# Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows

## Abstract

We use previous results from discrete element simulations of simple shear flows of rigid, identical spheres in the collisional regime to show that the volume fraction-dependence of the stresses is singular at the shear rigidity. Here, we identify the shear rigidity, which is a decreasing function of the interparticle friction, as the maximum volume fraction beyond which a random collisional assembly of grains cannot be sheared without developing force chains that span the entire domain. In the framework of extended kinetic theory, i.e., kinetic theory that accounts for the decreasing in the collisional dissipation due to the breaking of molecular chaos at volume fractions larger than 0.49, we also show that the volume fraction-dependence of the correlation length (measure of the velocity correlation) is singular at random close packing, independent of the interparticle friction. The difference in the singularities ensures that the ratio of the shear stress to the pressure at shear rigidity is different from zero even in the case of frictionless spheres: we identify that with the yield stress ratio of granular materials, and we show that the theoretical predictions, once the different singularities are inserted into the functions of extended kinetic theory, are in excellent agreement withmore »

- Authors:

- Politecnico di Milano, 20133 Milan (Italy)

- Publication Date:

- OSTI Identifier:
- 22403207

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Fluids (1994); Journal Volume: 27; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING; CHAOS THEORY; COMPUTERIZED SIMULATION; FLOW MODELS; FRICTION; GRANULAR MATERIALS; KINETIC EQUATIONS; RANDOMNESS; SHEAR; SINGULARITY; SPHERES; STOWING; STRESSES

### Citation Formats

```
Berzi, Diego, and Vescovi, Dalila.
```*Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows*. United States: N. p., 2015.
Web. doi:10.1063/1.4905461.

```
Berzi, Diego, & Vescovi, Dalila.
```*Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows*. United States. doi:10.1063/1.4905461.

```
Berzi, Diego, and Vescovi, Dalila. Thu .
"Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows". United States.
doi:10.1063/1.4905461.
```

```
@article{osti_22403207,
```

title = {Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows},

author = {Berzi, Diego and Vescovi, Dalila},

abstractNote = {We use previous results from discrete element simulations of simple shear flows of rigid, identical spheres in the collisional regime to show that the volume fraction-dependence of the stresses is singular at the shear rigidity. Here, we identify the shear rigidity, which is a decreasing function of the interparticle friction, as the maximum volume fraction beyond which a random collisional assembly of grains cannot be sheared without developing force chains that span the entire domain. In the framework of extended kinetic theory, i.e., kinetic theory that accounts for the decreasing in the collisional dissipation due to the breaking of molecular chaos at volume fractions larger than 0.49, we also show that the volume fraction-dependence of the correlation length (measure of the velocity correlation) is singular at random close packing, independent of the interparticle friction. The difference in the singularities ensures that the ratio of the shear stress to the pressure at shear rigidity is different from zero even in the case of frictionless spheres: we identify that with the yield stress ratio of granular materials, and we show that the theoretical predictions, once the different singularities are inserted into the functions of extended kinetic theory, are in excellent agreement with the results of numerical simulations.},

doi = {10.1063/1.4905461},

journal = {Physics of Fluids (1994)},

number = 1,

volume = 27,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}