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Area of Science:

  • Physics
  • Materials Science
  • Mechanical Engineering

Background:

  • Hertz's linear elastic theory is a cornerstone for analyzing sphere collisions.
  • Viscous dissipation often complicates elastic impact analyses.

Purpose of the Study:

  • To validate Hertz's theory for central sphere collisions within a viscoelastic framework.
  • To elucidate the role of viscous dissipation on collision outcomes.

Main Methods:

  • Developed a viscoelastic model for central sphere collisions.
  • Analyzed energy loss and its impact on collision parameters.

Main Results:

  • Hertz's theory accurately predicts collision time and maximum contact area despite significant energy loss.
  • Collision parameters show weak dependence on impact velocity.
  • Observed apparent size-dependent yield strength due to differential energy dissipation.

Conclusions:

  • Hertz's theory remains robust for predicting key collision metrics in viscoelastic scenarios.
  • Viscous dissipation's effect is less influential on collision time and contact area than anticipated.
  • Apparent yield strength variation is an artifact of energy dissipation differences across object sizes.