Anisotropy and lack of symmetry for a random aggregate of frictionless, elastic particles: theory and numerical simulations

Ragione, Luigi La; Oger, Luc; Recchia, Giuseppina; Sollazzo, Ana

doi:10.1098/rspa.2015.0013

Cited by 7 publications

(6 citation statements)

References 21 publications

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“…We identify in this regime an inelastic stiffness in which the response becomes incrementally frictionless and the major symmetry of the macroscopic stiffness is lost (e.g. [20,21]). Key parameters are the magnitude and direction of the probes applied to stressed, anisotropic states, compared with the strain under which the aggregate is initially loaded.…”

Section: Introductionmentioning

confidence: 99%

DEM simulation of anisotropic granular materials: elastic and inelastic behavior

et al. 2020

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In this work, Discrete Elements Method simulations are carried out to investigate the effective stiffness of an assembly of frictional, elastic spheres under anisotropic loading. Strain probes, following both forward and backward paths, are performed at several anisotropic levels and the corresponding stress is measured. For very small strain perturbations, we retrieve the linear elastic regime where the same response is measured when incremental loading and unloading are applied. Differently, for a greater magnitude of the incremental strain a different stress is measured, depending on the direction of the perturbation. In the case of unloading probes, the behavior stays elastic until non-linearity is reached.Under forward perturbations, the aggregate shows an intermediate inelastic stiffness, in which the main contribution comes from the normal contact forces. That is, when forward incremental probes are applied the behavior of anisotropic aggregates is an incremental frictionless behavior. In this regime we show that contacts roll or slide so the incremental tangential contact forces are zero. Graphical Abstract

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Section: Introductionmentioning

confidence: 99%

DEM simulation of anisotropic granular materials: elastic and inelastic behavior

et al. 2020

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“…As first shown by La Ragione et al (2015), the interaction of the fluctuations and the transverse anisotropy creates this property of , which is necessary for localization to occur. Numerical simulations are in progress and confirm the lack of symmetry for a frictional aggregate.…”

Section: Stiffness Tensormentioning

confidence: 93%

A micromechanical prediction of localization in a granular material

Ragione

Prantil

Jenkins

2015

Journal of the Mechanics and Physics of Solids

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“…The six coefficients are with and As suggested by La Ragione et al [17,36], it is the presence of fluctuations in the kinematics of contacting particles that leads to 4 ≠ 5 which implies the loss of major symmetry for the anisotropic stiffness tensor A ijkm . It is the term proportional to 2 and the volume strain in Eq.…”

Section: Incremental Stressmentioning

confidence: 99%

“…[14]) is or, with Eq. (36) Given Eq. ( 37), we obtain The coefficients 's depend on the relation between the volume strain and the shear strain which are present in the contact stiffness K N .…”

Section: Second-order Workmentioning

confidence: 99%

Fluctuations and failure in granular materials: theory and numerical simulations

La Ragione,

Recchia,

Darve

et al. 2024

Granular Matter

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We consider a dense aggregate of elastic, frictional particles isotropically compressed and next uniaxial strained at constant pressure. We show how failure can be predicted if fluctuations in the kinematics of contacting particles are introduced. We focus on the second order work and the possibility that at some stressed states it becomes negative under proper perturbations. Our analysis involves both a theoretical model and numerical simulations based upon the distinct element method (DEM). The theoretical model deals with contacting particles with incremental relative displacements that deviate from the average deformation in order to ensure their equilibrium. Because of this, the macroscopic stiffness tensor of the aggregate, that relates increments in stress with increments in strain, does not have the major symmetry. Consequently, in the hardening regime, we predict stressed states in which the second order work vanishes. The model seems transparent, and it makes clear and illustrative the role played by the fluctuations introduced in the kinematics of contacting particles in relation to the vanishing of second order work in an aggregate of compressed particles. The comparison with numerical simulations data supports the model. Graphical Abstract Statistical representation of the aggregate: conditional average.

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Anisotropy and lack of symmetry for a random aggregate of frictionless, elastic particles: theory and numerical simulations

Cited by 7 publications

References 21 publications

DEM simulation of anisotropic granular materials: elastic and inelastic behavior

DEM simulation of anisotropic granular materials: elastic and inelastic behavior

A micromechanical prediction of localization in a granular material

Fluctuations and failure in granular materials: theory and numerical simulations

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