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.

本文对不同材料密度的可变形球体的自由表面水进入过程中的水弹性耦合进行了数值研究。重点是流体动力、应力载荷、球体变形、球体的润湿面积和腔动力学，包括弹性球体的影响和自由表面流动中的水弹性耦合行为。结果表明，弹性波在球体中的传播与球体密度成比例。对于浸入水中的弹性球体，讨论了球体变形的变化及其能量转换机制。从空腔的接触点位置可以看出，球体的润湿面积与球体变形密切相关。第一个变形循环是润湿面积与球体密度关系的转折点。根据地图m* - η在这项工作中总结，球体变形对腔体形状的影响可以从材料特性和冲击条件粗略预测。