Discrete element modelling of large scale particle systems-I: exact scaling laws

作者：Feng Y T^*; Owen D R J

来源：Computational Particle Mechanics, 2014, 1(2): 159-168.

DOI：10.1007/s40571-014-0010-y

• Discrete element method
• Scale factor
• Exact scaling
• Interaction law
• Scale invariance

The discrete element method has emerged as a powerful predictive tool for the numerical modelling of many scientific and engineering problems involving discrete and discontinuous phenomena. There are nevertheless computational challenges to resolve before industrial scale applications can be effectively simulated. This multi-part paper aims to address some of the theoretical and computational issues central to achieving this goal. In the first part of this paper, a simple but generic theoretical framework is established for the development of a comprehensive set of scaling conditions, under which a scaled discrete element model can exactly reproduce the mechanical behaviour of a physical model. In particular, three basic physical quantities and their scale factors can be freely chosen. A special selection leads to a unique set of scale factors governing an exact scaling, which also gives rise to the requirement that all the interaction laws employed in a scaled model be scale-invariant. The subsequent examination reveals that most commonly used interaction laws, if all material (mechanical and physical) properties are treated as constant, do not possess such a feature and therefore cannot be directly employed in a scaled model. The problem can be solved by treating the scaled particles as pseudo-particles and by properly scaling the interaction laws. The resulting scaled interaction laws become scale-invariant and thus can be used in a scaled model.

• 出版日期2014-6