Abstract When elastic spheres enter the water from air, the fluid–structure interaction becomes a complex problem characterized by large deformations. This paper focuses on the deformation behaviors of elastic spheres during water entry. Based on a strong coupling method, a numerical approach to the water entry of elastic spheres is established and validated using the experimental data. In addition to the descriptions of the free surface flows under impacting elastic spheres, the physical mechanism underlying the continuous deformation behaviors of elastic spheres during water entry is also identified. The results show that the magnitude of the prolate deformation is smaller than that of the oblate deformation under the action of hydrodynamic pressure. Additionally, the deformation period of the elastic spheres is related to the material shear modulus, but not to the impact velocity. Previous experimental results describing a linear relationship between the deformation period and the combination parameter for time, D ∕ ( μ 0 ∕ ρ S ) 1 ∕ 2 , are confirmed. The magnitude of sphere deformation is affected by the material shear modulus and impact velocity. The results also show the change characteristics for the kinetic and strain energies of elastic spheres with respect to the water entry time.

中文翻译：

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入水过程中弹性球体变形行为的数值研究

摘要 当弹性球体从空气进入水中时，流固耦合成为一个以大变形为特征的复杂问题。本文重点研究弹性球体在入水过程中的变形行为。基于强耦合方法，建立了弹性球入水的数值方法，并使用实验数据进行了验证。除了对弹性球撞击下自由表面流动的描述外，还确定了弹性球在入水过程中连续变形行为的物理机制。结果表明，在动水压力作用下，扁长形变形的幅度小于扁扁形变形的幅度。此外，弹性球的变形周期与材料剪切模量有关，与冲击速度无关。先前的实验结果描述了变形周期与时间组合参数 D ∕ ( μ 0 ∕ ρ S ) 1 ∕ 2 之间的线性关系。球体变形的大小受材料剪切模量和冲击速度的影响。结果还显示了弹性球体的动能和应变能随入水时间的变化特征。