Effective Transport and Mechanical Properties of Two-Phase Materials Across the Order-Disorder Spectrum

Two-phase heterogeneous materials arise in a plethora of natural and synthetic situations, such as alloys, composites, geological media, complex fluids, and biological media, exhibit a wide-variety of microstructures, and thus display a broad-spectrum of effective physical properties. Elucidating how microstructural details (e.g., specific surface, phase volume fractions, geometries, and topologies) influence two-phase materials' effective transport and mechanical properties enhances our fundamental understanding of microstructure-property relationships, and is of great practical use in the design of structural and functional materials. Here, we use accurate "three-point" approximations and numerical simulations to examine the effective thermal/electrical conductivities and elastic moduli of a wide class of disordered 2D and 3D material microstructures, including various networks derived from tessellations of disordered stealthy hyperuniform point patterns. Our results reveal qualitative trends between the effective physical and phase-connectedness properties of microstructures. We also show that a virtually unknown three-point approximation predicts accurately the effective conductivities of highly clustered materials across volume fractions, including 3D networks. Finally, we show that certain disordered closed-cell foams derived from stealthy point patterns have nearly optimal conductivities and elastic moduli.