HIGHER-ORDER BOUNDS ON THE CONDUCTIVITY OF COMPOSITES FROM SYMMETRY CONSIDERATIONS

It is well known that symmetry considerations can lead to improved bou nds on, or even determine, the conductivity of two-component symmetric materials. The present work exploits symmetry properties to derive ex plicit higher-order bounds for three-component symmetric materials. Th e bounds contain geometric parameters. But even without any knowledge of these geometric parameters, substantial improvement on previous bou nds is made. This is discussed in the context of equiaxed polycrystals . Results include a parameter-independent pair of bounds that for some polycrystals becomes third-order, and a parameter-dependent third-ord er upper bound that can be partially attained.