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Limitations on the Use of Effective Properties for Multicomponent Materials

Published online by Cambridge University Press:  05 May 2011

R. Han ,
M. S. Ingber  and
S. C. Hsiao
R. Han*
Affiliation:
Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM 87131, U.S.A.
M. S. Ingber*
Affiliation:
Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM 87131, U.S.A.
S. C. Hsiao*
Affiliation:
Department of Hydraulic and Ocean Engineering, National Cheng-Kung University, Tainan, Taiwan 70101, R.O.C.
*
*Ph.D.
**Professor
***Assistant Professor, corresponding author
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Abstract

Multicomponent composite materials comprised of a dispersed phase suspended in a matrix material are important in a wide variety of scientific and engineering applications including electronic encapsulation, functionally graded materials, and fiber-reinforced structural components among others. Modelling of this class of composites is typically performed using an effective property approach. This approach presumes that the characteristic dimension of the dispersed phase elements is small in comparison to the characteristic length scale of the physical problem under consideration. However, it is not possible to predict a third effective elastic property based on two independent effective elastic properties as it is for homogeneous elastic isotropic materials. Therefore, a macroscale simulation based on an effective Young's modulus and Poisson ratio may yield poor results for a material subjected to shear loading since there is a potentially incorrect presumed effective shear modulus for the simulation. In the current research, boundary element simulations are performed for mesoscopic samples of composite materials to determine effective bulk moduli, shear moduli, Young's moduli, and Poisson ratios. From these analyses, limitations in the effective property approach can be examined.

Keywords

Composite materialsEffective elastic moduliBoundary element method
Type
Articles
Information
Journal of Mechanics , Volume 24 , Issue 1 , March 2008 , pp. 95 - 102
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2008

