Optimal third-order bounds on the effective properties of some composite media, and related problems
Abstract
The problem of the optimality of variational bounds for the effective coefficients of thermal conductivity and elastic modulus of two-phase composite media of random structure is considered. Special attention is paid to random dispersions of spheres, due to the simplicity of their mathematical description and to their importance as a reasonable model of many particulate media. The pivotal point is the quest for optimality of the estimates in the sense of whether or not they are the best under a given amount of statistical information. The basic tool for this study is the functional (Volterra-Wiener) series. It is shown that for a random dispersion of overlapping spheres, the bounds are, in general, non-optimal, and the optimality occurs up to the order of the square of the volume sphere concentration (c-squared). The bounds are explicitly calculated for overlapping spheres up to the order c-squared, and the obtained results are applied to an analysis of the applicability of some heuristic methods to the mechanics of composite materials.
- Publication:
-
Advances in Mechanics Uspekhi Mekhaniki
- Pub Date:
- 1991
- Bibcode:
- 1991AdMUM..14....3M
- Keywords:
-
- Composite Materials;
- Elastic Properties;
- Optimization;
- Particulate Reinforced Composites;
- Thermal Conductivity;
- Heuristic Methods;
- Kernel Functions;
- Modulus Of Elasticity;
- Spheres;
- Transport Theory;
- Variational Principles;
- Virial Theorem;
- Structural Mechanics