# Calibration of Discrete-Element-Method Parameters for Cohesive Materials Using Dynamic-Yield-Strength and Shear-Cell Experiments

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## Abstract

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## 1. Introduction and Objectives

- DEM simulations are computationally expensive and take a long time to complete due to small time-step sizes and large numbers of particles that are tracked as they move through the system.
- The approximation of complex particle shapes using spheres, usually done to reduce computational burden, might not reflect the true nature of the particles being simulated.
- Calibration of DEM parameters to match particle flow behavior in the experimental system is a challenge.

- Develop a DEM model for dynamic-yield-strength measurements and use it to calibrate the surface energy between particles.
- Develop a DEM model for a parallel-plate shear cell and calibrate the coefficient of sliding friction (CoSF) and the coefficient of rolling friction (CoRF) parameters for particle–particle interactions.

## 2. Experiment Setup

#### 2.1. Materials

#### 2.2. Dynamic Yield Strength Experiment

#### 2.3. Shear-Cell Experiment

## 3. Method and Simulation Setups

^{®}version 2.7.3 (DEM Solutions) [34]. The geometry for the shear-cell simulation was developed using the 3D-CAD package called SOLIDWORKS

^{®}(Dassault Systémes) [35], while the geometry for the DYS simulation was developed using tools in EDEM

^{®}.

^{®}, the contact and cohesive forces in the DEM models developed in this study were also accounted for by using the JKR normal contact model [12]. This contact model uses a parameter called surface energy ($\gamma $) to quantify the attractive nature of the particles. When surface energy is set to zero, the JKR model reduces to the Hertz contact model, a nonlinear spring-and-dashpot model based on the Hertz theory of elastic contacts [36]. The normal contact force between two spherical particles of radius ${R}_{1}$ and ${R}_{2}$ with a normal overlap, ${\delta}_{N}$ is given by [37]:

#### 3.1. Dynamic-Yield-Strength Simulation Setup

#### 3.2. Periodic Shear-Cell Simulation Setup

^{®}. Once the particles were compressed by the top plate, the bottom plate was made to move at a rate of 3.813e-05 m/s in the positive x-direction. This speed is the experimental angular velocity converted to linear speed. The shear stress on the top plate was recorded.

## 4. Results and Discussion

#### 4.1. Sensitivity Analysis: Dynamic Yield Strength

#### 4.2. Shear-Cell Sensitivity Results

#### 4.3. Surface-Energy Calibration Using DYS Simulations

- A different particle shear modulus chosen for the simulations. Here, a shear modulus of 1e7 Pa was tested.
- Particles were scaled-up for the simulations. Particle sizes were doubled for this test.
- Different sets of friction parameters were used. Both friction parameters were set to 0.5 for this test.

#### 4.4. Comparing Calibrated Setups with Shear Cell

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CoRF | Coefficient of Rolling Friction |

CoSF | Coefficient of Static Friction |

DEM | Discrete Element Method |

DYS | Dynamic Yield Strength |

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Properties | Blend |
---|---|

Bulk Density ($\mathrm{kg}/{\mathrm{m}}^{3}$) | 422 |

D50 ($\mathsf{\mu}\mathrm{m}$) | 14.30 |

Avg. Flow Factor | 1.7 |

**Table 2.**Discrete-element-method (DEM) material parameters for dymanic-yield-strength (DYS) and shear-cell base-case simulations.

Material Parameters | Particle | Wall |
---|---|---|

Density ($\mathrm{kg}/{\mathrm{m}}^{3}$) | 1000 | 8000 |

Poisson’s Ratio | 0.2 | 0.33 |

Shear Modulus (Pa) | $1{e}^{6}$ | $7.93{e}^{10}$ |

Surface Energy ($\mathrm{J}/{\mathrm{m}}^{2}$) | 0.45 | - |

Interaction Parameters | Particle-Particle | Particle-Wall |
---|---|---|

Coeff. of Restitution | 0.2 | 0.2 |

Coeff. of Sliding Friction | 0.4 | 0 |

Coeff. of Rolling Friction | 0.01 | 0 |

Simulation | Parameter Value | DYS (Pa) | Change w.r.t. Base Case (%) |
---|---|---|---|

Base case | - | 495 | - |

Poisson’s Ratio | 0.5 | 457 | −7.7 |

Coeff. of Restitution | 0.5 | 472 | −4.6 |

Shear Modulus (Pa) | $2.5{e}^{6}$ | 400 | −19.2 |

Surface Energy ($\mathrm{J}/{\mathrm{m}}^{2}$) | 1.125 | 1853 | 274.3 |

Coeff. of Sliding Friction | 1.0 | 402 | −18.8 |

Coeff. of Rolling Friction | 0.025 | 678 | 37.0 |

**Table 5.**Surface-energy and dynamic-yield-strength results from calibrated simulations. Note: CoSF, Coefficient of Sliding Friction. CoRF, Coefficient of Rolling Friction.

Simulation | Surface Energy ($\mathbf{J}/\mathbf{m}{}^{2}$) | DYS (Pa) |
---|---|---|

Target/Experimental result | - | 3242 |

Calibrated base case (CBC) | 2.15 | 3378 |

Shear modulus $1{e}^{7}$ Pa | 2.95 | 3220 |

Double particle size | 2.90 | 3351 |

CoSF and CoRF 0.5 | 0.95 | 3267 |

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**MDPI and ACS Style**

Karkala, S.; Davis, N.; Wassgren, C.; Shi, Y.; Liu, X.; Riemann, C.; Yacobian, G.; Ramachandran, R.
Calibration of Discrete-Element-Method Parameters for Cohesive Materials Using Dynamic-Yield-Strength and Shear-Cell Experiments. *Processes* **2019**, *7*, 278.
https://doi.org/10.3390/pr7050278

**AMA Style**

Karkala S, Davis N, Wassgren C, Shi Y, Liu X, Riemann C, Yacobian G, Ramachandran R.
Calibration of Discrete-Element-Method Parameters for Cohesive Materials Using Dynamic-Yield-Strength and Shear-Cell Experiments. *Processes*. 2019; 7(5):278.
https://doi.org/10.3390/pr7050278

**Chicago/Turabian Style**

Karkala, Subhodh, Nathan Davis, Carl Wassgren, Yanxiang Shi, Xue Liu, Christian Riemann, Gary Yacobian, and Rohit Ramachandran.
2019. "Calibration of Discrete-Element-Method Parameters for Cohesive Materials Using Dynamic-Yield-Strength and Shear-Cell Experiments" *Processes* 7, no. 5: 278.
https://doi.org/10.3390/pr7050278