obtained using numerical methods, and which are expected to be accurate. First, the transverse thermal conductivity is considered and the comparison of Maxwell’s methodology with results of Perrins et al. [8] is shown in Figure 4.2. The normalised effective transverse conductivity is defined by κTeff/κTm and the three materials considered are for isotropic fibres and matrix such that κf/κm=2,10,∞.
Figure 4.2 Comparison of results for normalised effective transverse thermal conductivity obtained using Maxwell’s methodology with those of Modified from Perrins et al. [8] for three different materials.
Figure 4.3 shows a comparison of transverse bulk modulus obtained using Maxwell’s methodology with results of Eischen and Torquato [9]. The normalised effective transverse bulk modulus is defined by kTeff/kTm and the three materials considered are for isotropic fibres and matrix such that μf/μm=135,22.5,6.75, μf/kf=0.75 and μm/km=0.33.
Figure 4.3 Comparison of results for normalised effective transverse bulk modulus obtained using Maxwell’s methodology with those of Modified from Eischen and Torquato [9] for three different materials.
Figure 4.4 shows a comparison of axial shear modulus obtained using Maxwell’s methodology with results of Symm [10]. The normalised effective axial shear modulus is defined by kAeff/kAm and the four materials considered are for isotropic fibres and matrix such that μf/μm=6,20,120,∞.
Figure 4.4 Comparison of results for normalised effective axial shear modulus obtained using Maxwell’s methodology with those of Modified from Symm [10] for four different materials.
Figure 4.5 shows a comparison of transverse shear modulus obtained using Maxwell’s methodology with results of Eischen and Torquato [9]. The normalised effective transverse shear modulus is defined by μteff/μm and the three materials considered are for isotropic fibres and matrix such that μf/μm=135,22.5,6.75, μf/kf=0.75 and μm/km=0.33.
Figure 4.5 Comparison of results for normalised effective transverse shear modulus obtained using Maxwell’s methodology with those of Modified from Eischen and Torquato [9] for three different materials.
References
1 1. Maxwell, J.C. (1873). A Treatise on Electricity and Magnetism, 1st ed. (3rd edition, 1892). Chapter 9, Vol. 1. Oxford: Clarendon Press.
2 2. McCartney, L.N. and Kelly, A. (2008). Maxwell’s far-field methodology applied to the prediction of properties of multi-phase isotropic particulate composites. Proceedings of the Royal Society A464: 423–446.
3 3. Hashin, Z. (1983). Analysis of composite materials - A survey. Journal of Applied Mechanics 50: 481–505.
4 4. Hasselman, D.P.H. and Johnson, L.F. (1987). Effective thermal conductivity of composites with interfacial thermal barrier resistance. Journal of Composite Materials 21: 508–515.
5 5. Torquato, S. (2002). Random Heterogeneous Materials. New York: Springer-Verlag.
6 6. McCartney, L.N. (2010). Maxwell’s far-field methodology predicting elastic properties of multiphase composites reinforced with aligned transversely isotropic spheroids. Philosophical Magazine 90: 4175–4207.
7 7. Hashin, Z. and Shtrikman, S. (1963). A variational approach to the theory of the elastic behaviour of multiphase composites. Journal of the Mechanics and Physics of Solids 11: 127–140.
8 8. Perrins, W.T., McKenzie, D.R., and McPhedran, R.C. (1979). Transport properties of regular arrays of cylinders. Proceedings of the Royal Society of London A369: 207–225.
9 9. Eischen, J.W. and Torquato, S. (1993). Determining elastic behaviour of composites by the boundary element method. Journal of Applied Physics 74 (1): 159–170.
10 10. Symm, G.T. (1970). The longitudinal shear modulus of a unidirectional fibrous composite. Journal of Composite Materials 4: 426–428.
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