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Macroscopic strains in granular materials accounting for grain rotations

机译：颗粒材料中的宏观应变解释了晶粒的旋转

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摘要

Granular materials are special materials, from the continuum-mechanical viewpoint, in the sense that they possess a clear microstructure of grains and intergrain contacts. In addition, the grains have translational as well as rotational degrees of freedom. Here a micromechanical expression is formulated for the average displacement gradient tensor in terms of the grain displacements and rotations for the two-dimensional case. It is based on a tessellation of the granular assembly into closed loops, along whose boundary the displacement field is defined in terms of the grain displacements and rotations. An important consideration for this expression is that it must satisfy the surface-additivity property, according to which the average displacement gradient of a combined two-dimensional surface is determined by the average displacement gradients of the constituent surfaces (and weighted by their areas). The developed micromechanical expression is verified by comparing its results with the macroscopic deformation as determined from the displacements at the boundary. Results of DEM simulations of a biaxial test (where the average rotation is equal to zero) and a shear test (where the average rotation is not equal to zero) are employed for this verification. The developed micromechanical expression for the displacement gradient is subsequently used to study deformation patterns in a complex case of a biaxial test where a shear band is formed.
机译：从连续力学的角度来看，粒状材料是特殊的材料，因为它们具有清晰的晶粒微结构和晶间接触。另外，颗粒具有平移和旋转自由度。在此，针对二维情况下的晶粒位移和旋转，针对平均位移梯度张量制定了微机械表达式。它基于将颗粒装配体细分为闭环的形式，沿着其边界，位移场是根据晶粒的位移和旋转来定义的。此表达式的重要考虑因素是它必须满足表面可加性，根据该属性，组合二维表面的平均位移梯度由组成表面的平均位移梯度确定（并由其面积加权）。通过将其结果与根据边界处的位移确定的宏观变形进行比较，可以验证所开发的微机械表达式。验证采用双轴测试（平均旋转等于零）和剪切测试（平均旋转不等于零）的DEM模拟结果。针对位移梯度开发的微机械表达式随后用于研究在形成剪切带的双轴测试的复杂情况下的变形模式。

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