Dynamic behaviors of visco-elastic thin-walled spherical shells impact onto a rigid plate

Abstract

As a representative structure, ping-pong balls are usually used to study the mechanical properties of thin-walled spherical shells. In a previous study, the dynamic behaviors of ping-pong balls impinged onto a rigid plate were investigated. It was found that the dynamic deformation energy of the balls could be several times higher than that under quasi-static compression, which could not be completely explained by elastic-plastic material property, strain-rate and inertial effects. In this paper, more impact tests were conducted and the details including the contact time, deformation and rebound behaviors with different impact velocities were reinvestigated. Based on the experimental results, visco-elastic material model is applied and the numerical simulation of thin-walled spherical shells impact onto a plate is performed, in which the influences of the visco-elastic parameters and the impact velocity on the dynamic behaviors are studied. By adjusting the visco-elastic parameters, the contact time, deformation, and the coefficient of restitution agree well with the experimental results. Keywords Impact; visco-elastic; coefficient of restitution; spherical shell.Dynamic behaviors of visco-elastic thin-walled spherical shells impact onto a rigid plate INTRODUCTIONDue to high load-carrying efficiency and good aerodynamic properties, thin-walled spherical shells are extensively applied not only in engineering structures, but also for sports facilities, such as aircraft, submarine, pressure vessels, oil containers, footballs, tennis balls and so on. Considering loading conditions, their large deformation and buckling behaviors compressed against a rigid plate attract great attentions of researchers.In earlier decades, theoretical and experimental studies about the deformation modes and contact force of elastic and rigid-plastic spherical shells have been done by Updike and Kalnins (1970;1972), Kitching et al (1975), De Olivera andWierzbicki (1982), Gupta et al (1999), most of which focused on the quasi-static cases and the dynamic effects were not considered. To examine the ener- gy absorption of metal hollow sphere (MHS) materials, Ruan et al (2006) investigated the dynamic crushing of 1D and 2D ping-pong ball arrays under in-plane impacts and found that a single ball's load-deformation relation can be used to predict the ball-array's load deformation behavior. Hubbard and Stronge (2001) conducted the impact tests for ping-pong balls onto a flat plate with velocity 0-20m/s, and obtained the contact time and coefficient of restitution. However, in their analytical modeling, they considered the balls to be pure elastic. As a result, the predictions for the contact time and coefficient of restitution were both higher than the experiments, while the predicted energy dissipation was too little. Besides, Stronge and Achsoft (2007), and Arakawa et al (2007Arakawa et al ( , 2009) studied the impact behaviors of basketballs and golf balls, respectively. Bao and Yu (2012) conducted numerical simulations about the dy...

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