Sorbonne Universités, UPMC Univ Paris 06, CNRS-UMR 7588, Institut des NanoSciences de Paris, 4 place Jussieu, 75005 Paris, France and Université Paris-Est Marne-la-Vallée, 5 Bd Descartes, Champs-sur-Marne, F-77454 Marne-la-Vallée cedex 2, France.
Soft Matter. 2017 Feb 15;13(7):1371-1383. doi: 10.1039/c6sm01567k.
In jammed packings of soft frictionless particles such as foams or emulsions, stress is transmitted via a network of mechanical contacts between neighbors. In generic simplified models of such materials, particle interaction energies are assumed to be pairwise additive. We report ab initio simulations of foam microstructures, showing that in general, this fundamental assumption is not justified: the conservation of bubble volumes introduces a many-body coupling between all the contacts of a given particle. It strongly modifies the relation between forces and displacements at individual contacts, in a way that cannot be captured by an effective two-body interaction. We report the impact of this effect on the linear and nonlinear elastic response of ordered bubble packings with coordination numbers ranging from 6 to 12, used as simple model systems, and we present an analytical model without free parameters which is valid as long as bubbles have an approximately spherical shape. It predicts the many-body coupling of particle contact forces, as well as the macroscopic mechanical response. For packing fractions approaching the jamming transition where contact forces go to zero, we derive an asymptotic two-body interaction law. It contains a logarithmic term, yielding a critical scaling that cannot be approximated by a power law.
在软摩擦粒子（如泡沫或乳液）的紧密堆积中，应力通过相邻粒子之间的机械接触网络传递。在这些材料的通用简化模型中，假设粒子相互作用能是可加的。我们报告了泡沫微观结构的从头算模拟，结果表明，一般来说，这个基本假设是不合理的：气泡体积的守恒会在给定粒子的所有接触之间引入多体耦合。它强烈改变了单个接触处力与位移之间的关系，这种关系无法通过有效的双体相互作用来捕捉。我们报告了这种效应对线性和非线性弹性响应的影响，研究了有序泡孔堆积的情况，其配位数从 6 到 12 不等，用作简单模型系统，我们提出了一个没有自由参数的解析模型，只要气泡具有近似的球形即可。它可以预测粒子接触力的多体耦合以及宏观力学响应。对于接近接触力趋于零的缠结转变的堆积分数，我们推导出了一种渐近双体相互作用定律。它包含一个对数项，产生一种不能用幂律近似的临界标度。
