Computing the composite coefficient of restitution for inelastic impact of dissimilar bodies

Abstract

This paper develops an analytical method for computing the composite coefficient of restitution (COR) for a collision between dissimilar bodies composed of strain-hardening materials. This method can be used for lumped parameter modeling of collisions in which yielding occurs during impact in either one or both colliding bodies. The effect of the strain-hardening coefficient and relative impact velocity on a composite COR of either similar or dissimilar bodies is investigated. It is shown that the effect of the strain-hardening coefficient is significant when yield stresses of the colliding bodies are close to one another. Furthermore, for a collision between dissimilar bodies, the composite COR depends mostly on the hardening modulus of the body with the more compliant contact region. Also, the composite COR decreases as relative impact velocity increases. Finally, a lumped parameter nonlinear spring model is used to predict the normal force-displacement behavior of the two dissimilar bodies in a collinear collision. This lumped parameter model can be extended to more complex granular flow simulations involving a large number of particles. The resulting analytical expression can be useful for rigid body dynamic analysis codes as well as in design analysis.