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Effect of Large Deflections during Impact of Inflated Thin-Walled Spherical Shell

A planar theory for oblique impact of an inflated thin-walled spherical shell (sports ball) against a rough rigid surface is presented and compared with rigid-body theory. This large deflection theory is based on assuming that during impact, the initially spherical ball flattens against the constraint surface while the remainder of the ball (moving with uniform translational velocity) remains undeformed. With the assumed deformation field, this theory for impact of a thin-walled shell includes a velocity discontinuity between the contact area that has been flattened and the moving part of the shell. During compression and restitution phases of contact, flow of momentum across the periphery of the flattened contact area results in a non-conservative momentum flux reaction. For a ball that is both translating and rotating, the distribution of the normal component of velocity for material entering and exiting the continuously changing flattened contact area results in a distribution of momentum flux force intensity around the periphery of the contact region and consequently, a momentum flux torque acting on the flattened sphere. This paper relates changes in rebound velocity and rate-of-spin of thin-walled inflated spherical shells that result from impact to structural properties as well as the maximum deflection.
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