  Open-cell graphitic foams were fabricated by chemical vapor deposition using
nickel templates and their compressive responses were measured over a range of
relative densities. The mechanical response required an interpretation in terms
of a hierarchical micromechanical model, spanning 3 distinct length scales. The
power law scaling of elastic modulus and yield strength versus relative density
suggests that the cell walls of the graphitic foam deform by bending. The
length scale of the unit cell of the foam is set by the length of the struts
comprising the cell wall, and is termed level I. The cell walls comprise hollow
triangular tubes, and bending of these strut-like tubes involves axial
stretching of the tube walls. This length scale is termed level II. In turn,
the tube walls form a wavy stack of graphitic layers, and this waviness induces
interlayer shear of the graphitic layers when the tube walls are subjected to
axial stretch. The thickness of the tube wall defines the third length scale,
termed level III. We show that the addition of a thin, flexible ceramic Al2O3
scaffold stiffens and strengthens the foam, yet preserves the power law
scaling. The hierarchical model gives fresh insight into the mechanical
properties of foams with cell walls made from emergent 2D layered solids.
