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In a solid, elasticity is described by the Young modulus E.

Let us consider a thin sheet of material of thickness h. The bending rigidity is usually Eh³.

I wanted to know if they are "abnormal" materials in which the bending rigidity is much smaller than Eh³, for example some polymers or foams...

Thanks !

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Yes; a continuous track (such as a tank track, for example) has a nonzero effective Young’s modulus but zero bending rigidity. This is true for any sheet containing revolute joints. The 1-D version is a chain. (These aren’t continuous materials, of course, but then neither is a foam, which you mentioned in your question.)

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