Disordered hyperuniform materials are an emerging class of exotic amorphous states of matter that endow them with singular physical properties, including large isotropic photonic band gaps, superior resistance to fracture, and nearly optimal electrical and thermal transport properties, to name but a few. Here we generalize the Fourier-space-based numerical construction procedure for designing and generating digital realizations of isotropic disordered hyperuniform two-phase heterogeneous materials (i.e., composites) developed by Chen and Torquato [Acta Mater. 142, 152 (2018)] to anisotropic microstructures with targeted spectral densities. Our generalized construction procedure explicitly incorporates the vector-dependent spectral density function ${\tilde{\chi }}_{{}_V}\left(\mathbf{k}\right)$ of arbitrary form that is realizable. We demonstrate the utility of the procedure by generating a wide spectrum of anisotropic stealthy hyperuniform microstructures with ${\tilde{\chi }}_{{}_V}\left(\mathbf{k}\right)=0$ for $\mathbf{k}\in \mathrm{\Omega }$, i.e., complete suppression of scattering in an “exclusion” region $\mathrm{\Omega }$ around the origin in Fourier space. We show how different exclusion-region shapes with various discrete symmetries, including circular-disk, elliptical-disk, square, rectangular, butterfly-shaped, and lemniscate-shaped regions of varying size, affect the resulting statistically anisotropic microstructures as a function of the phase volume fraction. The latter two cases of $\mathrm{\Omega }$ lead to directionally hyperuniform composites, which are stealthy hyperuniform only along certain directions and are nonhyperuniform along others. We find that while the circular-disk exclusion regions give rise to isotropic hyperuniform composite microstructures, the directional hyperuniform behaviors imposed by the shape asymmetry (or anisotropy) of certain exclusion regions give rise to distinct anisotropic structures and degree of uniformity in the distribution of the phases on intermediate and large length scales along different directions. Moreover, while the anisotropic exclusion regions impose strong constraints on the global symmetry of the resulting media, they can still possess structures at a local level that are nearly isotropic. Both the isotropic and anisotropic hyperuniform microstructures associated with the elliptical-disk, square, and rectangular $\mathrm{\Omega }$ possess phase-inversion symmetry over certain range of volume fractions and a percolation threshold ${\varphi }_c\approx 0.5$. On the other hand, the directionally hyperuniform microstructures associated with the butterfly-shaped and lemniscate-shaped $\mathrm{\Omega }$ do not possess phase-inversion symmetry and percolate along certain directions at much lower volume fractions. We also apply our general procedure to construct stealthy nonhyperuniform systems. Our construction algorithm enables one to control the statistical anisotropy of composite microstructures via the shape, size, and symmetries of $\mathrm{\Omega }$, which is crucial to engineering directional optical, transport, and mechanical properties of two-phase composite media.

• Received 25 July 2023
• Accepted 18 September 2023

DOI:https://doi.org/10.1103/PhysRevE.108.045306