Center for Soft Matter Research, Department of Physics, New York University, New York, NY 10003; and.
Laboratoire de Physique Théorique et Modèles Statistiques (Centre National de la Recherche Scientifique, Unité Mixte de Recherche 8626), Université de Paris-Sud, 91405 Orsay Cedex, France.
Proc Natl Acad Sci U S A. 2014 Oct 7;111(40):14382-7. doi: 10.1073/pnas.1406391111. Epub 2014 Sep 22.
Yield stress materials flow if a sufficiently large shear stress is applied. Although such materials are ubiquitous and relevant for industry, there is no accepted microscopic description of how they yield, even in the simplest situations in which temperature is negligible and in which flow inhomogeneities such as shear bands or fractures are absent. Here we propose a scaling description of the yielding transition in amorphous solids made of soft particles at zero temperature. Our description makes a connection between the Herschel-Bulkley exponent characterizing the singularity of the flow curve near the yield stress Σc, the extension and duration of the avalanches of plasticity observed at threshold, and the density P(x) of soft spots, or shear transformation zones, as a function of the stress increment x beyond which they yield. We argue that the critical exponents of the yielding transition may be expressed in terms of three independent exponents, θ, df, and z, characterizing, respectively, the density of soft spots, the fractal dimension of the avalanches, and their duration. Our description shares some similarity with the depinning transition that occurs when an elastic manifold is driven through a random potential, but also presents some striking differences. We test our arguments in an elasto-plastic model, an automaton model similar to those used in depinning, but with a different interaction kernel, and find satisfying agreement with our predictions in both two and three dimensions.
如果施加足够大的剪切应力，屈服应力材料就会流动。尽管这些材料无处不在，与工业密切相关，但即使在温度可以忽略不计且不存在剪切带或断裂等流动不均匀性的最简单情况下，也没有被普遍接受的关于它们如何屈服的微观描述。在这里，我们提出了一种在零温度下由软粒子组成的非晶固体屈服转变的标度描述。我们的描述将在屈服应力Σc 附近的流动曲线奇异处表征的赫谢尔-布尔克利指数与在阈值处观察到的塑性雪崩的扩展和持续时间，以及软点或剪切转换区的密度 P(x)联系起来，作为它们屈服时超过的应力增量 x 的函数。我们认为，屈服转变的临界指数可以用三个独立的指数θ、df 和 z 来表示，分别表征软点的密度、雪崩的分形维数和它们的持续时间。我们的描述与弹性流形通过随机势驱动时发生的去钉扎转变有些相似，但也存在一些显著的差异。我们在弹塑性模型、类似于去钉扎中使用的自动机模型中检验了我们的论点，但具有不同的相互作用核，并在二维和三维空间中都与我们的预测非常吻合。
