Literature survey of contact dynamics modelling(4)

Literature survey of contact dynamics modelling

plastic impactðe¼0Þ.The coe?cient of restitution depends on many elements,such as the geo-metry of the bodies in contact,the approach velocity,the material properties,the duration of contact and,possibly,friction[9].Related to the energy loss and coe?cient of restitution is the phenomenon of wave propagation.Since real bodies are not perfectly rigid,their parts are not instantaneously subjected to the same change of motion following the impact.The disturbance generated at the contact point travels in the body as stress(and deformation)waves with a?nite velocity[2,11].These waves produce oscillations and part of the impact(kinetic)energy is con-verted to the energy associated with this vibration.A useful parameter to quantify this situation is the ratio between the duration of impact and the period of the fundamental natural mode of vibration of the impacting bodies.The greater is this ratio,the smaller is the energy dissipation associated with the elastic waves since they can travel across the bodies many times before the impact ends.If this ratio is large enough,a quasi-equilibrium state is reached[2].These obser-vations are complemented by Stronge[11]who states that stress waves contribute to energy dissipation during collision if the relative size of the bodies is di?erent from unity.In this case,the waves in the larger body do not have su?cient time to re?ect from any boundary and,in essence, remain‘trapped’in the body.If the two impacting bodies are similar in size and material prop-erties,the vibration energy lost is negligible[11].The energy?ow associated with impact dynamics in the normal direction is illustrated in Fig.3.

The dependence of e on the approach velocity can be explained by considering the previously introduced ratio of the impact time to the fundamental period of vibration.If this ratio is large, then the coe?cient of restitution is mainly determined by the plastic deformation near the impact point.The velocity of impact determines the extension of plastic deformation and this accounts for the basic velocity sensitivity of the coe?cient of restitution of spherical http://www.77cn.com.cnually,bodies with a low ratio of surface area to volume(like spheres)present this kind of behavior[2,9].For slender bodies like beams or plates,the time of impact tends to be short compared with the period

of propagation of stress waves.Thus,a more signi?cant portion of the initial kinetic energy re-

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