The effective Young’s modulus of composites beyond the Voigt estimation due to the Poisson effect

• Published in: Composites science and technology 2009-10, Vol.69 (13), p.2198-2204
• Main Authors: Liu, Bin, Feng, Xue, Zhang, Si-Ming
• Format: Article
• Language: English
• Subjects: A. Layered structures; C. Elastic properties; Effective modulus; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Upper bound
• ISSN: 0266-3538; 1879-1050
• DOI: 10.1016/j.compscitech.2009.06.004

The Voigt estimation or the rule of mixture has been believed to be the upper bound of the effective Young’s modulus of composites. However, this is only true in the situations where the Poisson effect is not significant. In this paper, we accurately derived the effective compliance matrix for two-phase layered composites by accounting for the Poisson effect. It is interesting to find that the effective Young’s modulus in both transverse and longitudinal direction can exceed not only the Voigt estimation, but also the Young’s modulus of the stiffest constituent phase. Moreover, the longitudinal (or parallel connection) Young’s modulus is not always larger than the transverse (or serial connection) one. For isotropic composites, it has also been demonstrated that the Voigt estimation is not the upper bound for the effective Young’s modulus. Therefore, one should be careful in applying the well known bound estimations on the effective Young’s modulus of composites if one of the phases is near its incompressibility limit.