标题： 基于Bouc-Wen模型的增量碰撞定律：外力和特殊情况 显示英文标题

标题： Incremental Collision Laws Based on the Bouc-Wen Model: External Forces and Corner Cases

摘要： 在题为《凸粘塑性体二元直接共线碰撞的Bouc-Wen模型》并发表于《计算与非线性动力学杂志》（第20卷，第6期，2025年6月）的文章中，作者研究了采用基于Bouc-Wen滞后微分模型的两种增量碰撞定律的二元直接共线碰撞的数学模型。 结果显示这些模型具有良好的解析性质，并进行了若干模型参数识别研究，证明这些模型能够准确捕捉各种碰撞现象的本质。 在本文中，上述模型通过将外部力的影响建模为属于特定函数空间的时间相关输入进行了增强。 此外，模型具有良好解析性质的参数范围被扩展到之前出版物中未考虑的几个极端情况。 最后，对之前进行的模型参数识别研究进行了扩展，并提供了一个额外的模型参数识别研究，以尝试验证增强模型表示外部力影响的能力。 显示英文摘要

摘要： In the article titled "The Bouc-Wen Model for Binary Direct Collinear Collisions of Convex Viscoplastic Bodies" and published in the Journal of Computational and Nonlinear Dynamics (Volume 20, Issue 6, June 2025), the authors studied mathematical models of binary direct collinear collisions of convex viscoplastic bodies that employed two incremental collision laws based on the Bouc-Wen differential model of hysteresis. It was shown that the models possess favorable analytical properties, and several model parameter identification studies were conducted, demonstrating that the models can accurately capture the nature of a variety of collision phenomena. In this article, the aforementioned models are augmented by modeling the effects of external forces as time-dependent inputs that belong to a certain function space. Furthermore, the range of the parameters under which the models possess favorable analytical properties is extended to several corner cases that were not considered in the prior publication. Finally, the previously conducted model parameter identification studies are extended, and an additional model parameter identification study is provided in an attempt to validate the ability of the augmented models to represent the effects of external forces.