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

Mihails Milehins, Dan B. Marghitu

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.

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.

Paper Structure

This paper contains 16 sections, 5 theorems, 97 equations, 9 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Contributions and Outline
  3. Model of the Physical System
  4. The Bouc-Wen-Simon-Hunt-Crossley Collision Model
  5. The Bouc-Wen-Maxwell Collision Model
  6. Application Example
  7. Model Parameter Identification
  8. Background
  9. Kharaz and Gorham (2000)
  10. Cross (2011)
  11. Villegas et al (2021)
  12. Conclusions and Future Work
  13. Notation and Conventions
  14. Analysis of the BWSHCCM
  15. Analysis of the BWMCM
  16. ...and 1 more sections

Key Result

Proposition A.1

If the solutions of the system given by Eq. eq:sys are uniformly bounded, then the outputs of the system given by Eq. eq:sys are uniformly bounded.

Figures (9)

  • Figure 1: Bodies $\mathcal{B}_1$ and $\mathcal{B}_2$ at the time of the collision
  • Figure 2: System diagram for Section \ref{['sec:AE']}
  • Figure 3: Evolution of the contact interface and the locations of the centers of mass during a collision of two balls under the influence of external forces
  • Figure 4: Evolution of the relative velocity at the contact interface and the velocities of the centers of mass during a collision of two balls under the influence of external forces
  • Figure 5: Evolution of the contact force and the external forces during a collision of two balls under the influence of external forces
  • ...and 4 more figures

Theorems & Definitions (13)

  • Definition A.1
  • Definition A.2
  • Definition A.3
  • Proposition A.1
  • proof
  • Lemma B.1
  • proof
  • Proposition B.2
  • proof
  • Lemma C.1
  • ...and 3 more