Contact models for the multi-sphere discrete element method
Nathan Berry, Yonghao Zhang, Sina Haeri
Abstract
Five sources of critical error are identified for binary interactions of particles using the Multi-Sphere Discrete Element Method (MS-DEM) i.e. the occurrence of under-damping, two forms of over-damping error, over-stiffness effects, and force response inconsistencies due to erroneous contact area calculations. Algorithmic issues are found to be the source of over-stiffness effects, one form of over-damping and the erroneous contact area calculations. The remaining over-damping and under-damping errors are physical in nature. By defining different types of MS-DEM interactions, solutions are proposed which can successfully mitigate all of the identified errors. This includes the development of the concept of a locally reduced mass to attenuate the physics-based form of over-damping, and purely algorithmic considerations rectify the other form of over-damping as well as the over-stiffness effects and erroneous contact area calculations. This study focuses on two types of linear spring dash-pot models and two non-linear Hertzian models, however, it is demonstrated the nature of the errors and their respective solutions are generally independent of the contact model. As such, the solutions proposed should be considered for implementation with other contact models when using the MS-DEM, with a high likelihood of being applicable to other contact detection methods.