An Analytical Solution for Non-Linear Viscoelastic Impact

The paper presents an analytical solution for the centric viscoelastic impact of two smooth balls. contact period has phases, compression and restitution, delimited by moment corresponding to maximum deformation. motion system is described a nonlinear Hunt–Crossley equation that, when compared linear model, advantage hysteresis loop closing in origin. There only single available obtained from theorem momentum. In order solve problem, literature, there are accepted different supplementary hypotheses based on energy considerations. present paper, differential written under convenient form; it shown that can be integrated first integral found—this being main asset work. Then, all parameters calculated. effect coefficient restitution upon collision characteristics emphasized, presenting importance compliant materials, domain small coefficients restitution. results (variations approach, velocity, force vs. time loop) models due Lankarani Flores. For quasi-elastic collisions, practically same three models. smaller values good agreement Flores model. simplified algorithm calculus also presented. This avoids large volume required solving transcendental equations definite integrals mathematical method proposed, model given Hunt Crossley, extended elasto–visco–plastic