Fourier series-based discrete element method for computational mechanics of irregular-shaped particles

Lai, Zhengshou; Chen, Qiushi; Huang, Linchong

doi:10.1016/j.cma.2020.112873

Cited by 51 publications

(20 citation statements)

References 47 publications

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“…Since the 1980s, various non-disc/spherical or irregular particle shapes have been proposed in DEM including ellipses [16,17], ellipsoids [18], super-quadrics [19], cylinders [20], dilated or Minkowski-sum generated shapes [21,22,23], poly-ellipsoids [24,25] and poly-super-ellipsoids [26], polygons [27,28] and polyhedra [29,30,31,32]. More recent inclusions are level-set defined shapes based on CT scanned images [33], and analytical function represented smooth shapes, such as Fourier series-based for 2D shapes [34], NURBS (or B-spline) based [35] 3D shapes, spherical harmonic represented 3D objects [36,37], and isogeometric representation of 3D surfaces [38,39]. No doubt, these shapes significantly enhance the shape representation capability of DEM for industrial applications.…”

Section: Introductionmentioning

confidence: 99%

An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Basic framework and general contact model

Feng

2021

Computer Methods in Applied Mechanics and Engineering

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Section: Introductionmentioning

confidence: 99%

An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Basic framework and general contact model

Feng

2021

Computer Methods in Applied Mechanics and Engineering

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“…More recently, sophisticated basis functions have been utilized to enrich the representation of particle shapes. These include Fourier series for 2D shapes, 20 NURBS (or B‐spline), 21 or spherical harmonic 22,23 for 3D objects, and iso‐geometric for 3D surfaces 24,25 . The distinct advantage of these shapes over those previously mentioned is that these shapes can be constructed either as convex or concave, and therefore are more representative of real particles.…”

Section: Introductionmentioning

confidence: 99%

A generic energy‐conserving discrete element modeling strategy for concave particles represented by surface triangular meshes

Feng

2021

Numerical Meth Engineering

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A generic energy‐conserving linear normal contact model for concave particles in the discrete element method (DEM) is presented in this article. It is derived based on a recently enhanced general energy‐conserving contact theory for arbitrarily shaped particles. A set of more effective evaluation schemes required in the model are also given, which shows that only the intersection boundary between two contact shapes, instead of their contact region or surfaces, is required to be explicitly obtained, thereby substantially improving both efficiency and applicability of the proposed contact model over the previous version. A surface triangular mesh is used to represent any 3D concave particle. The computational issues associated with the contact of two surface triangulated 3D shapes, including the contact detection, the determination of intersection boundary segments, the computation of contact features and parallelization, critical time step, and friction and damping treatment for multiple contacts are described in detail. Two sets of numerical examples involving various concave 3D shapes with a large number of surface triangles are presented to demonstrate either the superb energy‐conserving property of the proposed model model, or its effectiveness, robustness, and universal nature for wider and more complex problems.

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“…However, it is not accurate to represent a particle with only one disc or sphere, because one disc or sphere on its own cannot capture all the characteristics of the complex geometrical shape of most granular particles. erefore, DEM modelling of granular materials in which the particles are represented by discs or spheres suffers from limited capability in capturing essential aspects of interparticle interactions and corresponding mechanical behaviors [2,3].…”

Section: Introductionmentioning

confidence: 99%

Multisphere Representation of Convex Polyhedral Particles for DEM Simulation

Zhang

Jia

et al. 2021

Advances in Civil Engineering

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The representation of particles of complex shapes is one of the key challenges of numerical simulations based on the discrete element method (DEM). A novel algorithm has been developed by the authors to accurately represent 2D arbitrary particles for DEM modelling. In this paper, the algorithm is extended from 2D to 3D to model convex polyhedral particles based on multisphere methods, which includes three steps: the placement of spheres at the corners, along the edges, and on the facets in sequence. To give a good representation of a polyhedral particle, the spheres are placed tangent to the particle surface in each step. All spheres placed in the three steps are clumped together into a clump in DEM. In addition, the mass properties of the clump are determined based on the corresponding polyhedral particle to obtain accurate simulation results. Finally, an example is used to validate the robust and automatic performance of the algorithm in generating a sphere clump model for an assembly of polyhedral particles. A current FORTRAN version of the algorithm is available by contacting the authors.

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Fourier series-based discrete element method for computational mechanics of irregular-shaped particles

Cited by 51 publications

References 47 publications

An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Basic framework and general contact model

An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Basic framework and general contact model

A generic energy‐conserving discrete element modeling strategy for concave particles represented by surface triangular meshes

Multisphere Representation of Convex Polyhedral Particles for DEM Simulation

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