Representation of Hashin–Shtrikman bounds of cubic crystal aggregates in terms of texture coefficients with application in materials design

Abstract The Hashin–Shtrikman bounds of aggregates of cubic crystals are explicitly represented in terms of tensorial texture coefficients. The formula is valid for arbitrary crystallographic textures and isotropic two-point statistics. The isotropy of the two-point statistics implies that the grain shape is isotropic on average. The new explicit representation has the advantage that the set of energetically admissible crystallographic textures and corresponding effective linear elastic properties can be directly determined and analyzed based on minimum principles of the elastic strain energy density. It is shown that all energetically admissible textures with maximum anisotropy have an effective elastic behavior with cubic sample symmetry. Furthermore, it is proven that there exist texture states without maximum anisotropy which have the extreme elastic properties peculiar to states with maximum anisotropy. This is an important result for the design of elastic material properties.