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For the purpose of modeling the mechanics of granular materials, the Discrete Element Method (DEM) is a convenient computational approach thanks to its direct description of grain-scale phenomena. For the DEM to output a predictive mechanical behavior, a faithful shape description of the physical grains is logically necessary, unless the contact model between numerically-simplified spherical particles would be artificially enriched [1]. Among the various DEM implementations enabling such a realistic shape description, the Level Set (LS) approach implicitly describes grains shape through the zero-level set of the distance function to a grain surface [2,3]. Doing so, shape description starts by defining on a particle-centered grid appropriate values for the shortest distance to the grain, which is by convention taken to be positive outside of the particle and negative inside, while being naturally zero over its surface. Ensuring the versatility of the method, such a discrete distance field can be obtained for any surface through, e.g., a Fast Marching Method algorithm. For the purpose of contact detection, surface nodes furthermore discretize the particle boundary and can be obtained at will from the distance field. The method logically induces significant computational costs, be it either in terms of memory for the distance grid, or in terms of simulation time for looping over surface nodes when searching for an intersection with another particle (showing negative distance values in its inner region). The latter costs are carefully assessed in the case of an implementation into the YADE [4] code and discussed with respect to the obtained precision of the method [5]. It is also shown how parallel, OpenMP, computing together with algorithmic improvements may help alleviating these costs, with a special focus on an optimized definition and manipulation of the surface nodes [6]. This eventually enables the method to be conveniently applied to various cases stemming from convex superquadrics to non-convex rock aggregates.
[1] T. Mohamed, J. Duriez, G. Veylon, L. Peyras (2022) DEM models using direct and indirect shape descriptions for Toyoura sand along monotonous loading paths, Computers and Geotechnics, vol. 142
[2] R. Kawamoto, E. Andò, G. Viggiani and J.E. Andrade (2016). Level set discrete element method for three-dimensional computations with triaxial case study. Journal of the Mechanics and Physics of Solids, vol. 91
[3] J. Duriez and C. Galusinski (2021) A Level Set-Discrete Element Method in YADE for numerical, micro-scale, geomechanics with refined grain shapes, Computers and Geosciences, vol. 157
[4] V. Angelidakis, K. Boschi, K. Brzeziński, R.A. Caulk, B. Chareyre, C.A. del Valle, J. Duriez et al. (2024) YADE - An extensible framework for the interactive simulation of multiscale, multiphase, and multiphysics particulate systems, Computer Physics Communications, vol. 304
[5] J. Duriez, S. Bonelli (2021) Precision and computational costs of Level Set-Discrete Element Method (LS-DEM) with respect to DEM, Computers and Geotechnics, vol. 134
[6] J. Duriez, C. Galusinski (2025) Faster and objective level set-DEM mechanical simulations of discrete systems with convex particles from contact history and particle surface considerations, Computer Physics Communications, vol. 316
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