Kamrin, KenKim, Seongmin2021-11-2220212021-11-162021-11Kim, Seongmin. 2021. Determining Nonlocal Granular Rheology from Discrete Element Simulations. Doctoral dissertation, Harvard University Graduate School of Arts and Sciences.28768248https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37370215We determine the constitutive equation of simple granular materials considering them as continuous fluids. Based on discrete element simulations, we propose two rheological models with different Rivlin-Ericksen tensor orders. In the first-order model, we identify that rescaling the shear-to-stress ratio $\mu$ by a power function of dimensionless granular temperature $\Theta$ makes the data from many different flow geometries collapse to a single curve which depends only on the inertial number $I$. The basic power-law structure appears robust to varying surface friction in both 2D and 3D systems. We also observe that $\phi$ is a function of $\mu$, which connects our rheology to kinetic theory and the nonlocal granular fluidity model. In order to describe stress anisotropy and secondary flows, we extend our model by including the second-order Rivlin Ericksen tensor. Using DEM data, we find the equations for three model parameters $\mu_1$, $\mu_2$, and $\mu_3$ as functions of $I$ and $\Theta$. We observe similar power-law scaling in $\mu_1$ and $\mu_2$ while $\mu_3$ distributes near zero for small $I$. The first and second normal stress differences $N_1$ and $N_2$ are also measured and discussed. We validate the models by running finite difference method simulations of inclined chute flows. We show that the second-order model predicts all the velocity components including secondary flows while the first-order model predicts velocity in the downstream direction only. Both models successfully predict the exponentially decaying velocity as $\Theta$ is included in the model parameters.application/pdfenAmorphous MaterialGranular FlowGranular MaterialGranular RheologyNonlocal RheologySoft MatterApplied physicsMechanical engineeringGeophysicsThesis or Dissertation2021-11-220000-0001-5766-7605