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Abstract. An explicit finite element (FE) tennis ball model which illustrates the effects of the viscoelastic materials of a tennis ball on ball deformation and bounce during normal impacts is presented. A tennis ball is composed of a rubber core and a fabric cover comprised of a woolnylon mix which exhibit non-linear strain rate properties during high velocity impacts. The rubber core model was developed and validated using low strain rate tensile tests on rubber samples as well as high velocity normal impacts of pressurised cores at velocities ranging from 15 m/s to 50 m/s. The impacts were recorded using a high speed video (HSV) camera to determine deformation, impact time and coefficient of restitution (COR). The material properties of the core model were tuned to match the HSV results. A two component anisotropic fabric model was created which included artificial Rayleigh damping to account for hysteresis effects, and the core model 'tuning' process was used to refine the cloth layer. The ball model's parameters were in good agreement with experimental data at all velocities for both cores and complete balls, and a time sequenced comparison of HSV ball motion and FE model confirmed the validity of the model. IntroductionThe early game of tennis, called real tennis, originated in France in the 13 th century and balls were made of wool covered with sheepskin. The game became so popular that a few hundred years later, the king Henry IV defined standards for the manufacturing of balls which had to be covered with white cloth and stuffed with strips of cloth tied with thread [1]. It is not until 1873 that Major Wingfield introduced lawn tennis which is the closest version of today's tennis, and the manufacturing process of tennis balls has barely changed since then.Three types of tennis balls including harder fast-speed balls for slow surfaces and larger slow-speed balls for fast surfaces are currently allowed by the International Tennis Federation [2], but the main balls used in professional championships are regular pressurised tennis balls, also called Type 2 balls. These balls consist of a rubber core covered by two dumbbell shaped pieces of cloth which are made of wool and nylon fibres in the weft direction and cotton fibres in the warp direction. During the manufacturing process, each dumbbell is cut from a large sheet of fabric at a 45 degree angle relative to the fibres' orientation to facilitate the application of the cloth on the core. The dumbbells are dipped into a rubber sealing solution and are semi-automatically applied to the cores. The balls are then heated into a press to cure the rubber solution, finish curing the core, and smoothen the seam formed by the excess rubber sealing solution after application of the dumbbells on the core. Finally, the ball goes through a steaming process to raise the cloth fibres and give it a fluffy aspect.

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