive relations (stress vs. strain) of laminated composites are introduced in addition to the stress–strain relations of a lamina. The constitutive relations of the generally anisotropic materials under linear elastic responses are presented in a simplified form for monoclinic, orthotropic, transversely isotropic, and isotropic materials because fiber-reinforced polymer (FRP) composite laminates are made from unidirectional, bidirectional, or even multidirectional lamina. It is assumed that laminate thickness, sum of composite lamina layers, is very small (~10% or less of the least dimension) compared to their other dimensions. Constitutive relations of composite laminates (combination of several laminae) can be reduced to plane stress condition because of disproportionately large dimensions in the other two directions. In other words, the laminate thickness is still very small compared to the other two dimensions. The constitutive relations of plane stress condition are used to establish both laminate stiffness (ABD) and compliance (abd) matrices. The hygro-thermomechanical responses of laminated composites are functions of the laminate stiffness matrix, and these responses are presented for in-plane stress versus strain relations at the end of this chapter. The main objective of this chapter is to present the stiffness formulation of FRP composite lamina and derive the lamina response under hygro-thermomechanical loads. In addition, stress and strain relationships in global coordinates through transformations are highlighted. It is important to reiterate that the stress–strain relation is independent of any applied loading or external actions induced by temperature or moisture.
