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首页> 外文期刊>Journal of industrial and management optimization >TOWARDS AN OPTIMIZATION THEORY FOR DEFORMING DENSE GRANULAR MATERIALS: MINIMUM COST MAXIMUM FLOW SOLUTIONS
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TOWARDS AN OPTIMIZATION THEORY FOR DEFORMING DENSE GRANULAR MATERIALS: MINIMUM COST MAXIMUM FLOW SOLUTIONS

机译：朝着使稠密颗粒材料变形的优化理论迈进：最低成本，最高流量解决方案

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We use concepts and techniques of network optimization theory to gain a better understanding of force transmission in dense granular materials. Specifically, we represent a deforming granular material over the different stages of a quasi-static biaxial compression test as a series of representative flow networks, and analyze force transmission through these networks. The forces in such a material are transmitted through the contacts between the constituent grains. As the sample deforms during the various stages of the biaxial test, these grains rearrange: while many contacts are preserved in this rearrangement process, some new contacts form and some old contacts break. We consider the maximum flow problem and the minimum cost maximum flow (MCMF) problem for the flow networks constructed from this evolving network of grain contacts. We identify the flow network bottleneck and establish the sufficient and necessary conditions for a minimum cut of the maximum flow problem to be unique. We also develop an algorithm to determine the MCMF pathway, i.e. a set of edges that always transmit non-zero flow in every solution of the MCMF problem. The bottlenecks of the flow networks develop in the locality of the persistent shear band, an intensively-studied phenomenon that has long been regarded as the signature failure microstructure for dense granular materials. The cooperative evolution of the most important structural building blocks for force transmission, i.e. the force chains and 3-cycles, is examined with respect to the MCMF pathways. We find that the majority of the particles in the major load-bearing columnar force chains and 3-cycles consistently participate in the MCMF pathways.
机译：我们使用网络优化理论的概念和技术来更好地理解致密颗粒材料中的力传递。具体来说，我们将准静态双轴压缩试验不同阶段的变形颗粒材料表示为一系列代表性的流动网络，并分析通过这些网络的力传递。这种材料中的力通过组成晶粒之间的接触传递。随着样品在双轴测试的各个阶段变形，这些晶粒会重新排列：尽管在此重新排列过程中保留了许多触点，但一些新的触点会形成而某些旧的触点会破裂。我们考虑了由这种不断发展的谷物接触网络构成的流动网络的最大流动问题和最小成本最大流动（MCMF）问题。我们确定了流量网络的瓶颈，并为使最大流量问题的最小割减变得唯一而建立了充分必要的条件。我们还开发了一种算法来确定MCMF路径，即在MCMF问题的每个解决方案中始终传输非零流量的一组边。流动网络的瓶颈在持久剪切带的局部发展，这是一个经过深入研究的现象，长期以来一直被认为是致密颗粒材料的特征破坏微观结构。针对MCMF路径，研究了用于力传递的最重要的结构构件（即力链和3个循环）的协同演化。我们发现，主要的承重柱状力链和3个循环中的大多数粒子始终参与MCMF路径。

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