This 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.

中文翻译：

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离散元素模型的Hertz型接触参数的混合校准方法

这项研究旨在提供一个混合校准框架，以估计二维和三维离散元素建模（DEM）的赫兹类型接触参数（颗粒尺度剪切模量和泊松比）。在统计各向同性的颗粒填料的基础上，得出了在小应变各向同性应力条件下，宏观材料参数（杨氏模量和泊松比）与颗粒体系的颗粒尺寸Hertz型接触参数之间的一组解析公式。但是，派生的解析解仅是一般模型的估计值。通过将每个DEM建模视为一个隐含的数学函数，将粒子级参数作为自变量，并将派生的解析解用作初始输入参数，提出了一种自动迭代方案来获得具有较高精度的校准参数。考虑到基于Hertz的离散元素模型中的高度非线性特征和宏观-微观关系的不连续性，本研究采用自适应矩估计算法，因为它具有处理成本函数噪声梯度的能力。所提出的方法在包括随机分布的单分散填料和多分散填料的几个数值案例中得到了验证。在校准效率和准确性方面已取得明显改善。本研究采用自适应矩估计算法，因为它具有处理代价函数噪声梯度的能力。所提出的方法在包括随机分布的单分散填料和多分散填料的几个数值案例中得到了验证。在校准效率和准确性方面已取得显着改善。本研究采用自适应矩估计算法，因为它具有处理代价函数噪声梯度的能力。所提出的方法在包括随机分布的单分散填料和多分散填料的几个数值案例中得到了验证。在校准效率和准确性方面已取得明显改善。