We address the attainability of the Hashin-Shtrikman (HS) bounds for multiphase composite materials. We demonstrate that the HS bounds are not always attainable and give new restrictions on the attainable HS bounds in terms of the conductivities and volume fractions of the constituent phases. New optimal microstructures are also constructed to attain the HS bounds. Combined together, these results allow for precise characterization of the set of effective properties for a wide range of composite materials.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Hashin-Shtrikman bounds
- composite materials
- new optimal microstructures