Calibration of linear contact stiffnesses in discrete element models using a hybrid analytical-computational framework

Abstract

Efficient selections of particle-scale contact parameters in discrete element modelling remain an open question. The aim of this study is to provide a hybrid calibration framework to estimate linear contact stiffnesses (normal and tangential) for both two-dimensional and three-dimensional simulations. Analytical formulas linking macroscopic parameters (Young's modulus, Poisson's ratio) to mesoscopic particle parameters for granular systems are derived based on statistically isotropic packings under small-strain isotropic stress conditions. By taking the derived analytical solutions as initial approximations, the gradient descent algorithm automatically obtains a reliable numerical estimation. The proposed framework is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. The results show that this hybrid method practically reduces the time for artificial trials and errors to obtain reasonable stiffness parameters. The proposed framework can be extended to other parameter calibration problems in DEM.

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

“…Thus, the calibration problem has to be converted to a minimisation problem where the values of the parameters are sought to minimise the difference between the simulated macroscopic responses and the targeted values. There are in theory many numerical schemes available that could be employed to solve the minimisation problem, such as the Newton Raphson method and gradient‐based methods …”

“…However, for a highly nonlinear discrete granular system, particularly for the Hertz‐type–based DEM models, the traditional methods suffer from the problems of existing many local optimums and/or poor convergence. The gradient‐based method proposed in our previous work (Qu et al) for the calibration of linear contact parameters has proved to be inefficient, and no successful calibration has been achieved for the current problem concerned.…”

“…As a continuation of a sequence of work to address parameter calibration problems in DEM, the main objective of this paper is to extend a hybrid analytical‐computational framework proposed in Qu et al to effectively approximate the contact parameters in the pressure‐dependent Hertz‐Mindlin–type contact models for both two‐dimensional (2D) and three‐dimensional (3D) cases. On the basis of Reuss's hypothesis, a set of simplified static solutions relating particle‐scale contact stiffnesses to macro material properties for Hertz‐Mindlin–type contact models are explicitly derived in Section 3 and compared with the numerical results in Section 4.…”

“…These semianalytical formulae then serve as the initial estimation for the subsequent iterative scheme that aims to further improve the calibration accuracy numerically. However, because of the highly nonlinear feature of discrete particle systems, which is made worse by the nonlinear relationship in the Hertz‐Mindlin–type contact model, the iterative scheme adopted in Qu et al tends to suffer from poor convergence for the problem concerned. Thus, an alternative algorithm called the adaptive moment estimation (Adam), which is developed for machine learning, is employed in Section 5 to automatically optimise the parameters to be calibrated.…”

Calibration of parallel bond parameters in bonded particle models via physics-informed adaptive moment optimisation

“…Recently, a hybrid analytical and computational framework has been developed by the authors [22,23] to calibrate the particle-scale linear and non-linear deformation parameters within an accuracy of 1% or 2% after a few iterations. In the current paper, we extend this work to the calibration of parallel bond parameters with a physics-informed gradient-based optimisation method, aiming at addressing more complicated parameter calibration problems in DEM.…”