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张洁课题组在Nature Communications发表关于颗粒体系中剪切局域化与长程应力关联的最新研究成果Connecting Shear Localization with the Long-range Correlated Polarized Stress Fields in Granular Materials

近日,上海交通大学自然科学研究院/物理与天文学院张洁课题组及其合作者在颗粒体系中发现了剪切局域化(shear localization)和长程关联的极化应力场之间的关系,研究成果Connecting Shear Localization with the Long-range Correlated Polarized Stress Fields in Granular Materials于2020年8月28日在线发表在Nature Communications杂志。

非晶固体的研究中一个长期难题是关于剪切局域化,即材料在剪切外场作用下,粒子重排(或塑性形变)集中发生在一个狭小的区域内。这种局域塑性行为在空间上往往存在协同性的关联,可以进一步形成剪切带,最终导致材料的断裂。这种现象不仅发生在颗粒材料(granular materials)中,在其他非晶固体(amorphous solids)中也有发现,比如分子玻璃(molecular glass),金属玻璃(metallic glass),胶体(colloids),乳剂(emulsions),泡沫(foams)等。它不仅对于材料研究具有重要意义,而且与岩土工程和地质灾害也有着紧密的联系。由于材料结构的无序性和复杂性,非晶固体中的剪切局域化问题一直存在着激烈的争论。

力链网络,剪切局域化区域与极化应力场的关联

对于一个均匀的各向同性的无序固体施加剪切,剪切局域化是如何产生的呢?张洁课题组研究发现,颗粒体系在剪切外场下产生的剪切局域化区域,与沿最大剪切应力方向的两个极化应力场之间存在很强的(反)相关性。通过对体系应力张量和对称性的分析,揭示了这种深刻的关联是旋转对称性破缺的结果。最后该项研究首次提供了实验上的证据,表明对于各向同性的非晶固体,局域压强在空间上是短程关联的同时,剪切应力存在着长程关联。

实空间中的剪切应力自关联函数

本项工作主要由博士生汪银桥完成,合作者有王宇杰教授,通讯作者为张洁教授。该研究工作得到了国家自然科学基金的支持。

此外,张洁课题组与美国布兰迪斯大学的Bulbul Chakraborty教授课题组合作研究,发现了非晶固体中弹性的产生机制。研究成果Emergent Elasticity in Amorphous Solids于2020年9月10日发表在Physical Review Letters。

傅里叶空间中的应力关联

与晶体中弹性起源于自发对称破缺不同,非晶固体中弹性起源于粒子局域的力平衡与力矩平衡。理论推导发现这些限制条件的数学结构与广义电磁场相同,在静电极限下,可以成功的描述非晶固体各向异性的弹性。局域力学约束产生弹性,对于不具有对称性破缺的系统提供了新的范例,类似于量子自旋液体中的emergent gauge theories。该理论推导得到的应力空间关联的长程关联性和pinch point singularity,得到了数值模拟和光弹性颗粒实验的直接验证。实验结果表明颗粒体系中的力链结构是无序弹性的次维度激发(sub-dimensional excitations),这种现象类似于分形子(fractons)。

本项工作解析理论和数值模拟部分由Jishnu N. Nampoothiri, Kabir Ramola, Subhro Bhattacharjee, and Bulbul Chakraborty完成,实验部分由博士生汪银桥和张洁教授共同完成,通讯作者为Bulbul Chakraborty教授。该实验研究工作得到了国家自然科学基金的支持。

On 28th August 2020, Nature Communications published the research about shear localization and long-range correlated polarized stress fields by Prof. Jie Zhang and his collaborator. The title of the paper is Connecting Shear Localization with the Long-range Correlated Polarized Stress Fields in Granular Materials.

One long-lasting puzzle in amorphous solids is shear localization, where local plastic deformation involves cooperative particle rearrangements in small regions of a few inter-particle distances, self-organizing into shear bands and eventually leading to the material failure. Understanding the connection between the structure and dynamics of amorphous solids is essential in physics, material sciences, geotechnical and civil engineering, and geophysics. Here we show a strong connection between shear localization and the intrinsic structures of internal stresses in an isotropically jammed granular material subject to shear. Specifically, we find strong (anti)correlations between the micro shear bands and two polarized stress fields along two directions of maximal shear. By exploring the tensorial characteristics and the rotational symmetry of force network, we reveal that such profound connection is a result of symmetry breaking by shear. Finally, we provide the solid experimental evidence of long-range correlated inherent shear stress in an isotropically jammed granular system.

The first author is Ph. D. student Yinqiao Wang, the corresponding author is Prof. Jie Zhang, and Prof. Yujie Wang is a co-author. This work is supported by NSFC.

On 10th September 2020, Physical Review Letters published the work collaborated by Prof. Bulbul Chakraborty’s group in Brandies University and Prof. Jie Zhang’s group. The title of the paper is Emergent Elasticity in Amorphous Solids.

The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues is not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the response of such athermal solids is governed by local conditions of mechanical equilibrium, i.e., force and torque balance of its constituents. Here we show that these constraints have the mathematical structure of a generalized electromagnetism, where the electrostatic limit successfully captures the anisotropic elasticity of amorphous solids. The emergence of elasticity from local mechanical constraints offers a new paradigm for systems with no broken symmetry, analogous to emergent gauge theories of quantum spin liquids. Specifically, our U(1) rank-2 symmetric tensor gauge theory of elasticity translates to the electromagnetism of fractonic phases of matter with the stress mapped to electric displacement and forces to vector charges. We corroborate our theoretical results with numerical simulations of soft frictionless disks in both two and three dimensions, and experiments on frictional disks in two dimensions. We also present experimental evidence indicating that force chains in granular media are subdimensional excitations of amorphous elasticity similar to fractons.

The theoretical and numerical work were done by Jishnu N. Nampoothiri, Kabir Ramola, Subhro Bhattacharjee and Bulbul Chakraborty. Yinqiao Wang and Prof. Jie Zhang performed experimental measurement and analyzed results. Prof. Bulbul Chakraborty is the corresponding author. The experimental work is supported by NSFC.