Setting up virgin stress conditions in discrete element models

Rojek, Jerzy; Karlis, G.F.; Malinowski, Łukasz; Beer, Gernot

doi:10.1016/j.compgeo.2012.07.009

Cited by 30 publications

(17 citation statements)

References 27 publications

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“…The displacement field, however, can be determined up to rigid modes. Assuming zero rotations and fixing zero displacements at the particle center x C , we can get the solution for the displacement of an arbitrary point x of the particle as

{false(u_{p} false)}_{i} = {false(ϵ_{p} false)}_{i j} ((), x_{j} - {false(x_{C} false)}_{j})

or, alternatively, in the matrix notation

u_{p} = ε_{p} false(boldx - x_{C} false),

where ε p is the strain matrix

ε_{p} = ([], \begin{matrix} center \\ array {(ϵ_{p})}_{11} & array {(ϵ_{p})}_{21} \\ array {(ϵ_{p})}_{12} & array {(ϵ_{p})}_{22} \end{matrix}) .

…”

Section: Formulation Of the Dem With Deformable Disksmentioning

confidence: 99%

The discrete element method with deformable particles

Rojek

Zubelewicz

Madan

et al. 2018

Numerical Meth Engineering

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Summary This work presents a new original formulation of the discrete element method (DEM) with deformable cylindrical particles. Uniform stress and strain fields are assumed to be induced in the particles under the action of contact forces. Particle deformation obtained by strain integration is taken into account in the evaluation of interparticle contact forces. The deformability of a particle yields a nonlocal contact model, it leads to the formation of new contacts, it changes the distribution of contact forces in the particle assembly, and it affects the macroscopic response of the particulate material. A numerical algorithm for the deformable DEM (DDEM) has been developed and implemented in the DEM program DEMPack. The new formulation implies only small modifications of the standard DEM algorithm. The DDEM algorithm has been verified on simple examples of an unconfined uniaxial compression of a rectangular specimen discretized with regularly spaced equal bonded particles and a square specimen represented with an irregular configuration of nonuniform‐sized bonded particles. The numerical results have been verified by a comparison with equivalent finite element method results and available analytical solutions. The micro‐macro relationships for elastic parameters have been obtained. The results have proved to have enhanced the modeling capabilities of the DDEM with respect to the standard DEM.

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{false(u_{p} false)}_{i} = {false(ϵ_{p} false)}_{i j} ((), x_{j} - {false(x_{C} false)}_{j})

or, alternatively, in the matrix notation

u_{p} = ε_{p} false(boldx - x_{C} false),

where ε p is the strain matrix

ε_{p} = ([], \begin{matrix} center \\ array {(ϵ_{p})}_{11} & array {(ϵ_{p})}_{21} \\ array {(ϵ_{p})}_{12} & array {(ϵ_{p})}_{22} \end{matrix}) .

…”

Section: Formulation Of the Dem With Deformable Disksmentioning

confidence: 99%

The discrete element method with deformable particles

Rojek

Zubelewicz

Madan

et al. 2018

Numerical Meth Engineering

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“…Recently, Scholtès and Donzé [17] applied an enhanced joint contact logic to represent the pre-existing fractures in the rock. Rojek et al [18] proposed a 2D virgin stress installation method in which an inverse displacement method is firstly used to generate stress-free particle assemblies configuration and then the kinematic loading and stress relaxation are employed to reach the expected virgin stress conditions. Currently it is still difficult to statically generate densely-compacted and stress-free rock sample in 3D.…”

