Stress defocusing in anisotropic compaction of thin sheets

We address the crumpling of thin sheets in between large scale curved cylinders. In contrast with the usual crushing of a paper ball, one curvature of the sheet is fixed here by the cylinders radius, yielding an anisotropic compaction. As compaction proceeds, it is found that sheets first develop singular folds involving ridges or developable cones, but eventually turn to regular folds free of any geometrical singularities, without ever having entered the plastic regime. This surprising uncrumpling transition corresponds to a stress defocusing. It is understood from a balance between bending and stretching energies on regular states.