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Analysis of three-dimensional micro-mechanical strain formulations for granular materials: Evaluation of accuracy

机译:颗粒材料的三维微机械应变公式分析:精度评估

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摘要

An important objective of recent research on micro-mechanics of granular materials is to develop macroscopic constitutive relations in terms of micro-mechanical quantities at inter-particle contacts. Although the micro-mechanical formulation of the stress tensor is well established, the corresponding formulation for the strain tensor has proven to be much more evasive, still being the subject of much discussion. In this paper, we study various micro-mechanical strain formulations for three-dimensional granular assemblies, following the work of Bagi in two dimensions (Bagi, 2006). All of these formulations are either based on an equivalent continuum approach, or follow the best-fit approach. Their accuracy is evaluated by comparing their results, using data from Discrete Element Method simulations on periodic assemblies, to the macroscopic deformation. It is found that Bagi's formulation (Bagi, 1996), which is based on the Delaunay tessellation of space, is the most accurate. Furthermore, the best-fit formulation based on particle displacements only did unexpectedly well, in contrast to previously reported results for two-dimensional assemblies.
机译:颗粒材料的微观力学的最新研究的一个重要目标是根据粒子间接触处的微观力学量发展宏观的本构关系。尽管已经很好地建立了应力张量的微机械公式,但应变张量的相应公式已被证明更容易规避,仍然是许多讨论的主题。在本文中,我们跟随Bagi在二维上的工作,研究了用于三维颗粒组件的各种微机械应变公式(Bagi,2006)。所有这些公式要么基于等效的连续方法,要么遵循最佳拟合方法。通过使用离散元素方法模拟的周期性装配数据与宏观变形进行比较,可以比较其结果,从而评估其准确性。人们发现,基于空间Delaunay细分的Bagi公式(Bagi,1996)是最准确的。此外,与先前报道的二维装配结果相反,基于粒子位移的最佳拟合公式仅出乎意料地出色。

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