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Generalised Hertz — Hunt — Crossley Collision Model

Authors: Borovin G.K., Lapshin V.V. Published: 05.12.2018
Published in issue: #6(81)/2018  
DOI: 10.18698/1812-3368-2018-6-18-30

 
Category: Mathematics and Mechanics | Chapter: Differential Equations and Mathematical Physics  
Keywords: collinear collision, coefficient of restitution, nonlinear dynamics

The paper considers a nonlinear visco-elastoplastic model for a collinear collision between a body and a fixed barrier. The model combines the Hertz and Hunt --- Crossley collision models. We show that both elastic and perfectly inelastic collisions are possible, depending on the values of model parameters. We obtained the first integrals to the equations of motion for the deformation and restitution phases, as well as a solution by quadrature to the equations of motion describing the body. We determined the coefficient of restitution, the kinetic energy lost in the collision, and how they depend on the impact velocity and the constants of viscous and dry friction. For the case of an elastic collision, the coefficient of restitution is a monotonically decreasing function of impact velocity. As the impact velocity tends to zero, the coefficient of restitution tends to a certain maximum value that does not exceed unity, depends on the constant of dry friction only and decreases as it increases

The study was supported by RFBR (grant no. 16-01-00521)

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