Maximizing the effective stiffness of laminate composite materials

The effective stiffness of laminate composites can be expressed explicitly and accurately as a function of several variables such as volume fractions and elastic constants of the constituent phases. Based on the stiffness function, an optimization procedure is proposed in this paper to maximize the effective Young's moduli of laminate composites in both longitudinal and transverse directions with respect to a number of design variables. By solving such a constrained optimization problem, a laminate composite can be designed by finding the optimal material properties of the constituent phases and their volume fractions. The effects of the volume fractions, the Young's moduli and the Poisson's ratios of the constituent phases in the effective composite stiffness are demonstrated through various design cases. It is shown that the optimized effective Young's moduli can reach values much higher than the well-known approximated Voigt estimation. Dramatic increases in the effective stiffness have also been found when the Poisson's ratios of the constituent phases approach the thermodynamic limits of −1 and 0.5. It is envisaged that with the proposed approach and modern fabrication technologies, laminate composites with exceptional effective stiffness can be easily designed and manufactured.