Implementation and validation of a bonded particle model to predict rheological properties of viscoelastic materials

This work focuses on implementing a particle-based method able to characterize viscoelastic materials whose rheological properties, such as storage modulus G’ and loss modulus G”, are known. It is based on the Bonded Particle Model, with the elastic constitutive relation here substituted with a viscoelastic one to capture time-scale effects. The Burgers model, vastly used in literature to model viscoelastic systems, is discretized and implemented. The test case used for calibration comprises of a cubic lattice, sheared with a periodic motion, to mimic the effect of a shear rheometer. After appropriate filtering of the stress response, the rheological properties are obtained, highlighting the effect of the lattice geometry, as well as the particle size, on the accuracy of the model. Moreover, the Burgers parameters are calibrated by analytically fitting the experimental dataset, showing the limitation of the Burgers model. The micro-contact parameters are obtained from the macro parameters through appropriate scaling. After completing a frequency sweep, the simulated G’ and G” show a relatively large error, around 25% for G’ for example. For this reason, a more robust model, namely the Generalized Maxwell Model, has been implemented. The calibration procedure is performed in the same fashion as for the Burgers model. Moreover, the tangential micro-contact parameters are scaled w.r.t. the normal ones. This scaling parameter, called α, is calibrated by minimizing the Root Mean Square Error between simulation and experimental data, giving errors below 10% in both G’ and G” for a large dataset. Additionally, a full ring plate-plate rheometer setup is simulated, and the simulation is compared with the given experimental dataset, again finding a good agreement.