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References

1.Torquato, S., “Random Heterogeneous Media: Microstructure and Improved Bounds on Effective Properties,” Appl. Mech. Rev., 44, pp. 37–76 (1991).CrossRefGoogle Scholar
2.Paquin, A., Saber, H. and Berveiller, M., “Integral Formulation and Self-Consistent Modelling of Elastoviscoplastic Behavior of Heterogeneous Materials,” Arch. Appl. Mech., 69, pp. 14–35 (1999).CrossRefGoogle Scholar
3.Hashin, Z., “Analysis of Composite Materials: A Survey,” J. Appl. Mech., 50, pp. 481–505 (1983).CrossRefGoogle Scholar
4.Nemat-Nasser, S. and Hori, M., “Micromechanics: Overall Properties of Heterogeneous Materials,” North-Holland Series in Applied Mathematics and Mechanics (1993).Google Scholar
5.Voigt, W., “Uber Die Beziehung Zwischen Den Beiden Elastizitatskonstanten Isotroper Korper,” Wied Ann., 38, pp. 573–587 (1889).CrossRefGoogle Scholar
6.Rayleigh, L., “On the Influence of Obstacles Arranged in Rectangular Order Upon the Properties of a Medium,” Phil. Mag., 34, pp. 481–502 (1892).CrossRefGoogle Scholar
7.Einstein, A., “Eine Theorie Der Grundlagen Der Thermodynamik,” Ann. Physik., 11, pp. 170–187(1903).CrossRefGoogle Scholar
8.Einstein, A., “Eine Neue Bestimmung Der Molek-Luldimensionen,” Ann. Physik., 19, pp. 289–306 (1906).CrossRefGoogle Scholar
9.Reuss, A., Berechnung der Fliessgrenze von Mischkristallen auf Grund der Plastizatatesbedingung fur eirkristalle. Z.,” Ang. Math. Mech., 9, pp. 49–58 (1929).CrossRefGoogle Scholar
10.Eshelby, J. D., “The Determination of the Elastic Field of an Ellipsoidal Inclusion and Related Problems,” Proc. Roy. Soc. A., 241, pp. 376–396 (1957).Google Scholar
11.Hashin, Z. and Shtrikman, S., “A Variational Approach to the Theory of the Elastic Behavior of Multiphase Materials,” J. Mech. Phys. Solids, 11, pp. 127–140 (1963).CrossRefGoogle Scholar
12.Hill, R., “A Self-Consistent Mechanics of Composite Materials,” J. Mech. Phys. Solids, 13, pp. 213–225 (1965).CrossRefGoogle Scholar
13.Chou, T.-W., Nomura, S. and Taya, M., “A Selfconsistent Approach to the Elastic Stiffness of Short-Fiber Composites,” J. Comp. Mat., 14, pp. 178–188 (1980).CrossRefGoogle Scholar
14.Ting, T. C. T., “The Stationary Values of Young's Modulus for Monoclinic and Triclinic Materials,” Journal of Mechanics, 21, pp. 249–253 (2005a).CrossRefGoogle Scholar
15.Ting, T. C. T., “Explicit Expressioin of the Stationary Values of Young's Modulus and the Shear Modulus for Anisotropic Elastic Materials,” Journal of Mechanics, 21, pp. 255–266 (2005b).CrossRefGoogle Scholar
16.Eischen, J. W. and Torquato, S., “Determining Elastic Behavior of Composites by the Boundary Element Method,” J. Appl. Physics, 74, pp. 159–170 (1993).CrossRefGoogle Scholar
17.Chati, M. K. and Mitra, A. K., “Prediction of Elastic Properties of Fiber-Reinforced Unidirectional Composites,” Eng. Anal. Bound. Elem., 21, pp. 235–244 (1998).CrossRefGoogle Scholar
18.Ingber, M. S. and Papathanasiou, T. D., “A Parallel-Supercomputing Investigation of the Stiffness of Aligned, Short-Fiber-Reinforced Composites Using the Boundary Element Method,” Int. J. Numer. Meth. Engrg., 40, pp. 3477–3491 (1997).3.0.CO;2-B>CrossRefGoogle Scholar
19.Okada, H., Fukui, Y. and Kumazawa, N., “Homogenization Analysis for Particulate Composite Materials Using the Boundary Element Method,” Comp. Mod. Engrg. Sci., 5, pp. 135–149 (2004).Google Scholar
20.Zohdi, T. I. and Wriggers, P., “Aspects of Computational Testing of the Mechanical Properties of Microheterogeneous Material Samples,” Int. J. Num. Meth. Engrg., 50, pp. 2573–2599 (2001).CrossRefGoogle Scholar
21.Okada, H., Liu, C. T., Ninomiya, T., Fukui, Y. and Kumazawa, N., “Analysis of Particulate Composite Materials Using an Element Overlay Technique,” Comp. Mod. Engrg. Sci., 6, pp. 333–347 (2004).Google Scholar
22.Liu, D. S., Chen, C. Y. and Chiou, D. Y., “3-D Modeling of a Composite Material Reinforced with Multiple Thickly Coated Particles using the Infinite Element Method,” Comp. Mod. Engr. Sci., 9, pp. 179–191 (2005).CrossRefGoogle Scholar
23.Brebbia, C. A., Telles, J. C. F. and Wrobel, L. C., “Boundary Element Techniques,” Theory and Applications in Engineering, Springer-Verlag, Berlin (1984).Google Scholar
24.Papathanasiou, T. D., Ingber, M. S., Mondy, L. A. and Graham, A. L., “The Effective Elastic Modulus of Fiber-Reinforce Composites,” J. Comp. Mat., 28, pp. 288–304(1994).CrossRefGoogle Scholar
25.Jeffrey, D. J. and Onishi, T., “The Forces and Couples Acting on two Nearly Touching Spheres in Low-Reynolds Number Flow,” ZAMP, 35, pp. 634–641 (1984).Google Scholar
26.Cooley, M. D. and ONeill, M. E., “On the Slow Motion Generated in a Viscous Fluid by the Approach of a Sphere to a Plane Wall or a Stationary Sphere,” Mathematika, 16, pp. 37–49 (1969).CrossRefGoogle Scholar