A hybrid calibration approach to Hertz‐type contact parameters for discrete element models

Abstract

SummaryThis study aims at providing a hybrid calibration framework to estimate Hertz‐type contact parameters (particle‐scale shear modulus and Poisson ratio) for both two‐dimensional and three‐dimensional discrete element modelling (DEM). On the basis of statistically isotropic granular packings, a set of analytical formulae between macroscopic material parameters (Young modulus and Poisson ratio) and particle‐scale Hertz‐type contact parameters for granular systems are derived under small‐strain isotropic stress conditions. However, the derived analytical solutions are only estimated values for general models. By viewing each DEM modelling as an implicit mathematical function taking the particle‐level parameters as independent variables and employing the derived analytical solutions as the initial input parameters, an automatic iterative scheme is proposed to obtain the calibrated parameters with higher accuracies. Considering highly nonlinear features and discontinuities of the macro‐micro relationship in Hertz‐based discrete element models, the adaptive moment estimation algorithm is adopted in this study because of its capacity of dealing with noise gradients of cost functions. The proposed method is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. Noticeable improvements in terms of calibration efficiency and accuracy have been made.