Jawaharlal Nehru Center for Advanced Scientific Research, Jakkur Campus, Bengaluru 560064, India.
TIFR Center for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India.
Phys Rev E. 2019 Jan;99(1-1):012123. doi: 10.1103/PhysRevE.99.012123.
The emergence of rigidity upon changes of temperature, density, or applied stresses in disordered assemblies of particles is of interest in a wide range of soft matter, from glass formers, gels, foams, and granular matter. Shear jamming of frictional grains presents an interesting special case wherein the application of shear stress leads to rigidity rather than its loss. The formation of self-organized structures that resist shear deformation offers an appealing geometric picture of shear jamming, which nevertheless is incompletely developed, and not well integrated with ideas concerning rigidity in frictionless systems. Exploiting the observation that athermally sheared sphere assemblies develop structural features necessary for shear jamming even in the absence of friction [H. A. Vinutha and S. Sastry, Nature Physics 12, 578 (2016)1745-247310.1038/nphys3658], we analyze conditions for jamming in such assemblies computationally. Solving force and torque balance conditions for their contact geometry, we show, and validate with frictional simulations, that the mean contact number Z equals D+1 (for spatial dimension D=2,3) at jamming for both finite and infinite friction, above the "random loose packing" limit density, at variance with previous analyses of frictional jamming. We show that the shear jamming threshold satisfies the marginal stability condition recently proposed for jamming in frictionless systems. Along lines explored in studying covalent glasses, we perform rigidity percolation analysis for D=2 and find that rigidity percolation precedes shear jamming, which, however, coincides with the percolation of over-constrained regions, leading to the identification of a regime analogous to the intermediate phase observed in covalent glasses. Together, these results provide a geometric description of shear jamming that relate closely with analyses of jamming, rigidity, and the glass transition in frictionless systems, and thus help develop a unified description of jamming phenomenology in diverse disordered matter.
无序颗粒组装体在温度、密度或外加应力变化时出现的刚性，在广泛的软物质中都很重要，包括玻璃形成体、凝胶、泡沫和颗粒物质。摩擦颗粒的剪切堵塞呈现出一个有趣的特例，即施加剪切应力会导致刚性，而不是失去刚性。抵抗剪切变形的自组织结构的形成提供了剪切堵塞的一个有吸引力的几何图像，但它仍不完善，并且与无摩擦系统中刚性的概念没有很好地结合。我们利用这样一个观察结果，即在无热剪切情况下，球组装体即使在没有摩擦的情况下，也会发展出剪切堵塞所必需的结构特征[H. A. Vinutha 和 S. Sastry, Nature Physics 12, 578 (2016)1745-247310.1038/nphys3658]，从计算上分析这种组装体发生堵塞的条件。通过求解其接触几何的力和力矩平衡条件，我们表明，在有限和无限摩擦的情况下，在“随机松散堆积”极限密度以上，平均接触数 Z 等于 D+1（空间维度 D=2,3），与之前对摩擦堵塞的分析结果不同。我们表明，剪切堵塞的阈值满足最近为无摩擦系统中堵塞提出的边缘稳定性条件。沿着研究共价玻璃时探索的路线，我们对 D=2 进行了刚性渗流分析，发现刚性渗流先于剪切堵塞，然而，这与过约束区域的渗流相吻合，导致识别出类似于在共价玻璃中观察到的中间相的一个区域。总之，这些结果为剪切堵塞提供了一个几何描述，与无摩擦系统中堵塞、刚性和玻璃化转变的分析密切相关，从而有助于在不同的无序物质中发展对堵塞现象学的统一描述。
