Modeling of Impact Dynamics: A Literature Survey

The purpose of this paper is to present a general overview of impact analysis and some of the most important approaches in this area. It is not intended to provide a tutorial on impact with all the required mathematical developments. The paper is a preliminary literature survey by the authors whose goal is to develop a sound and a practical methodology to analyze impact and implement it within the ADAMS program. 1. Introduction The dynamic analysis of multibody systems with kinematic constraints is a wellestablished area of mechanics. To make mathematical modeling possible, bodies are assumed to be perfectly rigid and joints to have no clearance. Many computer programs have been built on these assumptions although they include enhancements to model flexible bodies, friction and non-linear springs and dampers. One of the toughest physical phenomena to model is the impact between two bodies. Impact may be defined as a sudden change in the momentum of each contacting body, without a corresponding change in position. Impact is inherent to unilateral constraints, i.e. a constraint that acts at a given instant only in one direction of the common normal of contacting surfaces. The subject of impact attracts the interest of scientists and engineers from different areas of knowledge from astrophysics to robotics. The common goal is to develop theories that can predict the behavior of colliding objects. Our focus in this paper, however, will be mainly on impact modeling as it relates to rigid bodies. The mechanical engineer's interest in impact problems is motivated by the desire to develop valid models for mechanical systems where impact is inherent to their function (e.g. crushers, circuit breakers, presses). Other issues such as play in the joints and damage due to accidental or functional impact are also important to understand. In the evolution of impact theory four major aspects emerged as distinct (but not unrelated) subjects of interest. Depending on impact characteristics (velocity, materials), the assumptions made and the results sought, one aspect will become more predominant than the others thus leading to a solution approach to impact analysis. These four aspects are: • Classical mechanics • Elastic stress wave propagation • Contact mechanics • Plastic deformation Below is an overview of these four aspects.