Viscoelastic model calibration

Description

This text describes how to calibrate the DEM model for a viscoelastic paste using results from a rotational rheometer.

Introduction

This tutorial shows an application of the calibration template oscillatoryRheometerBurgers. The setup consists of a laterally-unconfined cubic lattice of spherical particles which undergoes periodic shear in the horizontal plane. The height of the lattice is equal to 10 particle’s diameters; see Figure 1. The amplitude of the oscillation, A, is set equal to 5% of the lattice’s height, h. The frequencies of the oscillations are: \omega_1 = 111.6\,rad/s, \omega_2 = 226.6\,rad/s and \omega_3 = 513.3\,rad/s.

_images/tutorial_viscoelasticCal.png

Figure 1: particle lattice undergoing periodic shearing.

The scope of this tutorial is to calibrate the asphalt tangential contact model so that the viscosity of the model material corresponds to the reference value over a certain interval of frequencies.

Detailed descriptions

Contact model

The contact model and the coarsegraining factor are defined in the file settings/contact_model.txt. The models used in this tutorial are: Hertz normal contact, asphalt tangential contact, asphalt cohesion model.

Material properties and particle size distribution

The values of the fixed material parameters and the initial, minimum and maximum values of the target material parameters are defined in the file settings/materials.txt.

Warning

Not all the parameters specified in materials.txt are used by the simulations, as it depends on the contact models selected in contact_model.txt

The particle size distribution is defined in the file settings/particle_sizes.txt.

Calibration case settings

The tutorial consists of a single calibration_case of the template oscillatoryRheometerBurgers. Some template-specific settings of the calibration case are defined in the file settings/tests.txt.

Other more general settings, like the number of iterations of the calibration procedure, can be found in the file settings/general.txt.

Running the tutorial and analyzing the results

The user can run the tutorial via command line as follows:

aspherix-calibration run -in viscoelastic_calibration.casx

The convergence of the calibration is reported in the file calibration/results/conv.dat, which reads as follows:

# nIter kelv_nu maxw_Y qf
  1        50500      550000    0.856388
  2        83500      550000    0.285046
  6        83500      850000    0.147139
 10        94500      850000   0.0407045
 14        94500      950000   0.0128663
 36      98166.7      883333   0.0100542

The iteration returning the lowest value of the quality function is the number 36. The comparison between the reference and the numerical viscosities obtained for iteration 36 is shown in Figure 2. As can be seen, the calibrated model is capable to reproduce very well the shear-thinning behaviour of the paste.

_images/tutorial_viscoelasticCal2.png

Figure 2: viscosity of the viscoelastic material as a function of the rheometer’s frequency (reference and simulation).

The viscosity is defined as \tau_{max}/(\epsilon_{max} \omega), where \tau_{max} is the maximum tangential stress and \epsilon_{max} is the maximum strain. As can be seen in Figure 3, \tau_{max} requires some time before reaching a steady-state value. In order to calculate properly the viscosity, it is necessary to set the number of periods to a value which is high enough to allow the reaching of the steady-state (in this case 70 seems to be enough). The template only averages the viscosities obtained from the second half of the force history plot in Figure 3.

_images/tutorial_viscoelasticCal3.png

Figure 3: tangential stress as a function of time obtained at iteration 36. Each iteration consists of 3 simulations performed with the rotation frequencies \omega_1 = 111.6\,rad/s, \omega_2 = 226.6\,rad/s and \omega_3 = 513.3\,rad/s. The number of periods that are simulated is equal to 70 to allow the reaching of a steady-state.