An iterative Bayesian filtering framework for fast and automated calibration of DEM models

The nonlinear, history-dependent macroscopic behavior of a granular material is rooted in the micromechanics between constituent particles and irreversible, plastic deformations reflected by changes in the microstructure. The discrete element method (DEM) can predict the evolution of the microstructure resulting from interparticle interactions. However, micromechanical parameters at contact and particle levels are generally unknown because of the diversity of granular materials with respect to their surfaces, shapes, disorder and anisotropy. The proposed iterative Bayesian filter consists in recursively updating the posterior distribution of model parameters and iterating the process with new samples drawn from a proposal density in highly probable parameter spaces. Over iterations the proposal density is progressively localized near the posterior modes, which allows automated zooming towards optimal solutions. The Dirichlet process Gaussian mixture is trained with sparse and high dimensional data from the previous iteration to update the proposal density. As an example, the probability distribution of the micromechanical parameters is estimated, conditioning on the experimentally measured stress-strain behavior of a granular assembly. Four micromechanical parameters, i.e., contact-level Young's modulus, interparticle friction, rolling stiffness and rolling friction, are chosen as strongly relevant for the macroscopic behavior. The a priori particle configuration is obtained from 3D X-ray computed tomography images. The a posteriori expectation of each micromechanical parameter converges within four iterations, leading to an excellent agreement between the experimental data and the numerical predictions. As new result, the proposed framework provides a deeper understanding of the correlations among micromechanical parameters and between the micro- and macro-parameters/quantities of interest, including their uncertainties. Therefore, the iterative Bayesian filtering framework has a great potential for quantifying parameter uncertainties and their propagation across various scales in granular materials.