This paper presents a numerical study of the hydroelastic coupling during the free-surface water entry of deformable spheres of different material densities.The focus is on the hydrodynamic forces,the stress loads,the sphere deformations,the wetted areas of the sphere and the cavity dynamics,including the impacting of the elastic spheres and the hydroelastic coupled behaviors in the free surface flows.It is shown that the elastic wave propagation in the sphere scales with the sphere density.For elastic spheres immersed in the water,the variation of the sphere deformations and its energy transformation mechanism are discussed.From the contact point positions of the cavity,it can be seen that the wetted area of the sphere is closely related with the sphere deformation.The first deformation cycle is a turning point in the relation between the wetted area and the sphere density.Based on the map of m*-η summarized in this work,the influence of the sphere deformation on the shape of the cavity can be roughly predicted from the material properties and the impact conditions.
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