Morphology-dependent Hashin-Shtrikman bounds on the effective properties of stress-gradient materials (Q2224608)

The authors extend the classical variational principle by Hashin-Shtrikman known for elastic composites to stress-gradient elastic materials. The variational principle is formulated within the framework of periodic homogenization. It is shown that, in many cases of interest, the third-order trial eigenstrain may be neglect, leading to only one (second-order) trial eigenstrain in the functional to optimize. It is established that even in the case of isotropy the bounds depend on some additional microstructural parameters.