Abstract: In an aspect, provided herein are low density materials, including shell-based materials, with three-dimensional architectures formed, in part, via self-assembly processes. Shell-based materials of some embodiments exhibit a combination of ultralow density (e.g., ?100 mg cm?3 and optionally ?10 100 mg cm?3) and non-periodic architectures characterized by low defect densities and geometries avoiding stress concentrations. Low density shell based materials of some embodiments have architectures characterized by small curvatures and lack of straight edges providing enhance mechanical response. In some embodiments, for example, the present low density materials, including shell-based materials, providing a combination target mechanical properties including high stiffness-to-density ratios, mechanical resilience and tolerance for deformation.

Abstract: In an aspect, a composite material system comprises: a structure having an architected three-dimensional geometry; wherein said three-dimensional geometry is monolithic and deterministic; and a matrix phase; wherein said matrix phase at least partially infiltrates said structure. In some embodiments, the three-dimensional geometry is a nano- or micro-architected three-dimensional geometry.