Abstract

By the micro-structural mechanics approach, this study establishes the quantitative stress–strain relationships at the elastic stage with respect to the microscopic features of the particles for anisotropic granular materials that are composed of regularly arranged elliptical particles with the same size. Firstly, the elliptical particle assembly is equated with a lattice network described by beam elements attached to the center of particles. Then, the elastic stress–strain relationships, which exactly show the features of orthotropic micropolar continuum, are established through analyzing the triangular and hexagonal cells based on the principle of energy balance. Finally, the analytical expressions of eight independent parameters in stress–strain relationships are obtained as the functions of particle shape, size, and microscopic contact stiffnesses. Further, the relationship between microscopic parameters and macroscopic elastic constants for anisotropic granular materials is proposed. The analytical expressions are verified by comparison between theoretical and discrete element method (DEM) results for elliptical particle assembly, and the influences of microscopic parameters on the macroscopic elastic constants are investigated in detail according to the proposed analytical expressions. Our work provides some useful insights for the microscopic explanation and the influences of microscopic parameters on the macroscopic mechanical behavior of granular materials.

Graphic abstract

中文翻译：

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从微观特征解析地获得的弹性常数，用于规则排列的椭圆形粒子组装

摘要

通过微观结构力学方法，本研究建立了弹性阶段相对于各向异性颗粒材料的颗粒微观特征的定量应力-应变关系，该各向异性颗粒材料由规则排列的相同尺寸的椭圆形颗粒组成。首先，椭圆形粒子组件等同于由附着在粒子中心的梁单元描述的晶格网络。然后，根据能量平衡原理，通过分析三角形和六边形单元，建立了精确显示正交各向异性微极连续体特征的弹性应力-应变关系。最后，获得了应力-应变关系中八个独立参数的解析表达式，它们是颗粒形状，尺寸，和微观接触刚度。此外，提出了各向异性粒状材料的微观参数与宏观弹性常数之间的关系。通过对椭圆颗粒组装的理论和离散元方法（DEM）结果进行比较，验证了解析表达式，并根据所提出的解析表达式详细研究了微观参数对宏观弹性常数的影响。我们的工作为微观解释和微观参数对粒状材料宏观力学行为的影响提供了一些有用的见解。通过对椭圆颗粒组装的理论和离散元方法（DEM）结果进行比较，验证了解析表达式，并根据所提出的解析表达式详细研究了微观参数对宏观弹性常数的影响。我们的工作为微观解释和微观参数对粒状材料宏观力学行为的影响提供了一些有用的见解。通过对椭圆颗粒组装的理论和离散元方法（DEM）结果进行比较，验证了解析表达式，并根据所提出的解析表达式详细研究了微观参数对宏观弹性常数的影响。我们的工作为微观解释和微观参数对粒状材料宏观力学行为的影响提供了一些有用的见解。

图形摘要