Section: Discrete Element Modeling (Dem) For Seabed Solid Materialsmentioning

confidence: 99%

Numerical Modeling of Excavation Process in Dredging Engineering

Chen

Miedema

Rhee

2015

Procedia Engineering

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The increase of world population has been requiring more and more lands for human activities, which is why the world dredging market has been significantly growing up during the past 20 years. In dredging engineering, underwater excavation process is one of the major procedures which involves complicated physics, no matter it is sand, clay or rock on the seabed. It is important to reasonably estimate the cutting force needed on the excavator blade, which will help to improve the design and reduce the wear of the equipment so that higher working efficiency can be achieved. However, it is known that the cutting force is greatly influenced by the local water pressure especially in deep water. The fluid flow will change the pore pressure distribution and meanwhile apply certain force to the solid particles. Since the experiments to measure the cutting force are expensive, a numerical model is then needed to describe the physics in it. In this paper, the author tends to use the discrete element modeling to describe the solid particle movement and particle-particle interactions, and the finite volume method to calculate the fluid pressure distribution and flow velocity. Besides, a coupling deck is used between the two models to exchange the information to describe the fluid-solid interaction. This research has proven the feasibility of applying such a method in the underwater excavation process. Further calibration and validation are still necessary depends on the soil properties of the seabed.

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“…The particle stresses σ p are derived by averaging over the particle volumes V p (Figure ) in terms of the contact forces f c acting on each particle using the following formula:

{bold-italicσ}_{p} = \frac{1}{V_{p}} true \sum_{c = 1}^{n_{p c}} {bolds}^{c} \otimes {boldf}^{c},

where n p c is the number of particles being in contact with the p th particle, s c is the vector connecting the element center with the contact point (see Figure ), f c is the contact force, and the symbol ⊗ denotes the outer (tensor) product. The averaging formula should also include reaction forces and other external surface forces (cf the work of Rojek et al). In the 2D formulation, the stress is represented by the matrix

{bold-italicσ}_{p} = ([], \begin{matrix} center \\ array {(σ_{p})}_{x x} & array {(σ_{p})}_{x y} & array 0 \\ array {(σ_{p})}_{y x} & array {(σ_{p})}_{y y} & array 0 \\ array 0 & array 0 & array {(σ_{p})}_{z z} \end{matrix}) for plane strain

{bold-italicσ}_{p} = ([], \begin{matrix} center \\ array {(σ_{p})}_{x x} & array {(σ_{p})}_{x y} \\ array {(σ_{p})}_{y x} \end{matrix})

…”

Section: General Framework Of the Ddemmentioning

confidence: 99%

“…The idea of the deformable discrete element method 10 FIGURE 2 Vectors used in the particle stress evaluation where n p c is the number of particles being in contact with the pth particle, s c is the vector connecting the element center with the contact point (see Figure 2), f c is the contact force, and the symbol ⊗ denotes the outer (tensor) product. The averaging formula (1) should also include reaction forces and other external surface forces (cf the work of Rojek et al 12 ).…”

Section: Figurementioning

confidence: 99%

Convergence and stability analysis of the deformable discrete element method

Madan

Rojek

Nosewicz

2019

Numerical Meth Engineering

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Summary This work investigates numerical properties of the algorithm of the discrete element method (DEM) employing deformable circular disks presented in the authors' earlier publication. The new formulation called the deformable DEM (DDEM) enhances the standard DEM (SDEM) by introducing an additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. An accurate computation of the contact forces would require an iterative solution of the implicit relationship between the contact forces and particle displacements. In order to preserve efficiency of the DEM, the new formulation has been adapted to the explicit time integration. It has been shown that the explicit DDEM algorithm is conditionally stable and there are two restrictions on its stability. Except for the limitation of the time step as in the SDEM, the stability in the DDEM is governed by the convergence criterion of the iterative solution of the contact forces. The convergence and stability limits have been determined analytically and numerically for selected regular and irregular configurations. It has also been found out that the critical time step in DDEM remains unchanged with respect to the SDEM.

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Setting up virgin stress conditions in discrete element models

Cited by 30 publications

References 27 publications

The discrete element method with deformable particles

The discrete element method with deformable particles

Numerical Modeling of Excavation Process in Dredging Engineering

Convergence and stability analysis of the deformable discrete element method

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