Multifunctionality of particulate composites via cross-property maps

Closed-form analytical expressions for the effective electrical (thermal) conductivity and elastic moduli of a wide class of three-dimensional isotropic particulate composites (dispersions) for all phase contrasts and volume fractions have been previously formulated. These property estimates were extracted from exact strong-contrast expansions that incorporate complete microstructural information. In this paper, we employ these analytical expressions to derive and apply "cross-property maps" that connect combinations of pairs of the aforementioned effective transport and elastic properties to one another for a wide class of dispersions in which the inclusions can have different shapes and sizes and are spatially distributed in a matrix with varying degrees of order/disorder. We illustrate cross-property maps for a variety of cases (e.g., incompressible or compressible composites with conducting/insulating inclusions that may be rigid or compliant or auxetic) for high inclusion volume fractions. All of the cross-property maps that involve the effective conductivity translate immediately into equivalent results for the effective dielectric constant, magnetic permeability, or diffusion coefficient because they are mathematically analogous. We discuss an example that enables us to design a disordered dispersion with desired values of the effective dielectric constant and effective Young's modulus. Cross-property maps and their extensions will facilitate the rational design of particulate media with different desirable multifunctional characteristics. Moreover, our investigation has implications for the application of machine-learning and other data-driven approaches for multifunctional materials discovery.