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Flexibility and brittleness are properties of solids. Because of its very unusual quantum properties (compared to nearly all other elements - hydrogen is weird too) flexibility and brittleness may not really apply to solid helium.

Helium CAN be turned into a solid - but it requires elevated pressures and REAAALLLY low temperatures. Because of quantum effects, it can remain liquid all the way to absolute zero at normal pressures. To get a solid requires pressures above about 2.5 MPa (25 bar) and temperatures down around 1 Kelvin. In theory you could get it solidify at room temperature if you could get it up to a pressure of 114,000 atmospheres (1,675,338 psi) but well before those pressures helium tends to diffuse into whatever solid forms the walls of its container - causing embrittlement, leading to fractures - aaaaannnnnnddddd - POW!

Suffice it to say that at such extreme temperatures flexibility is difficult to measure. At least one experiment found no penetration of a probe 0.6-mm in diameter until the force exerted exceeded 330 dyne - at which point it gradually penetrated the sample at a rate of about 3 µm/sec. As soon as the probe was withdrawn, the indentation "healed" - kind of like rubber rebounding after compression, but in this case it more like the helium flowing back into the depression. Apparently solid helium doesn't so much flex as flow.

Brittleness usually is defined as the response to stresses. As already noted, it sort of flows when subject to compressive stress. Solid helium als behaves strangely under shear stresses. It can be a "supersolid", i.e. a solid exhibiting superfluid characteristics like zero viscosity flow, consequently when placed under shear stress it may decouple from the the shearing surface making any measurements meaningless.

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