Bounds on the overall properties of composites with ellipsoidal inclusions

• Published in: Acta mechanica Sinica 2012-10, Vol.28 (5), p.1340-1355
• Main Authors: Wu, Lin-Zhi, Pan, Shi-Dong
• Format: Article
• Language: English
• Subjects: Classical and Continuum Physics; Computational Intelligence; Displacement; Engineering; Engineering Fluid Dynamics; Inclusions; Lower bounds; Mathematical analysis; Mathematical models; Modulus of elasticity; Research Paper; Stresses; Theoretical and Applied Mechanics; Variational principles; 变分原理; 复合材料; 夹杂物; 最小势能; 有效弹性模量; 椭球形; 界面条件; 综合性能
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-012-0102-y

A new model is put forward to bound the effective elastic moduli of composites with ellipsoidal inclusions. In the present paper, transition layer for each ellipsoidal inclusion is introduced to make the trial displacement field for the upper bound and the trial stress field for the lower bound satisfy the continuous interface conditions which are absolutely necessary for the application of variational principles. According to the principles of minimum potential energy and minimum complementary energy, the upper and lower bounds on the effective elastic moduli of composites with ellipsoidal inclusions are rigorously derived. The effects of the distribution and geometric parameters of ellipsoidal in- clusions on the bounds of the effective elastic moduli are an- alyzed in details. The present upper and lower bounds are still finite when the bulk and shear moduli of ellipsoidal inclusions tend to infinity and zero, respectively. It should be mentioned that the present method is simple and needs not calculate the complex integrals of multi-point correlation functions. Meanwhile, the present paper provides an entirely different way to bound the effective elastic moduli of composites with ellipsoidal inclusions, which can be developed to obtain a series of bounds by taking different trial displacement and stress fields.