J. Helsing, HIGHER-ORDER BOUNDS ON THE CONDUCTIVITY OF COMPOSITES FROM SYMMETRY CONSIDERATIONS, Proceedings - Royal Society. Mathematical and physical sciences, 443(1918), 1993, pp. 451-455
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.