Skip to Main content Skip to Navigation
Journal articles

A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations

Abstract : We formulate a discrete Lagrangian model for a set of interacting grains, which is purely elastic. The considered degrees of freedom for each grain include placement of barycenter and rotation. Further, we limit the study to the case of planar systems. A representative grain radius is introduced to express the deformation energy to be associated to relative displacements and rotations of interacting grains. We distinguish inter‐grains elongation/compression energy from inter‐grains shear and rotations energies, and we consider an exact finite kinematics in which grain rotations are independent of grain displacements. The equilibrium configurations of the grain assembly are calculated by minimization of deformation energy for selected imposed displacements and rotations at the boundaries. Behaviours of grain assemblies arranged in regular patterns, without and with defects, and similar mechanical properties are simulated. The values of shear, rotation, and compression elastic moduli are varied to investigate the shapes and thicknesses of the layers where deformation energy, relative displacement, and rotations are concentrated. It is found that these concentration bands are close to the boundaries and in correspondence of grain voids. The obtained results question the possibility of introducing a first gradient continuum models for granular media and justify the development of both numerical and theoretical methods for including frictional, plasticity, and damage phenomena in the proposed model.
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-02269692
Contributor : Christian Cardillo <>
Submitted on : Friday, August 23, 2019 - 11:02:00 AM
Last modification on : Saturday, August 24, 2019 - 1:09:59 AM
Document(s) archivé(s) le : Friday, January 10, 2020 - 3:02:06 AM

File

nag.2915.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02269692, version 1

Collections

Citation

Emilio Turco, Francesco Dell'Isola, Anil Misra. A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations. International Journal for Numerical and Analytical Methods in Geomechanics, Wiley, 2019, Special Issue: Special Issue on Particle Methods in Geomechanics, 43 (5), pp.1051-1079. ⟨hal-02269692⟩

Share

Metrics

Record views

30

Files downloads

51