Contact and compression of elastic spherical shells: the physics of a 'ping-pong' ball

We study the deformation of a thin elastic shell in different situations: case (i) contact with a rigid plane; and case (ii) subject to a localized load. In case (i), experiments show a first-order (discontinuous) transition between two different configurations: the first characterized by flat contact between the shell and the rigid plane and the second by an inversion of curvature leading to contact with the plane along a circular ridge. In addition, the 'slow' impact of an elastic ball presents, qualitatively, a highly anomalous behaviour of the restitution coefficient due to the dissipative energy caused by the friction between the shell and the rigid plane. Case (ii) does not present a transition for small deformations; however, for large deformations on a spherical shell there is a symmetry breaking of the axisymmetric fold shell into corners and polygons to diminish its energy.