Bulk Effective Moduli: Their Calculation and Usage for Describing Physical Properties of Composite Media
- PDF / 629,360 Bytes
- 10 Pages / 420.48 x 639 pts Page_size
- 8 Downloads / 211 Views
BULK EFFECTIVE MODULI: THEIR CALCULATION AND USAGE FOR DESCRIBING PHYSICAL PROPERTIES OF COMPOSITE MEDIA DAVID J. BERGMAN Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel ABSTRACT While not telling the whole story, the representation of a composite medium by a homogeneous effective medium is often an excellent approximation for describing its macroscopic physical properties. Modern methods for calculating the effective medium properties are reviewed with special emphasis on understanding both successes and limitations. Outstanding problems that can and should be tackled are identified. The successes include calculations of the electrical conductivity, dielectric coefficient, and elastic stiffness moduli of composites with a periodic microstructure, and the simulation of those properties for disordered composites near a percolation threshold by means of discrete models such as a random-resistor-network. For composites where the microstructure is either unknown or very complicated, a whole class of exact bounds have been found for these properties based on various types of limited information. Recently, advances have been made in calculating the weak field magneto-transport and the thermoelectric behavior of twocomponent composites, and also some types of nonlinear properties. An important challenge remains the calculation of magneto-transport at high magnetic fields. Another is the theoretical treatment of multicomponent composites. A third is to find relations between different effective properties of a composite that can enable us to learn about property A by measuring a different property B. This
is especially important when the measurement of A would destroy the sample, as when A is the yield stress, whereas the measurement of B is nondestructive, as when B is a small, nonlinear correction to the usual elastic stiffness moduli. I. INTRODUCTION
When two or more materials are mixed together to form a composite medium, details of the microstructure can have an important effect on the macroscopic properties. For example, in a metal-insulator mixture, the connectivity of the metal component is crucial in determining whether the composite has a non-vanishing macroscopic or bulk effective conductivity a.. Sometimes the effect of the microstructure is more subtle and less obvious, though not less important, which is why we need to have a theory to describe these effects. One of the early examples of such an effect can be found in a classic study of optical properties of ceramic-metal (cermet) films conducted by Ben Abeles and his associates many years ago [1]. In those experiments a peak was observed in the absorption spectrum, that depended on the composition of the film and was absent in the pure components. The authors correctly identified this peak as due to a microstructure dependent electrostatic resonance, though the simple approximation they used to try to describe it, namely, the Clausius - Mossotti or Maxwell Garnett theory, w
Data Loading...
