The Bouc-Wen Model for Binary Direct Collinear Collisions of Convex Viscoplastic Bodies

TL;DR

This paper develops and analyzes two mathematical models for binary collinear collisions of convex viscoplastic bodies using Bouc-Wen hysteresis models, demonstrating their analytical properties and good experimental agreement.

Contribution

It introduces two novel Bouc-Wen-based collision laws for viscoplastic bodies and proves their well-posedness, with parameter identification showing accurate modeling across velocities.

Findings

Models exhibit global existence, uniqueness, and boundedness.

Good agreement with experimental data across various velocities.

Parameterizations are independent of initial velocities.

Abstract

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 a nonlinear Hertzian elastic spring element and connected in parallel to a nonlinear displacement-dependent and velocity-dependent energy dissipation element. The BWMCL comprises of the Bouc-Wen model amended with a nonlinear Hertzian elastic spring element and connected in series to a linear velocity-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 values of their parameters. Furthermore, based on the results of two model parameter identification studies, we demonstrate that good agreement can be attained between experimental data and numerical approximations of the behavior of the mathematical models across a wide range of initial relative velocities of the colliding bodies while using parameterizations of the models that are independent of the initial relative velocity.