Global–local analysis of granular media in quasi-static equilibrium

Kaneko, Kenji; Terada, Kenjiro; Kyoya, Takashi; Kishino, Yuji

doi:10.1016/s0020-7683(03)00209-9

Cited by 63 publications

(44 citation statements)

References 12 publications

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“…Obviously, for deriving the solution of a boundary value problem, the equation of motion (9) and the constitutive response of the particles (6) and (7) should be complemented by the appropriate boundary conditions. As mentioned in the introduction, the numerical implementation of the microscale boundary conditions is based on the formulation presented in [16], and the main equations are summarized in Sect.…”

Section: Particle Contact Lawsmentioning

confidence: 99%

“…The accurate computation of the non-linear failure and deformation behavior of heterogeneous granular systems commonly requires a resolution of the complex mechanical interactions and deformation mechanisms at the particle scale, which can be adequately accounted for by using the discrete element method (DEM), see e.g., [1][2][3][4][5][6][7][8][9][10] and references therein. For practical granular systems composed of a vast number of particles, however, it is infeasible to simulate each particle as an individual discrete object, since this leads to DEM models with an enormously large number of degrees of freedom, and consequently, to impractical computation times.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Particle Contact Lawsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2017

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“…Some early works [11,16,20], have put in evidence the potential of the method to provide a refined description of complex constitutive behaviors. Indeed, FEMxDEM methods allow to couple the advantages of Discrete Elements and the efficiency of Finite Elements.…”

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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“…One can also look on the minimization approach as a kind of multi body contact problem [12][13][14] or a local-global solution strategy [15]. In these approaches, just as in the non-smooth contact dynamics method, contacts are generally modeled as infinitely stiff.…”

Section: Introductionmentioning

confidence: 99%

“…When friction and cohesion are employed even more interesting behavior is observed. [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Simulating granular materials by energy minimization

Krijgsman

Luding

2016

Comp. Part. Mech.

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Discrete element methods are extremely helpful in understanding the complex behaviors of granular media, as they give valuable insight into all internal variables of the system. In this paper, a novel discrete element method for performing simulations of granular media is presented, based on the minimization of the potential energy in the system. Contrary to most discrete element methods (i.e., soft-particle method, event-driven method, and non-smooth contact dynamics), the system does not evolve by (approximately) integrating Newtons equations of motion in time, but rather by searching for mechanical equilibrium solutions for the positions of all particles in the system, which is mathematically equivalent to locally minimizing the potential energy. The new method allows for the rapid creation of jammed initial conditions (to be used for further studies) and for the simulation of quasi-static deformation problems. The major advantage of the new method is that it allows for truly static deformations. The system does not evolve with time, but rather with the externally applied strain or load, so that there is no kinetic energy in the system, in contrast to other quasistatic methods. The performance of the algorithm for both types of applications of the method is tested. Therefore we look at the required number of iterations, for the system to converge to a stable solution. For each single iteration, the required computational effort scales linearly with the number of particles. During the process of creating initial conditions, the required number of iterations for two-dimensional systems scales with the square root of the number of particles in the system. The required number of iterations increases for systems closer to the jamming packing fraction. For a quasistatic pure shear deformation simulation, the results of the new method are validated by regular soft-particle dynamics simulations. The energy minimization algorithm is able to capture the evolution of the isotropic and deviatoric stress and fabric of the system. Both methods converge in the limit of quasi-static deformations, but show interestingly different results otherwise. For a shear amplitude of 4 %, as little as 100 sampling points seems to be a good compromise between accuracy and computational time needed.

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Global–local analysis of granular media in quasi-static equilibrium

Cited by 63 publications

References 12 publications

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

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

Simulating granular materials by energy minimization

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