Improved models for impact of Viscoplastic bodies

Abstract

Impact between two bodies is a complex phenomenon commonly occurs in many areas such as sports, automotive, geology and many more. Until now, modeling an impact is still a challenging task due to inherent imprecision of constitutive laws for the impact mechanics. Previously, impulse-momentum method was used as general principle to solve this dynamic problem. Then, impact is modeled by employing a lumped-parameter, which is represented by the spring and/or dashpot elements as a compliance at a small contact region around the point of contact. Through this method, the mechanics of contact during a short interval of impact event can be calculated. Formulation of the model using elastic, viscoelastic, elastoplastic or viscoplastic constitutive material behavior is employed as a contact law for the compliance at the small deforming region. At a very low impact velocity, an elastic model based on Hertz contact theory and the viscoelastic Hunt & Crossley model have accurately predicted impact responses. However, at higher impact velocities, a significant part of the initial kinetic energy is dissipated due to plastic deformation, stress wave propagation, sound, heat and other effects. An elastoplastic impact model can be used to predict the elastic-plastic deformation of the impacted bodies, however the effect of stress wave propagation is not considered in this model. This problem has been addressed by adopting a viscoplastic model that can predict the impact response which encompasses both elastic and plastic deformation and also considers the energy dissipated due to wave propagation. This study proposes two viscoplastic impact models that were developed from modification of previous viscoplastic models; Yigit and Ismail & Stronge models. The proposed model provides an alternative method to predict the impact responses by employing a linear spring element or combining a linear and nonlinear spring element in restitution phase of the compliance. The impact responses for several types of balls have been also studied by drop test experiments and finite element analysis. In experiment, various tests have been conducted to ensure accurate measurements of force and velocity for drops of different sports balls. On the other hand, an accurate finite element model (FE model) was developed and it was validated with previous FE model. As a result, the impact responses obtained from the proposed models have been validated with both experiment and FE analysis. In general, the proposed models can predict the maximum force and contact time with percentage error of less than 20 % and 11 % respectively. The proposed model was successfully improved the accuracy of impact response prediction for normal impact between two compact bodies. For the case of elastic impact, the proposed model gives the smallest energy loss of any of these previous models. Thus, it provides good estimation of contact forces and deformations, compared to the other viscoplastic models. Besides that, the impact responses for impact of different materials, sizes and impact velocities of the body have been obtained from the FE analysis. In overall, new developments for viscoplastic impact model and impact responses for colliding bodies were presented.