  Composites are ideally suited to achieve desirable multifunctional effective
properties since the best properties of different materials can be judiciously
combined with designed microstructures. Here we establish cross-property
relations for two-phase composite media that link effective elastic and
electromagnetic wave characteristics to one another, including the respective
effective wave speeds and attenuation coefficients, which facilitate
multifunctional material design. This is achieved by deriving accurate formulas
for the effective electromagnetic and elastodynamic properties that depend on
the wavelengths of the incident waves and the microstructure via the spectral
density. Our formulas enable us to explore the wave characteristics of a broad
class of disordered microstructures because they apply, unlike conventional
formulas, for a wide range of incident wavelengths, i.e., well beyond the
long-wavelength regime. This capability enables us to study the dynamic
properties of exotic disordered ``hyperuniform'' composites that can have
advantages over crystalline ones, such as nearly optimal, direction-independent
properties and robustness against defects. We specifically show that disordered
``stealthy'' hyperuniform microstructures exhibit novel wave characteristics,
e.g., low-pass filters that transmit waves ``isotropically'' up to a finite
wavenumber. Our cross-property relations for the effective wave characteristics
can be applied to design multifunctional composites via inverse techniques.
Design examples include structural components that require high stiffness and
electromagnetic absorption, heat-sinks for CPUs, and sound-absorbing housings
for motors that have to efficiently emit thermal radiation and suppress
mechanical vibrations, and nondestructive evaluation of the elastic moduli of
materials from the effective dielectric response.
