In investigations of the behaviour of granular materials, the conversion of discrete contact information, specifically the force and displacement data, into macroscopic quantities such as stress and strain is a fundamental approach. The expression for the average stress tensor, a well-established formulation, involves the summation over all interparticle contacts while considering both the contact force and geometric parameters such as the branch vector. However, for the three-dimensional case, a general micromechanical expression for the average strain tensor is still missing.

中文翻译：

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颗粒材料平均应变张量的三维微观力学表达式

在研究颗粒材料的行为时，将离散的接触信息（特别是力和位移数据）转换为宏观量（如应力和应变）是一种基本方法。平均应力张量的表达式是一个成熟的公式，涉及所有粒子间接触的总和，同时考虑接触力和几何参数，例如分支矢量。然而，对于三维情况，仍然缺少平均应变张量的一般微观力学表达式。