The Bouc-Wen Model for Binary Direct Collinear Collisions of Convex Viscoplastic Bodies
<|reference_start|>The Bouc-Wen Model for Binary Direct Collinear Collisions of Convex Viscoplastic Bodies: We study mathematical models of binary direct collinear collisions of convex viscoplastic bodies based on two incremental collision laws that employ the Bouc-Wen differential model of hysteresis to represent the elastoplastic behavior of the materials of the colliding bodies. These collision laws are the Bouc-Wen-Simon-Hunt-Crossley collision law (BWSHCCL) and the Bouc-Wen-Maxwell collision law (BWMCL). The BWSHCCL comprises of the Bouc-Wen model amended with the nonlinear Hertzian elastic spring element and connected in parallel to a nonlinear displacement-dependent and rate-dependent energy dissipation element. The BWMCL comprises of the Bouc-Wen model amended with the nonlinear Hertzian elastic spring element and connected in series to a linear rate-dependent energy dissipation element. The mathematical models of the collision process are presented in the form of finite-dimensional initial value problems. We show that the models possess favorable analytical properties (e.g., global existence, uniqueness and boundedness of the solutions) under suitable restrictions on the ranges of their parameters. Furthermore, we show that excellent agreement can be achieved between the experimental data and the data from the numerical simulation of the mathematical models across a wide range of initial relative velocities and material properties of the colliding bodies while using parameterizations that are independent of the initial relative velocity.<|reference_end|>
@article{milehins2024the,
    title={The Bouc-Wen Model for Binary Direct Collinear Collisions of Convex
  Viscoplastic Bodies},
    author={Mihails Milehins and Dan B. Marghitu},
    journal={arXiv preprint arXiv:2410.08147},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.08147},
    primaryClass={physics.class-ph cs.SY eess.SY}
}