[论文解读] Memory of jamming and shear-jamming (in soft and granular matter)

Nishant Kumar, Stefan Luding|arXiv (Cornell University)|Jul 23, 2014

Granular flow and fluidized beds被引用 1

一句话总结

本文提出了一种可变的、与历史相关的阻塞密度作为新的状态变量，以捕捉软材料和颗粒材料中形变历史的记忆效应，从而建立一个统一的、可预测的宏观模型，通过多尺度分形能量景观将微观结构与宏观流动行为联系起来。该模型解释了各向同性压缩如何通过缓慢的对数增长提升阻塞密度，而剪切变形则通过体积膨胀或致密化机制引发快速的指数级变化。

ABSTRACT

Soft, disordered, micro-structured materials are ubiquitous in nature and industry, and are different from ordinary fluids or solids, with unusual, interesting static and flow properties. The transition from fluid to solid -at the so-called jamming density- features a multitude of complex mechanisms, but there is no unified theoretical framework that explains them all. In this study, a simple yet quantitative and predictive model is presented, which allows for a variable, changing jamming density, encompassing the memory of the deformation history and explaining a multitude of phenomena at and around jamming. The jamming density, now introduced as a new state-variable, changes due to the deformation history and relates the system's macroscopic response to its microstructure. The packing efficiency can increase logarithmically slow under gentle repeated (isotropic) compression, leading to an increase of the jamming density. In contrast, shear deformations cause anisotropy, changing the packing efficiency exponentially fast with either dilatancy or compactancy. The memory of the system near jamming can be explained by a microstatistical model that involves a multiscale, fractal energy landscape and links the microscopic particle picture to the macroscopic continuum description, providing a unified explanation for the qualitatively different flow-behavior for different deformation modes. To complement our work, a recipe to extract the history-dependent jamming density from experimentally accessible data is proposed, and alternative state-variables are compared. The proposed simple macroscopic constitutive model is calibrated with the memory of microstructure. Such approach can help understanding predicting and mitigating failure of structures or geophysical hazards, and will bring forward industrial process design/optimization, and help solving scientific challenges in fundamental research.

研究动机与目标

• 解决缺乏统一理论框架来解释软材料和颗粒材料中复杂阻塞转变的问题。
• 量化形变历史（尤其是剪切和各向同性压缩）对阻塞密度和堆积效率的影响。
• 开发一种包含微观结构记忆的可预测宏观本构模型。
• 提供一种从实验数据中提取与历史相关的阻塞密度的实用方法。
• 通过单一、基于微观统计的框架，统一不同形变模式下的多种流动行为。

提出的方法

• 引入阻塞密度作为新的状态变量，其演化依赖于形变历史，从而实现对材料宏观响应的预测。
• 采用多尺度分形能量景观模型，将微观粒子构型与连续体层面的力学行为联系起来。
• 将各向同性压缩建模为由于堆积效率逐步提升而引起的阻塞密度对数增长。
• 将剪切形变建模为堆积效率的指数级变化，导致体积膨胀或致密化，具体取决于剪切模式。
• 推导出一个基于微观结构记忆校准的本构模型，利用实验可测数据提取与历史相关的阻塞密度。
• 比较多种替代状态变量，并在不同形变模式下验证所提模型的预测能力。

实验结果

研究问题

• RQ1 形变历史（特别是各向同性压缩）如何影响软材料和颗粒材料中的阻塞密度？
• RQ2 剪切形变期间堆积效率发生指数级变化的机制是什么？这些机制在体积膨胀与致密化区域之间有何不同？
• RQ3 如何通过单一统一模型解释在各向同性压缩与剪切作用下观察到的定性不同的流动行为？
• RQ4 微观结构记忆在决定接近阻塞转变点的宏观力学响应中起什么作用？
• RQ5 如何从实验数据中提取与历史相关的阻塞密度以实现实际应用？

主要发现

• 重复各向同性压缩使阻塞密度呈对数增长，表明堆积效率存在缓慢而累积的记忆效应。
• 剪切形变引起各向异性和堆积效率的指数级快速变化，导致根据剪切模式的不同而出现体积膨胀或致密化。
• 所提出的模型通过单一、与历史相关的状态变量，成功统一了不同形变模式下的多种流动行为。
• 基于分形能量景观的微观统计模型，为微观粒子排列与宏观连续体响应之间提供了物理解释。
• 已建立一种实用方法，可从实验可测数据中提取与历史相关的阻塞密度，从而实现模型校准与验证。
• 该框架可提升对结构失效和地质灾害的预测与缓解能力，并支持工业过程的优化。