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Describing the plastic deformation of aluminium softball bats


Hollow aluminium bats were introduced over 30 years ago to provide improved durability over wooden bats. Since their introduction, however, interest in hollow bats has focused almost exclusively around their hitting performance. The aim of this study was to take advantage of the progress that has been made in predicting bat performance using finite elements and apply it to describe bat durability. Accordingly, the plastic deformation from a ball impact of a single-wall aluminum bat was numerically modelled. The bat deformation from the finite-element analysis was then compared with experiment using a high-speed bat test machine. The ball was modelled as an isotropic, homogeneous, viscoelastic sphere. The viscoelastic parameters of the ball model were found from instrumented, high-speed, rigid-wall ball impacts. The rigid-wall ball impacts were modelled numerically and showed good agreement with the experimentally obtained response. The strain response of the combined bat-ball model was verified with a strain-gauged bat at intermediate ball impact speeds in the elastic range. The strain response of the bat-ball model exhibited positive correlation with the experimental measurements. High-speed bat-ball impacts were performed experimentally and simulated numerically at increasing impact speeds which induced correspondingly increased dent sizes in the bat. The plastic deformation from the numerical model found good agreement with experiment provided the aluminium work hardening and strain rate effects were appropriately described. The inclusion of strain rate effects was shown to have a significant effect on the bat deformations produced in the finite-element simulations. They also helped explain the existence of high bat stresses found in many performance models.

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Correspondence to Lloyd Smith.

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Biesen, E., Smith, L. Describing the plastic deformation of aluminium softball bats. Sports Eng 10, 185–193 (2007).

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  • bat performance
  • plasticity
  • softball