oscillatoryRheometerBurgers

Overview

Template Info

Target Parameters: maxw_Y kelv_Y kelv_nu
Contact Models: cohesion asphalt tangential burgers_asphalt
Particle Shapes: sphere

This case simulates an oscillatory rheometer sweeping different angular frequencies and it is used to calibrate the viscoelastic models gran cohesion asphalt and tangential burgers_asphalt (see section Calibration suggestions for more information on the models). The calibration template is sensitive to the target parameters maxw_Y, kelv_Y, kelv_nu, which stand for the Young’s Modulus of the Maxwell body, the Youngs’s Modulus and the viscosity of the Kelvin body respectively.

The setup consists of a laterally-unconfined packet of particles which undergoes periodic shear. The height of the packing is defined via the numberOfParticlesInZ keyword and the shape via the lattice_type keyword. Two different packing types are possible: cubic (see sketch below) and hexagonal close packing.

The amplitude of the oscillation in percentage of the packing height (i.e., the maximum shear strain times 100) is expressed via the strainPercentage keyword. A maximum of 30 angular frequencies can be selected via the angularVelocity_1, ..., angularVelocity_30 keywords. The viscosity of the material, defined as $\nu = \tau_{max}/(\epsilon_{max} \omega)$ where $\tau_{max}$ is the maximum shear stress, $\epsilon_{max}$ is the maximum shear strain and $\omega$ is the angular frequency, is calculated and compared to reference values.

Calibration suggestions

For small shear strains (e.g., istrainPercentage = 5) the gran cohesion asphalt model model does not play an effective role, as the particles very rarely have a negative overlap (i.e., particles are mostly attached). Hence, a calibration of the parameters of the cohesion asphalt model should not be pursued in this case.

Regarding the parameters of the gran tangential burgers_asphalt model, it has been observed that by changing the Young’s modulus of the Maxwell body it is possible to match the viscosity in magnitude, while by changing the viscosity of the Kelvin body it is possible to change the shear-thinning behaviour of the material at the different angular frequencies.

The viscosity of the Maxwell body controls the thixotropic behaviour of the material. Small values of the Maxwell viscosity requires longer simulation times before the viscosity can reach a steady-state. Since the reference information is the material viscosity at steady-state, this parameter can be kept constant and high enough to guarantee a rapid convergence to the steady-state viscosity. By changing the Young’s modulus of the Kelvin body no significant changes has been observed.

The oscillatory rheometer can be run in parallel when using runMode shellScript. Then, the frequency sweep is computed on multiple partitions, the number can be controlled via the NPROC parameter. Note that usually there is no real gain beyond NPROC 2: one processor then runs the lowest frequency, and the other one runs all other frequencies. Only when running very narrowly spaced frequencies (eg. $\omega_2 < 2 \omega_1$ ), increasing NPROC will result in actual increase in simulation speed.

Quality function

The quality function is calculated as the mean-square deviation between the experimental and the simulation data, normalized by the maximum simulation value squared:

$f_q = \frac{\sum_{i=1}^P \left( \nu_{sim}(\omega_i) - \nu_{ref}(\omega_i) \right)^2}{P (\max{\nu_{sim}})^2}$

where $\nu_{sim}$ and $\nu_{ref}$ are the simulated and experimental viscosities, $\omega_i$ is the generic angular frequency and $P$ is the number of angular frequency spanned during the frequency sweep.

Measurement file

The text file containing the experimental measurements must have two columns: one for the angular frequencies (expressed rad/s) and the other for the material viscosity (expressed in Pa s). The data in each row should be either space-, tab- or comma-separated. An example of measurment file is given below.

# frequency [rad/s] viscosiy [Pa s]
279960886 78120.16628
189839968 45214.52292
572892445 28462.25023
77531671 15699.21565
24841882 13253.5802
19975448 6684.952969
5981209 3952.995275
6055466 2452.652682
6875271 1883.825665
3246147 1461.785542

Template parameters

General settings

Parameter	Default
scaleweight	1
pairGranModel	hertz
pairTangential	burgers_asphalt
pairCohesion	asphalt
NPROC	1
dumpT	0.01 s
dump	1

Specific settings

Variable	Default	Meaning
numberOfParticlesInZ	4	Number of particles in z direction
strainPercentage	5.0	Maximum amplitude in percentage of packing height (i.e., maximum shear strain times 100)
lattice_type	1	0 = cubic packing (sc), 1 = hexagonal close packing (hcp)
timestep	2.5e-6	time step size
nPeriods	5	Number of periods to be simulated for each angular frequency
angularVelocity_1	6.283185307	Angular frequency nr. 1 [rad/s]
angularVelocity_2	12.566370614	Angular frequency nr. 2 [rad/s]
angularVelocity_3 … angularVelocity_30	0	Angular frequency nr. 3 to 30 [rad/s]