LPTMS, CNRS, Univ. Paris-Sud, Université Paris Saclay, Orsay, France.
Soft Matter. 2018 May 9;14(18):3640-3651. doi: 10.1039/c7sm02510f.
The deformation of disordered solids relies on swift and localised rearrangements of particles. The inspection of soft vibrational modes can help predict the locations of these rearrangements, while the strain that they actually redistribute mediates collective effects. Here, we study soft modes and strain redistribution in a two-dimensional continuous mesoscopic model based on a Ginzburg-Landau free energy for perfect solids, supplemented with a plastic disorder potential that accounts for shear softening and rearrangements. Regardless of the disorder strength, our numerical simulations show soft modes that are always sharply peaked at the softest point of the material (unlike what happens for the depinning of an elastic interface). Contrary to widespread views, the deformation halo around this peak does not always have a quadrupolar (Eshelby-like) shape. Instead, for finite and narrowly-distributed disorder, it looks like a fracture, with a strain field that concentrates along some easy directions. These findings are rationalised with analytical calculations in the case where the plastic disorder is confined to a point-like 'impurity'. In this case, we unveil a continuous family of elastic propagators, which are identical for the soft modes and for the equilibrium configurations. This family interpolates between the standard quadrupolar propagator and the fracture-like one as the anisotropy of the elastic medium is increased. Therefore, we expect to see a fracture-like propagator when extended regions on the brink of failure have already softened along the shear direction and thus rendered the material anisotropic, but not failed yet. We speculate that this might be the case in carefully aged glasses just before macroscopic failure.
无序固体的变形依赖于粒子的迅速和局部重排。软振动模式的检查可以帮助预测这些重排的位置，而它们实际重新分配的应变则介导了集体效应。在这里，我们研究了基于完美固体的吉布斯-朗道自由能的二维连续介观模型中的软模式和应变重新分配，并补充了一个塑性无序势，该势可以解释剪切软化和重排。无论无序强度如何，我们的数值模拟都表明，软模式总是在材料最软点处呈现尖锐峰值（与弹性界面去钉扎时的情况不同）。与普遍观点相反，在这个峰值周围的变形晕圈并不总是具有四极子（埃舍尔式）形状。相反，对于有限且分布狭窄的无序，它看起来像一个断裂，应变场集中在一些容易的方向上。在塑性无序仅限于点状“杂质”的情况下，我们用解析计算对这些发现进行了合理化。在这种情况下，我们揭示了一组连续的弹性传播子，它们对于软模式和平衡构型是相同的。随着弹性介质各向异性的增加，这个家族在标准四极子传播子和断裂样传播子之间进行插值。因此，当已经沿着剪切方向软化并且材料变得各向异性的即将失效的扩展区域尚未失效时，我们预计会看到断裂样的传播子，但尚未失效。我们推测，在宏观失效之前，精心老化的玻璃可能就是这种情况。
