Frictional granular mechanics: A variational approach

Abstract

SUMMARYThe mechanical properties of a cohesionless granular material are evaluated from grain-scale simulations. Intergranular interactions, including friction and sliding, are modeled by a set of contact rules based on the theories of Hertz, Mindlin, and Deresiewicz. A computer generated, three-dimensional, irregular pack of spherical grains is loaded by incremental displacement of its boundaries. Deformation is described by a sequence of static equilibrium configurations of the pack. A variational approach is employed to find the equilibrium configurations by minimizing the total work against the intergranular loads. Effective elastic moduli are evaluated from the intergranular forces and the deformation of the pack. Good agreement between the computed and measured moduli, achieved with no adjustment of material parameters, establishes the physical soundness of the proposed model.

Refractive Index Matching

“…Using our data we find Y 0 to be about 15 MPa, which is close to what we would expect for the elastic modulus of a glass sphere pack (Holtzman et al, 2010). Thus Y/Y 0 represents the strength of contact enhancement.…”

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

“…In mentioned paper, there is no reference to conservation of elastic energy, and the integration scheme used is based on an incremental sequential determination of the solution of the Newton force balance, calculated grain by grain, time step after time step. This concept is being still used, eg, in Kuhn and Radja and Dubois; however, occasionally, a variational point of view is accepted in the literature (see Holtzman et al). We also note that in the classical DEM algorithms, the grain interactions are treated from the viewpoint of Hertz–Cattaneo–Mindlin contact analysis.…”

Micromechanical model of weakly‐cemented sediments

“…A significant increase in sample stiffness was observed in experiments as a result of adding small amounts of cement at the grain contacts . To demonstrate this effect, we compare the results for sample (a) with QuSGM simulations of triaxial test on uncemented samples . Using a frictionless contact model provides Young's modulus of 0–0.5 GPa for axial stresses of 0–24 MPa .…”

“…The total moment applied on grain i relative to its center is evaluated from the sum of the torsional and shear components, M ij = M ij ( t ) + M ij ( s ) , where M ij ( s ) = R ij × Q ij . We note that the small effect of intergranular torsion on the macroscopic stress makes the macroscopic elastic moduli relatively insensitive to the exact value of (and C s ).…”

“…The inability of models with weaker intergranular stiffness-deformation dependence to reproduce the experimental data demonstrates the highly-nonlinear nature of the intergranular deformation. Our results highlight the importance of accounting for grain-scale mechanisms in modeling granular materials, and provide a plausible explanation for the nonlinear behavior of weakly-cemented sediments.We use a conjugate gradient algorithm to find the minimum of …, see [7,19]. When … is at a minimum, its gradient with respect to Â, r  … D OEF 1 : : : F N M 1 =R 1 : : : M N =R N , vanishes.…”