FEM × DEM modelling of cohesive granular materials: Numerical homogenisation and multi-scale simulations

Nguyen, Trung Kiên; Combe, Gaël; Caillerie, Denis; Desrues, Jacques

doi:10.2478/s11600-014-0228-3

Cited by 74 publications

(68 citation statements)

References 23 publications

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“…We also note that the spatial correlations show marked similarities to the turbulence in fluids, a promising indication that this type of analysis can be used to explore the origins of the macroscopic friction in confined granular materials. Turbulence is one of the most complex, but ubiquitous, phenomena observed in Nature and it is related with the underlying mechanisms responsible for the micro-macro upscale causing wide-ranging effects on classical systems, like macroscopic friction in granular solids or turbulent flow regime in fluids [1][2][3][4]. The presence of multiple scales in time and space is an additional defy to a comprehensive theoretical description, and a particular effort is made in the literature to perform experiments and simulations in order to validate the proposed theoretical descriptions, particularly Tsallis nonextensive (NE) statistical mechanics [5][6][7][8].…”

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confidence: 99%

Experimental Validation of a Nonextensive Scaling Law in Confined Granular Media

et al. 2015

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In this letter, we address the relationship between the statistical fluctuations of grain displacements for a full quasistatic plane shear experiment, and the corresponding anomalous diffusion exponent, α. We experimentally validate a particular case of the so-called Tsallis-Bukman scaling law, α = 2/(3 − q), where q is obtained by fitting the probability density function (PDF) of the measured fluctuations with a q-Gaussian distribution, and the diffusion exponent is measured independently during the experiment. Applying an original technique, we are able to evince a transition from an anomalous diffusion regime to a Brownian behavior as a function of the length of the strain-window used to calculate the displacements of grains in experiments. The outstanding conformity of fitting curves to a massive amount of experimental data shows a clear broadening of the fluctuation PDFs as the length of the strain-window decreases, and an increment in the value of the diffusion exponent -anomalous diffusion. Regardless of the size of the strain-window considered in the measurements, we show that the Tsallis-Bukman scaling law remains valid, which is the first experimental verification of this relationship for a classical system at different diffusion regimes. We also note that the spatial correlations show marked similarities to the turbulence in fluids, a promising indication that this type of analysis can be used to explore the origins of the macroscopic friction in confined granular materials. Turbulence is one of the most complex, but ubiquitous, phenomena observed in Nature and it is related with the underlying mechanisms responsible for the micro-macro upscale causing wide-ranging effects on classical systems, like macroscopic friction in granular solids or turbulent flow regime in fluids [1][2][3][4]. The presence of multiple scales in time and space is an additional defy to a comprehensive theoretical description, and a particular effort is made in the literature to perform experiments and simulations in order to validate the proposed theoretical descriptions, particularly Tsallis nonextensive (NE) statistical mechanics [5][6][7][8].A paradigmatic work relating anomalous diffusion and turbulent-like behavior in confined granular media was presented by Radjai and Roux [4], using numerical simulations, and confirmed qualitatively by experiments by Combe and collaborators [7,8]. Radjai and Roux coined a new expression to characterize the analogies between fluctuations of particle velocities in quasistatic granular flows and the velocity fields observed in turbulent fluid flow in high Reynolds number regime, the "granulence". Most of the evidences of the granulence are based in simulations using discrete element method (DEM) but, unfortunately, one can verify a lack of quantitative experimental verification in the last years, limiting the knowledge of the micromechanics of this system based almost exclusively on numerical evidences.In the present work, we aim exactly to fill this gap by contributing with the experiment...

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Experimental Validation of a Nonextensive Scaling Law in Confined Granular Media

et al. 2015

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“…The use of a discrete element formulation to resolve the RVE problem has been addressed in Refs. [345][346][347] among others, in particular for granular media. Another approach to solve the boundary value problem at the microscale is the boundary element method, studied, for instance, by Kaminski [348], Okada et al [349], and Prochazka [350].…”

Section: Analysis At the Rve Levelmentioning

confidence: 99%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

190

138

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The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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“…In [16] this framework is applied for developing multi-scale insights into classical geomechanical problems, such as retaining wall and footing problems. Coupled FEM-DEM approaches are commonly validated by analysing the macroscopic structural response in experimental tests typical for granular media, such as a biaxial compression test [11,15,[17][18][19], a slope stability test [20], or a (cyclic) shear test [15].…”

Section: Introductionmentioning

confidence: 99%

Multi-scale modelling of granular materials: numerical framework and study on micro-structural features

2018

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A multi-scale model for the analysis of granular systems is proposed, which combines the principles of a coupled FEM-DEM approach with a novel servo-control methodology for the implementation of appropriate micro-scale boundary conditions. A mesh convergence study is performed, whereby the results of a quasi-static biaxial compression test are compared with those obtained by direct numerical simulations. The comparison demonstrates the capability of the multi-scale method to realistically capture the macro-scale response, even for macroscopic domains characterized by a relatively coarse mesh; this makes it possible to accurately analyse large-scale granular systems in a computationally efficient manner. The multi-scale framework is applied to study in a systematic manner the role of individual micro-structural characteristics on the effective macro-scale response. The effect of particle contact friction, particle rotation, and initial fabric anisotropy on the overall response is considered, as measured in terms of the evolution of the effective stress, the volumetric deformation, the average coordination number and the induced anisotropy. The trends observed are in accordance with notions from physics, and observations from experiments and other DEM simulations presented in the literature. Hence, it is concluded that the present framework provides an adequate tool for exploring the effect of micro-structural characteristics on the macroscopic response of large-scale granular structures.

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FEM × DEM modelling of cohesive granular materials: Numerical homogenisation and multi-scale simulations

Cited by 74 publications

References 23 publications

Experimental Validation of a Nonextensive Scaling Law in Confined Granular Media

Experimental Validation of a Nonextensive Scaling Law in Confined Granular Media

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Multi-scale modelling of granular materials: numerical framework and study on micro-structural features

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