多体系统碰撞动力学中接触力模型的研究进展

接触碰撞行为作为大自然与多体系统中的常见现象,其接触力模型对于多体系统的碰撞行为机理研究与性能预测至关重要.静态弹塑性接触模型与考虑能量耗散的连续接触力模型是研究接触碰撞行为的两类不同方法,在多体系统碰撞动力学中存在诸多共性与差异.本文分别从上述两类接触模型的发展历程入手,详细介绍了两类模型的区别与联系.首先,根据阻尼项分母中是否含有初始碰撞速度将连续接触力模型分为黏性接触力模型与迟滞接触力模型,讨论了能量指数与Hertz接触刚度之间的关系,阐述了现有连续接触力模型在计算弹塑性材料接触碰撞行为时存在的问题.其次,着重介绍了分段连续的准静态弹塑性接触力模型(可连续从完全弹性转换到完全塑性接触阶段),分析了利用此类弹塑性接触力模型计算碰撞行为的技术特点.同时,以恢复系数为桥梁和借助线性化的弹塑性接触刚度,避免了Hertz刚度对弹塑性接触刚度的计算误差,根据碰撞前后多体系统的能量与动能守恒推导了弹塑性接触模型等效的迟滞阻尼因子.探索了连续接触力模型与准静态弹塑性接触力模型之间的内在联系,数值计算结果定量说明了人为阻尼项代表的能量耗散与弹塑性接触力模型中加卸载路径代表的能量耗散具有等效性.另外...

RESEARCH PROGRESS OF CONTACT FORCE MODELS IN THE COLLISION MECHANICS OF MULTIBODY SYSTEM

Impact behavior is a ubiquitous phenomenon in multibody systems. The contact force model is a pivotal tool to predict the contact characteristics of multibody systems. At present, there are two kinds of contact models used for calculating impact behaviors: the static elastoplastic contact force model and the continuous contact force models with energy dissipation. There are many similarities and discrepancies among them in the impact dynamics of multibody systems. This review starts with the introduction of development history of these two kinds of contact models followed by their development progress and background illustrated in detail. Firstly, whether the initial impact velocity is contained in the denominator of damping term severs as a criterion to classify the continuous contact force model as two types of models that are the contact force model with hysteresis damping factor and the other one with viscous damping factor. The relationship between the power exponent and Hertz contact stiffness is analyzed. The problems in calculating the elastic-plastic contact collision behavior by using the existing continuous contact force models are discussed. Secondly, the static elastoplastic contact force models with the continuous transition between the pure elastic and full plastic are introduced, and its characteristic is illustrated when calculating the elastoplastic collision events. The coefficient of restitution acts as the bridge to connect the static elastoplastic contact model and dynamic dashpot model as a complete system. In order to sidestep the error from the Hertz contact stiffness in calculating the elastoplastic impact behavior, a new viscous damping factor is derived by means of the linear elastoplastic contact stiffness based on energy conservation. The intrinsic connection between the static elastoplastic model and the dashpot model is explored, which proves that the artificial damping describing energy dissipation is equivalent to the one generated by the discrepancy between the loading and unloading paths. In order to avoid the numerical singularity caused by the initial impact velocity in the denominator of damping when calculating the dynamic performance of granular matter, a continuous contact force model with viscous damping is obtained by solving a linear single degree of freedom underdamped vibration system. One-dimension chain is taken as the numerical example to validate that the new dashpot model is more accurate than the one used in the EDEM software. Finally, the current research status of impact dynamics of multibody systems is reviewed, and the development trend and future challenges of contact force models are briefly summarized.