Estimates of elastic moduli for granular material with anisotropic random packing structure

Chang, Ching S.; Chao, Sao Jeng; Chang, Yehui

doi:10.1016/0020-7683(94)00225-l

Cited by 113 publications

(68 citation statements)

References 14 publications

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“…The distribution of the branch-vector length gL J (l) can be described by a direction-dependent density function such as equation (14). A possible form of equation (14) is to introduce a directiondependent l L Table I.…”

Section: The Distribution Function Of Branch-vector-length Glmentioning

confidence: 99%

Micromechanics model for elastic stiffness of non-spherical granular assembly

Dong

Pan

1999

Int. J. Numer. Anal. Meth. Geomech.

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SUMMARYThis paper presents a micromechanics model for the elastic sti!ness of a non-spherical granular assembly. The microstructural continuum model of ideal spherical assembly is extended for non-ideal assembly. The presented work takes the e!ects of gradation, shape, and preferred orientation into account by introducing a directional distribution function of branch-vector length. The microstructure of a granular assembly is described by the distributions of packing structure, branch-vector length, and particle number per unit volume. These distributions account or the random nature of a realistic granular material. The microfeatures relevant to the description of non-deal particle assembly are elaborated. The in#uences of various directiondependent and direction-independent microfeatures on the elastic sti!ness are demonstrated. Hypothetical non-ideal granular assemblies are used to study the e!ects of gradation, shape and preferred orientation. Based on the proposed model, the paper discusses the inherent anisotropy in a non-ideal granular assembly. The presented work also makes use of a generalized static hypothesis to estimate the contact-force distribution for speci"c microstructure and stress state. With the estimated contact-force and the Hertz}Mindlin contact theory, the elastic sti!ness of a particulate assembly can be evaluated. Hence, the e!ects of geometric fabric and anisotropic stress state on the elastic sti!ness can be deliberated. Consequently, the e!ects of geometric fabric and kinetic fabric of a natural granular material can be evaluated independently. It is shown that the proposed model can reasonably capture the phenomena of inherent anisotropy and stress-induced anisotropy of a non-spherical granular assembly under small strain. Copyright 1999 John Wiley & Sons, Ltd.

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Section: The Distribution Function Of Branch-vector-length Glmentioning

confidence: 99%

Micromechanics model for elastic stiffness of non-spherical granular assembly

Dong

Pan

1999

Int. J. Numer. Anal. Meth. Geomech.

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“…16,17,18,19,20,21) are calculated from the polynomial-based response functions with use of a direct algebraic differentiation in MAPLE. They are defined in the neighborhood of one of the expected values of the volume fraction of interface defects E (w) ∈ [0.1, 0.2, ..., 0.5] and are non-dimensional.…”

Section: Deterministic Computational Analysismentioning

confidence: 99%

“…Therefore, a homogenization method [13,14] is recommended to reduce this complexity by scale reduction in complex composite structures from a three-scale approach to traditional micro-macroanalysis where two separate scales are really necessary. Such a reduction gains specific importance when anisotropic packaging of the particles or fibers is assumed into the RVE [17][18][19][20], because inserting additional imperfect interfaces or interphases dramatically complicates meshing of the entire structure; it is also really necessary when statistical simulation techniques [21,22] are employed together with the complex finite element method (FEM) composite model.…”

Section: Introductionmentioning

confidence: 99%

Homogenization of carbon/polymer composites with anisotropic distribution of particles and stochastic interface defects

Sokołowski

Kamiński

2018

Acta Mech

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The main objective is to investigate an effect of anisotropic distribution of the reinforcing particles in a cubic representative volume element (RVE) of the carbon-polymer composite including stochastic interphases on its homogenized elastic characteristics. This is done using a probabilistic homogenization technique implemented using a triple approach based on the stochastic perturbation method, Monte Carlo simulation as well as on the semi-analytical approach. On the other hand, the finite element method solution to the uniform deformations of this RVE is carried out in the system ABAQUS. This composite model consists of two neighboring scales-the micro-contact scale relevant to the imperfect interface and the micro-scale-having 27 particles inside a cubic volume of the polymeric matrix. Stochastic interface defects in the form of semi-spheres with Gaussian radius are replaced with the interphase having probabilistically averaged elastic properties, and then such a three-component composite is subjected to computational homogenization on the microscale. The computational experiments described here include FEM error analysis, sensitivity assessment, deterministic results as well as the basic probabilistic moments and coefficients (expectations, deviations, skewness and kurtosis) of all the components of the effective elasticity tensor. They also include quantification of anisotropy of this stiffness tensor using the Zener, Chung-Buessem and the universal anisotropy indexes. A new tensor anisotropy index is proposed that quantifies anisotropy on the basis of all not null tensor coefficients and remains effective also for tensors other than cubic (orthotropic, triclinic and also monoclinic). Some comparison with previous analyses concerning the isotropic case is also included to demonstrate the anisotropy effect as well as the numerical effort to study randomness in composites with anisotropic distribution of reinforcements and inclusions.

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“…The macroscopic properties are controlled by the "microscopic" contact forces and torques [19,42,49,58,101]. Non-linear contacts [92,106], frequency-dependence [85,118] and also scattering and attenuation in other "particle type" materials [27] have been reported.…”

Section: Introductionmentioning

confidence: 99%

sound wave propagation in dry granular materials : simulations, theory and experiments

Mouraille¹

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Estimates of elastic moduli for granular material with anisotropic random packing structure

Cited by 113 publications

References 14 publications

Micromechanics model for elastic stiffness of non-spherical granular assembly

Micromechanics model for elastic stiffness of non-spherical granular assembly

Homogenization of carbon/polymer composites with anisotropic distribution of particles and stochastic interface defects

sound wave propagation in dry granular materials : simulations, theory and experiments

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