Someone argues: "Pushing a dent into the wall of an aluminium drinks can with a thumb…
PHYSICS · Subjective · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids
Bending, Ringing, Breaking and Flowing, Ch Buckling, plates and elastic foundations
Problem
Someone argues: "Pushing a dent into the wall of an aluminium drinks can with a thumb costs about the same energy whether the metal bends into the new shape or stretches into it, since both are just ways of moving the same amount of metal out of its rest shape." The can wall has thickness h=0.10mm; a thumb produces a dent of depth w=2.0mm over a roughly circular patch of span L=20mm. Using the scaling for bending versus stretching energy of a thin sheet, decide whether the claim is right, and state by roughly what factor the two energies differ for this dent.