A study of the influence of REV variability in double‐scale FEM ×DEM analysis

Shahin, Ghassan; Desrues, Jacques; Pont, Stefano Dal; Combe, Gaël; Argilaga, Albert

doi:10.1002/nme.5202

Cited by 30 publications

(25 citation statements)

References 29 publications

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“…This stress measure is obtained from the first Piola-Kirchhoff stressP computed through (14) by using the common transformation rule:…”

Section: Micro-to-macro: Macroscopic Stress and Hill-mandel Conditionmentioning

confidence: 99%

“…The purpose of the dynamic relaxation method is to reach static equilibrium from the equations of motion in a relatively fast and numerically robust fashion, by effectively dissipating the kinetic energy of the modelled system. This requires the computation of the effective macroscopic stress tensorP, calculated from expression (14) via the boundary forces acting on the granular micro-structure, but circumvents the additional computation of the (computationally expensive) constitutive tangent matrix typically required in implicit time marching schemes. Correspondingly, the macro-scale balance equation, originally given by relation (18), takes the form…”

Section: Dynamic Relaxationmentioning

confidence: 99%

“…Several examples of coupled FEM-DEM approaches for granular materials have been presented in the literature. In [13,14] a quasi-static multi-scale method is formulated within the framework of small deformations, whereby the role of the particle microstructure on the effective frictional failure response of macroscopic samples is analysed, with a special focus on the initiation of strain localization. In [15] a small-strain multi-scale framework is proposed that elegantly computes the mechanical response for various monotonic and cyclic loading prob-lems, whereby drained as well as undrained conditions are considered.…”

Section: Introductionmentioning

confidence: 99%

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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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“…This stress measure is obtained from the first Piola-Kirchhoff stressP computed through (14) by using the common transformation rule:…”

Section: Micro-to-macro: Macroscopic Stress and Hill-mandel Conditionmentioning

confidence: 99%

Section: Dynamic Relaxationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2018

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“…This is accomplished by simulating the macro-scale problem under consideration with the finite element method (FEM), whereby in every integration point the response to the corresponding deformation is calculated by means of a DEM model that accurately and efficiently represents the complex particle behavior at the micro-scale. Examples of coupled FEM-DEM approaches for granular materials can be found in [11][12][13][14][15], illustrating the use of various averaging theorems for relating force and displacement measures at the particle micro-scale to stress and strain measures at the structural macro-scale. Specific aspects that should deserve more attention in FEM-DEM homogenization methods, but often are neglected for reasons of simplicity, refer to (1) the Hill-Mandel micro-heterogeneity condition, which enforces consistency of energy at the microand macro-scales, (2) the effect of particle rotations in the formulation of micro-to-macro scale-transitions, and (3) a rigorous generalization of the multi-scale approach within the theory of large deformations.…”

Section: Introductionmentioning

confidence: 99%

Formulation and numerical implementation of micro-scale boundary conditions for particle aggregates

2017

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Novel numerical algorithms are presented for the implementation of micro-scale boundary conditions of particle aggregates modelled with the discrete element method. The algorithms are based on a servo-control methodology, using a feedback principle comparable to that of algorithms commonly applied within control theory of dynamic systems. The boundary conditions are defined in accordance with the large deformation theory, and are imposed on a frame of boundary particles surrounding the interior granular microstructure. Following the formulation presented in Miehe et al. (Int J Numer Methods Eng 83(8-9): 1206-1236, 2010, first three types of classical boundary conditions are considered, in accordance with (1) a homogeneous deformation and zero particle rotation (D), (2) a periodic particle displacement and rotation (P), and (3) a uniform particle force and free particle rotation (T). The algorithms can be straightforwardly combined with commercially available discrete element codes, thereby enabling the determination of the solution of boundary-value problems at the micro-scale only, or at multiple scales via a micro-to-macro coupling with a finite element model. The performance of the algorithms is tested by means of discrete element method simulations on regular monodisperse packings and irregular polydisperse packings composed of frictional particles, which were subjected to various loading paths. The simulations provide responses with the typical stiff and soft bounds for the (D) and (T) boundary conditions, respectively, and illustrate for the (P) boundary condition a relatively fast convergence of the apparent macroscopic properties under an increasing packing size. Finally, a homogenization framework is derived for the implementation of mixed (D)-(P)-(T) boundary conditions that satisfy the Hill-Mandel micro-heterogeneity condition on energy consistency at the micro-and macro-scales of the granular system. The numerical algorithm for the mixed boundary conditions is developed and tested for the case of an infinite layer subjected to a vertical compressive stress and a horizontal shear deformation, whereby the response computed for a layer of cohesive particles is compared against that for a layer of frictional particles.

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“…Indeed, FEMxDEM methods allow to couple the advantages of Discrete Elements and the efficiency of Finite Elements. Later works have enhanced and extended this approach to the study of anisotropy [7,18], granular cohesion [19], material heterogeneity [25], real scale engineering applications [18,8], more realistic constitutive behaviors using 3D DEM [12,26], macroscale hydro-mechanical coupling [26,10]. More recently, [12] have embedded non-local regularization at the macro-scale and [9] has developed a full micromacro 3D approach.…”

Section: Introductionmentioning

confidence: 99%

Restoring Mesh Independency in FEM-DEM Multi-scale Modelling of Strain Localization Using Second Gradient Regularization

Desrues

Argilaga

Pont

et al. 2017

Springer Series in Geomechanics and Geoengineering

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Continuum media from classical mechanics cannot appropriately reproduce the evolution of materials exhibiting strong heterogeneities in the strain field, e.g. strain localization. Models without a microscale representation cannot properly reproduce the microscale mechanisms that trigger the strain localization, in addition, first gradient relations don't present any length parameter in the formulation. This results in a model without a characteristic length that cannot exhibit any objective band width. In this paper, techniques to introduce an internal length will be enumerated. Microstuctured materials will be retained and in particular Second Gradient model will be exposed and used along with a FEMxDEM approach. Numerical results showing the abilities of the enriched model will conclude the text.

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A study of the influence of REV variability in double‐scale FEM ×DEM analysis

Cited by 30 publications

References 29 publications

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

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

Formulation and numerical implementation of micro-scale boundary conditions for particle aggregates

Restoring Mesh Independency in FEM-DEM Multi-scale Modelling of Strain Localization Using Second Gradient Regularization

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