Anisotropic elastic theory of preloaded granular media

Gay, Cyprien; Silveira, Rava Azeredo da

doi:10.1209/epl/i2004-10162-1

Cited by 10 publications

(8 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the ordered case, transmission occurs chiefly along the lattice directions of the packing, with some friction-dependent widening with depth. This is consistent with the general predictions of anisotropic elasticity [13,21,22,23] but experimental limitations could not rule out predictions of hyperbolic models for a weakly disordered system [24]. The case of the pentagons shows a single peak that broadens linearly with depth, consistent with an elastic-like picture.…”

Section: Two-dimensional Photoelastic Experimentssupporting

confidence: 64%

Sensitivity of the stress response function to packing preparation

Atman¹,

Brunet²,

Geng³

et al. 2005

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

A granular assembly composed of a collection of identical grains may pack under different microscopic configurations with microscopic features that are sensitive to the preparation history. A given configuration may also change in response to external actions such as compression, shearing etc. We show using a mechanical response function method developed experimentally and numerically, that the macroscopic stress profiles are strongly dependent on these preparation procedures. These results were obtained for both two and three dimensions. The method reveals that, under a given preparation history, the macroscopic symmetries of the granular material is affected and in most cases significant departures from isotropy should be observed. This suggests a new path toward a non-intrusive test of granular material constitutive properties.

show abstract

Section: Two-dimensional Photoelastic Experimentssupporting

confidence: 64%

Sensitivity of the stress response function to packing preparation

Atman¹,

Brunet²,

Geng³

et al. 2005

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…The optimal choice ω * only vanishes when the stress tensor and the fabric tensor defined as the average of n ij ⊗ n ij over contacts, weighted by L T ij , share the same eigenvectors. This conclusion,wich was reached before by Jenkins and La Ragione [73], and independently by Gay and da Silveira [74], on directly estimating the stress increments corresponding to a prescribed strain, is retrieved here as an illustration of the variational approach. Returning now to the case of isotropic packings of monodisperse spherical beads of diameter a, the fabric tensor is isotropic, which ensures ω * .…”

Section: Appendix D: Voigt and Reuss Bounds For Elastic Moduli In A Smentioning

confidence: 57%

Internal states of model isotropic granular packings. III. Elastic properties

2007

View full text Add to dashboard Cite

In this third and final paper of a series, elastic properties of numerically simulated isotropic packings of spherical beads assembled by different procedures, as described in the first companion paper, and then subjected to a varying confining pressure, as reported in the second companion paper, are investigated. In addition to the pressure, which determines the stiffness of contacts because of Hertz's law, elastic moduli are chiefly sensitive to the coordination number z , which should not be regarded as a function of the packing density. Comparisons of numerical and experimental results for glass beads in the 10 kPa-10 MPa pressure range reveal similar differences between dry samples prepared in a dense state by vibrations and lubricated packings, so that the greater stiffness of the latter, in spite of their lower density, can be attributed to a larger coordination number. Effective medium type approaches, or Voigt and Reuss bounds, provide good estimates of bulk modulus B , which can be accurately bracketed, but badly fail for shear modulus G , especially in low z configurations under low pressure. This is due to the different response of tenuous, fragile networks to changes in load direction, as compared to load intensity. In poorly coordinated packings, the shear modulus, normalized by the average contact stiffness, tends to vary proportionally to the degree of force indeterminacy per unit volume, even though this quantity does not vanish in the rigid limit. The elastic range extends to small strain intervals and compares well with experimental observations on sands. The origins of nonelastic response are discussed. We conclude that elastic moduli provide access to mechanically important information about coordination numbers, which escape direct measurement techniques, and indicate further perspectives.

show abstract

“…Beyond the simplest form of Voigt approximation, estimates of moduli should be improved [18,25,26] on imposing a suitably chosen common spin to all particles. This spin vanishes whenever the strain tensor commutes with the fabric tensor F (defined by F αβ = n α n β ).…”

Section: Voigt Approximationmentioning

confidence: 99%

Numerical study of one-dimensional compression of granular materials. II. Elastic moduli, stresses, and microstructure

et al. 2017

View full text Add to dashboard Cite

The elastic moduli of a transversely isotropic model granular material, made of slightly polydisperse elastic-frictional spherical beads, in equilibrium along a one-dimensional (oedometric) compression path, as described in the companion paper [M. H. Khalili et al., Phys. Rev. E 95, 032907 (2017)]10.1103/PhysRevE.95.032907, are investigated by numerical simulations. The relations of the five independent moduli to stresses, density, coordination number, fabric and force anisotropies are studied for different internal material states along the oedometric loading path. It is observed that elastic moduli, as in isotropic packs, are primarily determined by the coordination number, with anomalously small shear moduli in poorly coordinated systems, whatever their density. Such states also exhibit faster increasing moduli in compression, and larger off-diagonal moduli and Poisson ratios. Anisotropy affects the longitudinal moduli C_{11} in the axial direction and C_{22} in the transverse directions, and the shear modulus in the transverse plane C_{44}, more than the shear modulus in a plane containing the axial direction C_{55}. The results are compared to available experiments on anisotropic bead packs, revealing, despite likely differences in internal states, a very similar range of stiffness level (linked to coordination), and semiquantitative agreement as regards the influence of anisotropy. Effective medium theory (the Voigt approach) provides quite inaccurate predictions of the moduli. It also significantly underestimates ratios C_{11}/C_{22} (varying between 1 and 2.2) and C_{55}/C_{44} (varying from 1 to 1.6), which characterize elastic anisotropy, except in relatively weakly anisotropic states. The bulk modulus for isotropic compression and the compliance corresponding to stress increments proportional to the previous stress values are the only elastic coefficients to be correctly estimated by available predictive relations. We discuss the influences of fabric and force anisotropies onto elastic anisotropy, showing in particular that the former dominates in sample series that are directly assembled in anisotropic configurations and keep a roughly constant lateral to axial stress ratio under compression.

show abstract

Anisotropic elastic theory of preloaded granular media

Cited by 10 publications

References 40 publications

Sensitivity of the stress response function to packing preparation

Sensitivity of the stress response function to packing preparation

Internal states of model isotropic granular packings. III. Elastic properties

Numerical study of one-dimensional compression of granular materials. II. Elastic moduli, stresses, and microstructure

Contact Info

Product

Resources

About