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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.

Theoretische Schranken --- Materialdesign --- Materials design --- Homogenisierung --- Theoretical bounds --- Homogenization --- Polycrystals --- Polykristalle --- Mehrphasige Materialien --- Multiphase materials