Abstract A semianalytical model was proposed to study the vertical impact of a slender rod striking a rigid flat surface. Within the semianalytical model, we considered the longitudinal vibration of the rod by using continuum mechanics while employing a plastic contact model, an equivalent spring model, to describe the contact of the linear hardening hemispherical tip and a rigid flat surface. The predicted displacement and velocity histories along the rod agreed well with the corresponding finite element simulations. In addition, from the proposed semianalytical model, we determined that there was a critical length/diameter ratio that can be used for any plastic contact of a linear hardening rod. The critical length/diameter ratio was approximately 17 for a rod made of 316 stainless steel. Below this critical length/diameter ratio, the rod behaved as a rigid body, i.e., the velocities of different sections of the rod reversed simultaneously during the impact. Above this critical length/diameter ratio, the velocity of the top section reversed much earlier than the other sections of the rod; hence, the slenderness effect should be accounted for in these conditions.

中文翻译：

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316不锈钢棒垂直冲击的半解析模型

摘要 提出了一个半解析模型来研究细长杆撞击刚性平面的垂直冲击。在半解析模型中，我们使用连续介质力学考虑杆的纵向振动，同时使用塑性接触模型，等效弹簧模型来描述线性硬化半球尖端和刚性平面的接触。沿杆的预测位移和速度历史与相应的有限元模拟非常吻合。此外，根据建议的半解析模型，我们确定存在一个临界长度/直径比，可用于线性硬化棒的任何塑性接触。对于由 316 不锈钢制成的杆，临界长度/直径比约为 17。低于这个临界长度/直径比，杆表现为刚体，即杆不同部分的速度在撞击过程中同时反转。超过这个临界长度/直径比，顶部的速度比杆的其他部分早得多；因此，在这些条件下应考虑细长效应。