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I noticed that whenever I bunch up aluminum foil (into a ball), it becomes extremely hard to compress.
If I use another piece of the same amount of aluminum foil, and keep folding it in, I arrive at a much smaller volume. It is full of air and much lighter than the same shape of solid aluminum, though, it is still extremely hard to compress.
Question:
"If you, the reader, were to rip a page from this journal and crumple it, squeezing it with your hands into a ball as hard as you can, the resulting object is still more than 75% air. What gives this crumpled sheet its surprising strength and how does the ultimate size of the sheet depend on the forces applied?" [emph. added] —Matan et al., "Crumpling a thin sheet"
Crumpling produces ridges—corrugations—that are both low in amplitude and wavy:
(Lin et al., "X-ray tomography of a crumpled plastoelastic thin sheet"
The phenomenon of increased flexural rigidity through corrugation allows wavy brick walls to be both thin and sturdy, with relatively little lateral instability:
Upon crumpling, the material gets in the way of itself, and substantial jumps in compressive loading are repeatedly needed to buckle new regions. (A terser description is "metastable states of regions jammed through steric hindrance.")
Contrast this behavior with that of a long smooth sheet of foil, which buckles easily because it lacks lateral support, because the critical load scales with the length squared, and because initial postbuckling can proceed by a smoothly increasing load.
"...[M]ore than half of the interior is still filled with air. This volume fraction is much smaller than the fcc packing, 0.74, and the resistance divergence point, 0.75, in elastic sheets. One question arises: How does this structure derive its incredible resistance from such an inefficient packing compared to the granular system? One reason is that the system is constantly trapped in metastable states due to the non-Markovian nature of the process. Another conceivable answer is from the material science. It is known in mechanical engineering that a beam buckles under an axial load when its length exceeds 50 to 200 times of its thickness. For a shorter beam, the deformation switches from the bending modulus to the normally much-larger Young’s modulus. In other words, each material has an intrinsic minimum size of facet, below which it takes an enormously large stress. We believe this causes the poor packing of the hollow polyhedrons surrounded by these facets inside the crumpled structure. The surprising thing is that, rather than complicating the structure, the plasticity enables the interior to reach a higher fractal dimension and more homogeneous packing, both of which contribute to its high mechanical resistance." [emph. added] —Lin et al., "X-ray tomography of a crumpled plastoelastic thin sheet
Deboeuf et al. "A comparative study of crumpling and folding of thin sheets"
"Despite the complexity, crumpled sheets (as well as origami structures) are comprised of only a handful of building block structures. The four most [dominant are] the bend, the fold, the d-cone, and the stretching ridge... Slender systems are easily bent due to the tiny energetic cost of bending when compared to stretching... Folds are primarily a result of plasticity, meaning energy loss has occurred and memory has been created in the sheet (typically required for origami). Confining a sheet in three dimensions (as in crumpling a ball) leads to constraints on the sheet that can no longer be satisfied by bending alone. Confinement forces a sheet to stretch. Stretching comes at a high cost, so the system minimizes the total amount of stretching present. In thin, marginally confined systems, stretching is typically localized to a (near) singular point known as a developable cone (d-cone). Finally, if confinement is increased and two d-cones are created in a sheet, they are linked by a structure known as a stretching ridge... Crumples are complex but are trustworthy materials. They are structures dominated by bending at many different length scales similar to a single stretching ridge." [emph. added] —Croll et al., "The compressive strength of crumpled matter"
Croll et al., "The compressive strength of crumpled matter"
Essentially, the structure formed by crumpling has some 3-D truss-like characteristics requiring substantial additional plastic deformation to obtain progressive crushing, even though much of the structure is empty air. In comparison, simple folding—even of multiple layers—requires plastic deformation only at the surfaces of each sheet, with the neutral axis (i.e., the middle of each sheet) remaining largely undeformed.
For additional discussion, references, and useful keywords, see also Lin et al.'s "Crumpling under an ambient pressure," Balankin et al.'s "Statistics of energy dissipation and stress relaxation in a crumpling network of randomly folded aluminum foils," and Habibi et al.'s "Effect of the material properties on the crumpling of a thin sheet."
Aluminum (and most solids) are nearly impossible to compress (i.e. very high bulk modulus). What you are doing when crumpling or flexing a loose sheet of metal is causing it to move and buckle, not sustain compressive stresses.
Once you get it in a ball shape where the aluminum has air gaps but is contacting metal to metal in a skeletal structure, you are resisting the actual compressive strength of the metal. Like trying to crush a sintered metal ball with your hands.
Why does bunched up aluminum foil become so extremely hard to compress?
It is hard to compress if we compare with the first steps of forming the Al foil ball.
But pure Al has a compressive strength of about $12 \; \rm{kg_f/mm}^2$. So the order of magnitude of the force to compress a piece of Al of $1 \; \rm{cm}^2$ of cross section is $1$ ton.
I believe that our grip power is well below that. Nevertheless we can deform a little bit a ball of Al foil using both hands. The ball is deformed to a kind of ellipsoid, that can be restored to a spherical shape by compressing it in orthogonal directions. It is the same process that could be made by a compressing machine in a ball of pure Al. But employing a much bigger force.
So, what we make from the foil is a very soft ball of Al because there is much air inside between the surfaces.
