Inelastic impact and the coefficient of restitution
A model for the impact between a structurally deformable sphere and a rigid flat surface is presented. It includes a nonlinear contact element that accounts for energy loss due to local plastic deformation or flattening of the sphere, a viscous element that accounts for energy loss due to wave propagation and/or damping, and a linear stiffness element that accounts for recoil effect during and after contact. A piece-wise linear version of the model is also presented, which facilitates normalization of the governing equations with helpful insights into the impact problem. It is demonstrated that the impact problem could be characterized by two non-dimensional parameters, namely the relative stiffness l, which accounts for recoil effect, plastic deformation and/or flattening of the ball, and the damping ratio, z, which accounts for viscous and/or wave propagation effects. It is shown that the impact response and the Coefficient of Restitution are dependent on both parameters. The model predictions are compared to experimental measurements for sports balls that are excellent examples of deformable spheres, with promising results.
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