  The mechanical response of cellular materials with spinodal topologies is
numerically and experimentally investigated. Spinodal microstructures are
generated by the numerical solution of the Cahn-Hilliard equation. Two
different topologies are investigated: "solid models," where one of the two
phases is modeled as a solid material and the remaining volume is void space;
and "shell models," where the interface between the two phases is assumed to be
a solid shell, with the rest of the volume modeled as void space. In both
cases, a wide range of relative densities and spinodal characteristic feature
sizes are investigated. The topology and morphology of all the numerically
generated models are carefully characterized to extract key geometrical
features and ensure that the distribution of curvatures and the aging law are
consistent with the physics of spinodal decomposition. Finite element meshes
are generated for each model, and the uniaxial compressive stiffness and
strength are extracted. We show that while solid spinodal models in the density
range of 30-70% are relatively inefficient (i.e., their strength and stiffness
exhibit a high-power scaling with relative density), shell spinodal models in
the density range of 0.01-1% are exceptionally stiff and strong. Spinodal shell
materials are also shown to be remarkably imperfection insensitive. These
findings are verified experimentally by in-situ uniaxial compression of
polymeric samples printed at the microscale by Direct Laser Writing (DLW). At
low relative densities, the strength and stiffness of shell spinodal models
outperform those of most lattice materials and approach theoretical bounds for
isotropic cellular materials. Most importantly, these materials can be produced
by self-assembly techniques over a range of length scales, providing unique
scalability.
