Arbitrarily Shaped DEM Model Based on Level Set Method

The level set method, first introduced by Osher and Sethian (J Comput Phys 78:12–49, 1988), is a common and efficient method for calculating the motion of an interface and tracking its evolution (Osher and Sethian in J Comput Phys 78:12–49, 1988; Caselles et al. in Numer Math 66:1–31, 1993; Osher and Fedkiw in J Comput Phys 169:463–502, 2001; Sethian in J Comput Phys 169:503–555, 2001). Because these interfaces easily form sharp corners, internal cracks, and merge together in a robust way (Sukumar et al. in Comput Methods Appl Mech Eng 190:6183–6200, 2001; Wang et al. in J Comput Phys 221:395–421, 2007; Tran et al. in Int J Numer Methods Eng 85:1436–1459, 2011), the level set method has a wide range of applications, including solid modeling, crack characterization, image processing, and segmentation (Hettich and Ramm in Comp Methods Appl Mech Eng 195:4753–4767, 2006; Hettich et al. in Comput Methods Appl Mech Eng 197:414–424, 2008; Legrain et al. in Int J Numer Methods Eng 86:915–934, 2011). For the complex morphology of non-spherical granular materials, XRCT is used to obtain the image data of arbitrarily shaped particles, and the geometrical morphology of particles is mathematically characterized by the level set method according to the gradient of the X-ray attenuation (Vlahini et al. in Granular Matter 16:9–21, 2014; Macedo et al. in Granular Matter 20:73, 2018). A smooth distance function between two particles is established by the level set method, and the translation and rotation of the particles and the next collision between particles are accurately predicted (Stafford and Jackson in J Comput Phys 229:3295–3315, 2010; Vlahinic et al. in Acta Geotech 12:85–95, 2017). Recently, the level set method combined with the discrete element method can be used to reasonably simulate the motion behaviors of non-spherical granular materials (Tahmasebi in Comput Geotech 100:52–61, 2018; Duriez and Bonelli in Comput Geotech 134:104033, 2021; Duriez and Galusinski in Comput Geosci 157:104936, 2021). The shape parameters of non-spherical particles such as aspect ratio, circularity, and main geometric direction are extracted by the level set method and then input into the DEM simulations (Jerves et al. in Acta Geotech 11:493–503, 2016, Granular Matter 19:30, 2017; Harmon et al. in Comput Methods Appl Mech Eng 365:112961, 2020). The combination of level set methods and discrete element methods is used not only to capture mechanical behaviors as macroscopic scales (such as stress–strain and volume-strain results of the triaxial test), but also to reproduce shear bands in a similar way to experiments, as well as local and particle-scale quantities (such as local deviatoric stress and particle rotation) (Kawamoto et al. in J Mech Phys Solids 91:1–13, 2016; Lim et al. in Acta Geotech 11:243–253, 2016; Kawamoto et al. in J Mech Phys Solids 111:375–392, 2018). Meanwhile, the combination of these two methods has the ability to reflect the contact force distribution within granular systems composed of arbitrarily shaped particles and provides quantitative estimates of the evolution of force chains and fabric orientations (Li et al. in Granular Matter 21:43, 2019; Bhattacharya et al. in Acta Geotech 16:113–132, 2021; Harmon et al. in Comput Methods Appl Mech Eng 373:113486, 2021).