Contact and compression of elastic spherical shells : the physics of a ` ping ± pong ’ ball

We study the deformation of a thin elastic shell in di€ erent situations: case (i) contact with a rigid plane; and case (ii) subject to a localized load. In case (i), experiments show a ® rst-order (discontinuous) transition between two di€ erent con® gurations: the ® rst characterized by ̄ at 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 s̀low’ impact of an elastic ball presents, qualitatively, a highly anomalous behaviour of the restitution coe cient 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. §