Date of Award
Doctor of Philosophy
Agricultural and Biosystems Engineering
Agricultural and Biosystems Engineering
Mehari Z. Tekeste
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
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.
Matthew W Schramm
Schramm, Matthew W., "A methodology of calibrating flexible fibers in the discrete element method for simulating wheat straw shear" (2019). Graduate Theses and Dissertations. 17776.