Elastic anisotropy and wave propagation properties of multifunctional hollow sphere foams

Obtaining multifunctionality from microstructures instead of constituents provides a new direction for developing multifunctional materials. Periodic hollow sphere foams (HSFs) offer one lightweight structural motif with open and closed cells, high energy absorption, low thermal conductivity, snap-through instability, and triple negative material indices. Here, we investigate the direction-dependent mechanical property, instability, and elastic wave isolation behavior of HSFs. Explicit formulas, stereographic projections, and general scaling relationships are developed to quantify and visualize the anisotropic mechanical properties of HSFs. By investigating the directional wave propagation in HSFs, extremely wide phononic band gaps are identified in the HSFs. The derived formulas and the simulation-informed parametric maps allow the design of HSFs with desired static and dynamic anisotropic property profiles, including tailorable direction-dependent stiffness/shear modulus, negative Poisson's ratio, and wave isolation properties. Building upon these results, multifunctional design concepts of HSFs are further set forth. This study not only reveals tailorable mechanical anisotropy and band gap in HSFs, but also develops a general approach to investigate the direction-dependent properties of periodic materials, enabling multifunctional applications where lightweight, direction-dependent property, wave attenuation, and programmability are required simultaneously.