Attainability of the Hashin–Shtrikman bounds for two-phase well-ordered composites with a nonlinear phase

The Hashin–Shtrikman (HS) bounds for two-phase well-ordered composites are known to be attained by certain sequentially laminated constructions when the constituent phases exhibit a linear behavior. This implies that the bounds are optimal for that class of materials. In this Note we show that the bounds are still attained by sequentially laminated constructions when one of the phases is nonlinear, and that, consequently, they are optimal for a larger class of materials.