A methodology for calibrating flexible fibers for use in discrete element method (DEM)

simulations was developed, specifically for crop-machine simulations of wheat straw. The

calibration procedure utilized three different tests, the cantilever beam test, the 3-point-bending

test, and the uniaxial compression test. The calibration was validated with the direct shear test.

The cantilever beam test and 3-point-bending test were utilized together to determine the

Poisson’s ratio and the bond damping coefficient, while the uniaxial compression test determined

the contact Young’s modulus, bond Young’s modulus, and particle-particle friction parameters.

To determine the calibration value of each particle parameter, surrogate models were

developed by performing a simulated design of experiment (DOE) for each of the calibration

simulations. The surrogate models were developed by fitting linear models to a specific output of

a simulation that can be measured in a laboratory, given specific input DEM parameter values.

The surrogate model for the cantilever beam test found a direct relationship between the global

damping coefficient (how quickly a fiber loses its energy) and the local bond damping

coefficient (the coefficient used in the DEM simulations that removes energy from a bond

between two spheres). A direct relationship between the square root of the bond Young’s

modulus and the frequency of oscillation of the fiber was also found. The surrogate models

found from the cantilever beam tests were then used to find the DEM bond Young’s modulus

and DEM bond local damping coefficient parameters that would reproduce a specific oscillation

frequency and global damping value as a validation step. The validation simulation produced

local bond damping coefficient and oscillation frequency values with percent errors of 0.9% and

1.8% respectively.

The 3-point-bending calibration test yielded a single surrogate model that related the

calculated Young’s modulus strongly with the bond Young’s modulus and weakly with the

Poisson’s ratio. With only a single equation, there exists infinitely many solutions due to the two

free parameters of bond Young’s modulus and Poisson’s ratio. As this model incorporates the

bond Young’s modulus, the surrogate model obtained from the cantilever beam test can be used

in conjunction with the model obtained from the 3-point-bending test to obtain unique solutions.

Using the surrogate model, obtained from the 3-point-bending test, to find the DEM parameters,

a simulation of the 3-point-bending was performed to try to recreate the mean Young’s modulus

result from the laboratory tests. The simulation was able to reproduce the mean calculated

Young’s modulus, which was estimated from 3-point bending test, with a percent error of 3.11%.

To obtain bulk properties, the uniaxial compression test was used to create the surrogate

models. Surrogate models were produced for each of three plunger sizes with diameters of 50

mm, 150 mm and 255 mm in which a specifically sized plunger was lowered onto a bed of

fibers. The validation step for the uniaxial compression simulation and the overall validation

utilizing the direct shear test, only the surrogate model for the 225 mm plunger was used. The

surrogate models related the force on a plunger with the depth of the plunger insertion, bond

Young’s modulus, contact Young’s modulus, and the particle-particle friction. Using the

surrogate model to reproduce the mean forces obtained from the laboratory uniaxial

compressions tests, a max percent error of 25% was found. The surrogate model over predicted

the force versus displacement curve but was able to reproduce the overlying shape of the curve.

Having all the surrogate models, the direct shear test was used to validate the DEM

methodology. The laboratory direct shear tests were done at three different normal stresses with

three replicates at each normal stress while the simulation was done at eight different normal

stress. The values that the simulation was attempting to reproduce were the internal friction angle

and the apparent cohesion. There was no evidence of a statistical difference between simulation

and laboratory of either the internal friction angle or the apparent cohesion at a 95% confidence

interval. This shows that the DEM methodology for calibrating DEM flexible-fiber of wheat

straw was successful and can be applied to simulate crop (wheat straw)-machine simulations.