Comparison of micromechanics methods for effective properties of multiphase viscoelastic composites

In this paper we examine the use of several popular micromechanics methods for determination of effective composite properties when all phases are viscoelastic. The elasticity-based Mori-Tanaka method and the finite element method of cells are used, both via implementation of the elastic-viscoelastic correspondence principle. The finite element technique considers two different periodic microstructures, square and hexagonal arrays, the results of which are compared with each other and the Mori-Tanaka predictions. The resultant effective properties for viscoelastic composites are determined at a wide range of frequencies and compared with transformed Hashin-Shtrikman bounds and Gibiansky-Milton bounds. The Mori-Tanaka method in the transformed domain is by far the simplest to implement and it is shown that the method replicates the major features of the storage and loss moduli of the composite, including location and magnitude of the double loss peaks from the glass-rubber transition of each phase. It is also illustrated that the Mori-Tanaka method predicts a nearly log-linear relationship between resultant property and volume fraction at a given frequency. Limitations of the Mori-Tanaka method for viscoelastic composites are highlighted.

[1]  J. Aboudi.  Mechanics of composite materials - A unified micromechanical approach , 1991 .

[2]  Tungyang Chen,et al.  Stress fields in composites with coated inclusions , 1989 .

[3]  G. Weng,et al.  Anisotropic stress-strain relations and complex moduli of a viscoelastic composite with aligned spheroidal inclusions , 1994 .

[4]  Y. Benveniste,et al.  A new approach to the application of Mori-Tanaka's theory in composite materials , 1987 .

[5]  George J. Weng,et al.  Some elastic properties of reinforced solids, with special reference to isotropic ones containing spherical inclusions , 1984 .

[6]  Ahmed K. Noor,et al.  Effective thermoelastic and thermal properties of unidirectional fiber-reinforced composites and their sensitivity coefficients , 1993 .

[7]  Graeme W. Milton,et al.  On the effective viscoelastic moduli of two-phase media. I. Rigorous bounds on the complex bulk modulus , 1993, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[8]  Z. Hashin.  Analysis of Composite Materials—A Survey , 1983 .

[9]  R. Lakes,et al.  Bounds on the complex bulk and shear moduli of a two-dimensional two-phase viscoelastic composite , 1997 .

[10]  Y. Fung.  Foundations of solid mechanics , 1965 .

[11]  Zvi Hashin,et al.  On elastic behaviour of fibre reinforced materials of arbitrary transverse phase geometry , 1965 .

[12]  S. Jun,et al.  Elastic moduli of two-dimensional composites with sliding inclusions : a comparison of effective medium theories , 1993 .

[13]  Toshio Mura,et al.  Micromechanics of defects in solids , 1982 .

[14]  L. Brinson,et al.  Thermorheologically complex behavior of multi-phase viscoelastic materials , 1991 .

[15]  G. P. Tandon,et al.  Average stress in the matrix and effective moduli of randomly oriented composites , 1986 .

[16]  Richard Schapery,et al.  Stress Analysis of Viscoelastic Composite Materials , 1967 .

[17]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[18]  G. Weng.  THE THEORETICAL CONNECTION BETWEEN MORI-TANAKA'S THEORY AND THE HASHIN-SHTRIKMAN-WALPOLE BOUNDS , 1990 .

[19]  R. Christensen,et al.  Solutions for effective shear properties in three phase sphere and cylinder models , 1979 .

[20]  George J. Weng,et al.  Strain-Rate Sensitivity, Relaxation Behavior, and Complex Moduli of a Class of Isotropic Viscoelastic Composites , 1994 .

[21]  M. Paley,et al.  Micromechanical analysis of composites by the generalized cells model , 1992 .

[22]  G. Weng,et al.  The influence of inclusion shape on the overall viscoelastic behavior of composites , 1992 .

[23]  Wolfgang G. Knauss,et al.  Finite Element Analysis of Multiphase Viscoelastic Solids , 1992 .