Incremental Collision Laws Based on the Bouc–Wen Model: Improved Collision Models and Further Results

Abstract 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. 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.