Generalized bridging domain method for coupling finite elements with discrete elements

Tu, Fubin; Ling, Daosheng; Bu, Lingfang; Yang, Qingda

doi:10.1016/j.cma.2014.03.023

Cited by 21 publications

(18 citation statements)

References 31 publications

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“…The multiscale model for coupling DEs with FEs is shown schematically in Because the contact interaction between two adjacent DE particles is local, the separate edge coupling method is adopted for coupling DEM-FEM. The separate edge coupling method is a special case that is degenerated from the generalized bridging domain method [29]. In generalized bridging domain method, independent weighting functions α(x) and β(x) are used for different models to weight the material properties to generate new models with transitional domains or artificially truncated boundaries, where the weighting functions span from 1 to 0.…”

Section: Separate Edge Coupling Methodsmentioning

confidence: 99%

“…When determining the compensation forces F C and f C , the compatibility conditions between different models must be enforced. There are two types of compatibility conditions: (i) displacement/velocity compatibility condition; (ii) force/stress compatibility condition [29]. In this paper, only the displacement/velocity compatibility requirement is taken into account.…”

Section: Separate Edge Coupling Methodsmentioning

confidence: 99%

“…During the last decade, a large number of concurrent coupled DEM-FEM methods have been proposed or used [22][23][24][25][26][27][28][29]. The main differences among them can be distinguished based on three aspects: (i) method to derive the governing equation; (ii) width of the coupling domain; and (iii) compatibility condition.…”

Section: Introductionmentioning

confidence: 99%

“…separately adjust the displacement of one model to match the other in different zones of the coupling domain) or mutually (e.g. adjust the displacements of both models in the coupling domain to achieve compatibility) on different models depending on if it is necessary to guarantee the equilibrium [29]. The reliability of a coupled DEM-FEM scheme in avoiding spurious reflections, such as highfrequency waves greater than the cutoff frequency of the FE model that are reflected in the coupling zone [31,32], must be validated.…”

Section: Introductionmentioning

confidence: 99%

“…Table I lists a summary of the existing coupled DEM-FEM methods. The separate edge coupling method, which is a degenerated case of the generalized bridging domain method, is effective in avoiding spurious reflections [29]. The compatibility conditions of dissimilar models in the separate edge coupling method are separately obtained and imposed on their own, which makes it easy to be achieved.…”

Section: Introductionmentioning

confidence: 99%

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DEM–FEM analysis of soil failure process via the separate edge coupling method

Ling

et al. 2017

Num Anal Meth Geomechanics

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The concurrent multiscale method, which couples the discrete element method (DEM) for predicting the local micro-scale evolution of the soil particle skeleton with the finite element method (FEM) for estimating the remaining macro-scale continuum deformation, is a versatile tool for modeling the failure process of soil masses. This paper presents the separate edge coupling method, which is degenerated from the generalized bridging domain method and is good at eliminating spurious reflections that are induced by coupling models of different scales, to capture the granular behavior in the domain of interest and to coarsen the mesh to save computational cost in the remaining domain. Cundall non-viscous damping was used as numerical damping to dissipate the kinetic energy for simulating static failure problems. The proposed coupled DEM-FEM scheme was adopted to model the wave propagation in a 1D steel bar, a soil slope because of the effect of a shallow foundation and a plane-strain cone penetration test (CPT). The numerical results show that the separate edge coupling method is effective when it is adopted for a problem with Cundall non-viscous damping; it qualitatively reproduces the failure process of the soil masses and is consistent with the full micro-scale discrete element model. Stress discontinuity is found in the coupling domain.Before the cone's penetration (s = 0.0 m), the distribution of the contact normal directions is heterogeneous because of gravity (most of the contact normals are near in y direction), which can also be observed from the force chains (contact normals and normal contact forces) in Figure 15. As the cone tip approaches the monitoring point (e.g., s = 0.25 m), the soil particles rotate because of the cone's disturbance, and most of the contact normal directions are 60°and 120°from the x axis Figure 14. Mesh and DE particles for different penetration depths: (a) s = 0.1 m; (b) s = 0.3 m; (c) s = 0.5 m. [Colour figure can be viewed at wileyonlinelibrary.com] Figure 16. Distributions of the contact normal directions at (0.71 m, 0.67 m): (a) s = 0.0 m; (b) s = 0.25 m; (c) s = 0.5 m. [Colour figure can be viewed at wileyonlinelibrary.com] Figure 17. Variation of the void ratio at (0.71 m, 0.67 m).Figure 18. Stress field σ y for different penetration depths: (a) 0 m, (b) 0.1 m, (c) 0.3 m and (d) 0.5 m. [Colour figure can be viewed at wileyonlinelibrary.com]

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Section: Separate Edge Coupling Methodsmentioning

confidence: 99%

Section: Separate Edge Coupling Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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DEM–FEM analysis of soil failure process via the separate edge coupling method

Ling

et al. 2017

Num Anal Meth Geomechanics

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A review of multiscale numerical modeling of rock mechanics and rock engineering

Wei,

Li,

Zhao

2024

Deep Underground Science and Engineering

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Rock is geometrically and mechanically multiscale in nature, and the traditional phenomenological laws at the macroscale cannot render a quantitative relationship between microscopic damage of rocks and overall rock structural degradation. This may lead to problems in the evaluation of rock structure stability and safe life. Multiscale numerical modeling is regarded as an effective way to gain insight into factors affecting rock properties from a cross‐scale view. This study compiles the history of theoretical developments and numerical techniques related to rock multiscale issues according to different modeling architectures, that is, the homogenization theory, the hierarchical approach, and the concurrent approach. For these approaches, their benefits, drawbacks, and application scope are underlined. Despite the considerable attempts that have been made, some key issues still result in multiple challenges. Therefore, this study points out the perspectives of rock multiscale issues so as to provide a research direction for the future. The review results show that, in addition to numerical techniques, for example, high‐performance computing, more attention should be paid to the development of an advanced constitutive model with consideration of fine geometrical descriptions of rock to facilitate solutions to multiscale problems in rock mechanics and rock engineering.

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A local grid refinement scheme for B‐spline material point method

Sun

Gan

Huang

et al. 2020

Numerical Meth Engineering

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A local grid refinement scheme for the material point method with B-spline basis functions (BSMPM) is developed based on the concept of bridging domain approach. The fine grid is defined in the local large-deformation regions to accurately capture the complex material responses, whereas other spatial domains are discritized by coarse grids. In the overlapping domain between the fine and coarse grids, the constraint of particle displacements obtained with different grids is enforced using the Lagrange multiplier method to eliminate the spurious stress reflection at the fine/coarse grid interface. Representative numerical examples have shown that the BSMPM simulations with the proposed local grid refinement scheme could provide the solutions in good agreement with those obtained with the uniformly fine grid, and that no significant spurious stress reflection is induced at the fine/coarse grid interface, even for the bridging domain size as small as the cell size of the fine grid. It is also found that the proposed local grid refinement method can significantly reduce the BSMPM computational time compared with the cases for uniformly fine grids. A multitime-step algorithm is presented and shown to considerably enhance the efficiency of the present local grid refinement scheme with no compromise in accuracy.

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Generalized bridging domain method for coupling finite elements with discrete elements

Cited by 21 publications

References 31 publications

DEM–FEM analysis of soil failure process via the separate edge coupling method

DEM–FEM analysis of soil failure process via the separate edge coupling method

A review of multiscale numerical modeling of rock mechanics and rock engineering

A local grid refinement scheme for B‐spline material point method

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