Analysis of the Mean Pressure for Elastic Impact Considering Wave Propagation

Impact events exist widely in engineering and are the forefront problems in mechanic filed. For the impact, stress wave propagation inevitably occurs and a velocity metric is normally employed to consider the expansion of the contact boundary. Based on the expansion speed of the contact boundary and the wave speeds of the longitudinal and Rayleigh waves, the impact process can be divided into supersonic, transonic and subsonic stages, which appear sequentially in the impact process. However, the effect of stress waves on the impact response has never been studied in detail and no available theoretical solution can be employed to describe the stress distributions in these three stages. To comprehensively understand the effect of stress waves on the impact response, the relationship between the mean pressure and the contact radius is studied by simulating the process of a rigid sphere impacting the elastic half-space. It is found that the mean pressure is the product of the material wave impedance and the impact velocity in the supersonic stage, transonic stage and part of the subsonic stage and the mean pressure corresponds to value calculated by Hertzian pressure distribution in the rest part of the subsonic stage and the whole unloading process.