This work approaches the fields of homogenization and of materials design for the linear and
nonlinear mechanical properties with prescribed properties-profile. The set of achievable
properties is bounded by the zeroth-order bounds (which are material specific) the first-order
bounds (containing volume fractions of the phases) and the second-order Hashin-Shtrikman bounds
with eigenfields in terms of tensorial texture coefficients for arbitrarily anisotropic
textured materials.
