Linear and nonlinear elastic behavior of multidirectional laminates

Laminated composites appear throughout engineering, nature, and physiology because of their low weight and high structural performance. Tailored, multilayered laminates comprised of layers with varying orientation and material composition offer the potential for dramatic improvements in the ratios of strength and stiffness to weight compared to their isotropic and homogeneous metallic counterparts. In this chapter, we present the mathematical framework of composite laminates that can be used to optimize the design of such materials. Both the classical theory suitable for the analysis of thin structures as well as the first-order shear deformation theory useful if the structure is thicker or its transverse shear stiffness is low are presented. The chapter concludes with a discussion of modern applications for which material nonlinearity is important to design, and a summary of the phenomenological, nonlinear quasi-elastic frameworks that exist for design.