The Minkowski overlap and the energy‐conserving contact model for discrete element modeling of convex nonspherical particles

Feng, Y. T.; Tan, Yuanqiang

doi:10.1002/nme.6800

Cited by 11 publications

(5 citation statements)

References 21 publications

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“…Advanced shape representations, e.g., using the finite element basis functions, and energy-conserving contact laws, as reported in Refs. [21][22][23] might further improve the accuracy of interaction force computations between particles and convex/concave surfaces.…”

Section: Discussionmentioning

confidence: 99%

CG-enriched concurrent multi-scale modeling of dynamic surface interactions between discrete particles and solid continua

2023

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The interaction between granular materials and deformable structures is relevant to many industries, such as mining, construction, and powder processing. Surface coupling between the discrete (DEM) and the finite element method (FEM) is commonly used to numerically describe particle-continuum interactions. Using a recently developed "surface-coupling" method, enriched by coarse graining, a micro-macro transition technique to extract continuum fields from discrete particle data, we study the time evolution of linear momenta and energies in various particle-continuum systems and their dependencies on the coarse-graining (CG) width, the support of the smoothing kernel. Via three numerical examples including (1) a dense granular flow impacting on a flexible obstacle, (2) a viscoelastic cube bouncing and resting on a frictional granular bed, and (3) a monolayer of particles flowing on a cantilever, we show that CG-enriched surface coupling not only leads to more accurate predictions but also reduces excess energies numerically generated by the coupling method, and CG is more effective as the particle-structure interaction becomes dynamic. By varying the CG width, we observe stronger attenuation, decreasing the magnitudes of high-frequency oscillations, facilitating stress relaxation in dissipative coupled systems, and that the identification of the optimal CG width is indeed problem-dependent.

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Section: Discussionmentioning

confidence: 99%

CG-enriched concurrent multi-scale modeling of dynamic surface interactions between discrete particles and solid continua

2023

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“…A geometric shape (2D or 3D) is considered to be the set of all individual points contained in the shape. 4,32 Consider two blocks A and B. Their Minkowski sum, denoted as A ⊕ B, is obtained by adding every point in A to every point in B:…”

Section: Minkowski Difference and Contact Statementioning

confidence: 99%

“…The Gilbert-Johnson-Keerthi (GJK) proposed by Gilbert et al 36 does not need to construct Minkowski difference of two convex polygons explicitly, but check if the origin is enclosed in the Minkowski difference through iterations using support points of the polygons. The detail of the GJK algorithm can be found in Feng and Tan 32,33 and is also outlined in Algorithm 5 for the completeness.…”

Section: Overlap Checking Of Two Polygonsmentioning

confidence: 99%

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A Minkowski difference‐based advancing front packing technique for generating convex noncircular particles in complex domains

Xia

Gong

et al. 2023

Numerical Meth Engineering

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In this work, a Minkowski difference‐based advancing front approach is proposed to generate convex and non‐circular particles in a predefined computational domain. Two specific algorithms are developed to handle the contact conformity of generated particles with the boundaries of the computational domain. The first, called the open form, is used to handle the smooth contact of generated particles with (external) boundaries, while the other, called the closed form, is proposed to handle the internal boundaries of a computational domain with a complex cavity. The Gilbert‐Johnson‐Keerthi (GJK) method is used to efficiently solve the contact detection between the newly generated particle at the front and existing particles. Furthermore, the problem of one‐sided particle lifting, which can cause some defects in the packing structure in existing advancing front methods during packing generation, is highlighted and an effective solution is developed. Several examples of increasing complexity are used to demonstrate the efficiency and applicability of the proposed packing generation approach. The numerical results show that the generated packing is not only more uniform, but also achieves a higher packing density than existing advancing front methods.

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“…This introduces certain roughness to the deformable bodies' surface and can be avoided by using mathematically well-defined geometric objects (e.g., curved walls [42]), mapped from the finite element. Other shape representations, including signed distance functions [60], level set methods [42,61,62], and Minkowski sums [63] could also be used. Secondly, currently, only the traction due to particle-wall interaction forces are mapped onto the finite elements; the kinetic traction due to velocity fluctuations is not explicitly considered.…”

Section: Outlooksmentioning

confidence: 99%

Concurrent multi-scale modeling of granular materials: Role of coarse-graining in FEM-DEM coupling

Cheng

2023

Preprint

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The finite element method (FEM) and the discrete element method (DEM) are two commonly used techniques in modeling different types of materials. FEM is used for materials that behave like a continuous substance, while DEM is used for materials that can be seen as individual particles. Sometimes, it's necessary to combine these two methods to get a more accurate representation of the granular material's behavior. This is typically done by directly connecting the individual particles in DEM with the larger elements in FEM.A technique called coarse-graining (CG) is used to bridge the gap between these two methods. It takes the data from the individual particles and turns it into smooth, continuous fields that follow the laws of continuous materials. By choosing a specific scale, the coarse-grained fields are then mixed together and applied to the FEM model. In this research, we explore a new way of combining FEM and DEM, both for surfaces and volumes. When dealing with surfaces, we convert the discrete contact forces between particles and surfaces into a smooth, continuous traction field that is then applied to the FEM model. For volumes, we enhance the homogenization process with additional functions to connect the discrete particles, their coarse-grained fields, and the finite element formulation.This new approach offers better accuracy and symmetry in surface coupling, reducing the energy produced during the combination of FEM and DEM, and for volume coupling, it significantly decreases numerical dissipation, especially when the load applied contains high-frequency components. This technique has the potential to be expanded beyond the current examples. It could be applied to different types of materials and governing equations, allowing for more advanced multi-scale and multi-physical modeling methods.

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The Minkowski overlap and the energy‐conserving contact model for discrete element modeling of convex nonspherical particles

Cited by 11 publications

References 21 publications

CG-enriched concurrent multi-scale modeling of dynamic surface interactions between discrete particles and solid continua

CG-enriched concurrent multi-scale modeling of dynamic surface interactions between discrete particles and solid continua

A Minkowski difference‐based advancing front packing technique for generating convex noncircular particles in complex domains

Concurrent multi-scale modeling of granular materials: Role of coarse-graining in FEM-DEM coupling

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