New optimal microstructures and restrictions on the attainable Hashin–Shtrikman bounds for multiphase composite materials

Abstract

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.

Keywords:

• composite materials
• new optimal microstructures
• Hashin–Shtrikman bounds

Acknowledgements

The author gratefully acknowledges the support of the Texas Center for Superconductivity, University of Houston (TcSUH) through ST#44870.