Conductivity of a composite containing uniformly oriented penny–shaped cracks or perfectly conducting discs

We consider the problem of determining the effective conductivity of a composite material consisting of parallel discs embedded in an isotropic matrix. A method of multipole expansion is used for computing the conductivity for the cases of perfectly conducting discs and non–conducting discs or penny–shaped cracks. Both the cases of periodic and random arrangements of discs or cracks are considered. It is shown that, in general, the conductivity is quite sensitive to the details of the arrangement of the discs. The results of computations are compared with those obtained using an effective–medium approximation and with a bound on conductivity.

[1]  Alexander Z. Zinchenko,et al.  Effective conductivity of loaded granular materials by numerical simulation , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[2]  C. Nan,et al.  Effective thermal conductivity of particulate composites with interfacial thermal resistance , 1997 .

[3]  V. Kushch.  Conductivity of a periodic particle composite with transversely isotropic phases , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[4]  Shih-Yuan Lu,et al.  Effective conductivity of composites containing aligned spheroidal inclusions of finite conductivity , 1996 .

[5]  Alexander Z. Zinchenko,et al.  An efficient algorithm for calculating multiparticle thermal interaction in a concentrated dispersion of spheres , 1994 .

[6]  N. Fares.  Effective stiffness of a periodically cracked 3-D solid , 1993 .

[7]  Sia Nemat-Nasser,et al.  Solids with periodically distributed cracks , 1993 .

[8]  J. Brady,et al.  The effective conductivity of random suspensions of spherical particles , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[9]  Shih‐Yuan Lu,et al.  Effective thermal conductivity of composites containing spheroidal inclusions , 1990 .

[10]  T. Miloh,et al.  An exact solution for the effective thermal conductivity of cracked bodies with oriented elliptical cracks , 1989 .

[11]  C. Yao,et al.  Bulk thermal conductivity of composites with spherical inclusions , 1988 .

[12]  D. Hasselman,et al.  Effective Thermal Conductivity of Composites with Interfacial Thermal Barrier Resistance , 1987 .

[13]  L. Poladian,et al.  Effective transport properties of periodic composite materials , 1986, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[14]  J. Willis.  Bounds and self-consistent estimates for the overall properties of anisotropic composites , 1977 .

[15]  B. Budiansky,et al.  Elastic moduli of a cracked solid , 1976 .