浸没条件下离散质点系的平均应力张量
Mean Stress Tensor of Discrete Particle Systems in Submerged Conditions
摘要：
平均应力张量对于研究颗粒材料的动力学至关重要。在本文中，我们使用汉密尔顿的最小作用原理推导出的平均应力张量的离散颗粒组件受到液压力场，以及严格的条件，适当定义的代表性体积元（RVE）。我们努力背后的主要目标是将粒子物理学升级为涉及谷物和水之间复杂相互作用的系统的声音应力张量。我们确定的贡献，从不平衡力，液压力，重力，外力，和粒子波动的平均应力张量。在这样做时，当颗粒系统经受复杂环境时，例如，水下条件利用离散元法（DEM）和格子玻尔兹曼方法（LBM）对干燥和饱和颗粒体系进行了三轴试验模拟，验证了所得公式的正确性。结果表明，推导的公式可以准确地计算具有各种体积力场的离散组件的应力张量。我们使用经过验证的DEM-LBM模拟淹没颗粒柱坍塌，探索在颗粒尺度上发生的物理现象，并展示其潜力。我们提供了一个新的视角的基础上的颗粒组装尺度追求流固相互作用。由于应力分析在颗粒材料本构模型中的重要性，这项工作可以帮助更好地获得饱和或淹没颗粒系统的应力-应变关系。
英文摘要：
The mean stress tensor is essential to investigate the dynamics of granular material. In this paper, we use Hamilton's principle of least action to derive the averaged stress tensor of discrete granular assemblies subjected to hydraulic force fields, as well as rigorous conditions for a proper definition of the Representative Volume Element (RVE). The main goal behind our efforts is to upscale particle physics into a sound stress tensor for systems involving the complex interaction between grains and water. We identify the contributions from the unbalanced forces, hydraulic forces, gravity, external forces, and particle fluctuation to the mean stress tensor. In doing so, it is convenient to separate the influence of different force fields when the granular system is subjected to complex environments, e.g., subaqueous conditions. The obtained formula is then validated by triaxial test simulations of dry and saturated granular systems using the Discrete Element Method (DEM) and the Lattice-Boltzmann Method (LBM). The results show that the deduced formula can accurately calculate the stress tensor of discrete assemblies with various body-force fields. We used validated DEM-LBM simulations of submerged granular column collapses to explore the physics happening at the grain scale with this mathematical formalism and showcase its potential. We provide a new perspective based on the granular assembly scale to pursue the fluid-solid interaction. Due to the importance of stress analysis in the constitutive modelling of granular materials, this work could help to better obtain the stress-strain relationship of saturated or submerged granular systems.
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