The maximum dissipation principle in rigid-body dynamics with inelastic impacts
The maximum dissipation principle in rigid-body dynamics with inelastic impacts
复制标题
非弹性冲击刚体动力学中的最大耗散原理
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
U. Rüde
中科院分区：
文献类型：
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作者：
T. Preclik;S. Eibl;U. Rüde
为有碰撞的刚体动力学建立一致的理论是一个复杂的问题。20年前，斯图尔特发表了第一个关于纯非弹性碰撞的一致理论，以及一个类似于库仑摩擦的脉冲摩擦模型。在本文中，我们证明了即使在单接触的情况下，相容碰撞模型也可以表现出具有不同耗散程度的多个解。用基于最大耗散原理的模型代替基于库仑摩擦的冲击摩擦模型，解决了单接触碰撞问题中的非唯一性问题。建立了交替碰撞模型，给出了描述刚体动力学的积分方程组，该模型采用非脉冲、非柔度接触模型，并建立了使耗散最大化的纯非弹性碰撞模型。给出了单接触碰撞问题的解析解。然后将这些模型嵌入到时间步进方案中。将宏观行为比作大规模颗粒流问题中的库仑摩擦。
Formulating a consistent theory for rigid-body dynamics with impacts is an intricate problem. Twenty years ago Stewart published the first consistent theory with purely inelastic impacts and an impulsive friction model analogous to Coulomb friction. In this paper we demonstrate that the consistent impact model can exhibit multiple solutions with a varying degree of dissipation even in the single-contact case. Replacing the impulsive friction model based on Coulomb friction by a model based on the maximum dissipation principle resolves the non-uniqueness in the single-contact impact problem. The paper constructs the alternative impact model and presents integral equations describing rigid-body dynamics with a non-impulsive and non-compliant contact model and an associated purely inelastic impact model maximizing dissipation. An analytic solution is derived for the single-contact impact problem. The models are then embedded into a time-stepping scheme. The macroscopic behaviour is compared to Coulomb friction in a large-scale granular flow problem.