Abstract:
In order to study the dynamic effects on the snap-through behaviour of an elastic spherical shell under normal impact, ping-pong balls were accelerated by projectiles fired from an air-gun and impinged onto a rigid plate with the velocity ranging 10-50m/s. Apart from the force-displacement relationship, a particular attention was paid to the evolution of the contact zone between the ball and the plate, as recorded by a high-speed digital camera. As a result, the impact duration, the maximum contact diameter, and the contact diameter at snap-through buckling under different impact velocities were obtained. An axi-symmetric finite element model is generated and the dynamic simulation is conducted using ABAQUS/Explicit. Based on the experiments and simulations, a theoretical model is proposed, which simplifies the deformed shape by piecewise constant-curvature regions, but captures the major features of the deformation process of a thin-walled spherical shell, such as the onset of the snap-through buckling, the evolution of the contact zone, etc. By taking into account the inertia effects in the deformed regions and minimizing the total work done, the evolution of the deformed shape of the shell is revealed. The theoretical predictions for the contact force and contact diameter are in good agreement, while it is concluded that the local inertia is mainly responsible for the difference between the dynamic deformation behavior and the quasi-static one.