Effects of hard planar walls with a particle scale roughness on the spatial correlations of non-affine strain in amorphous solids are investigated via molecular dynamics simulations. When determined within layers parallel to the wall plane, normalized non-affine strain correlations are enhanced within layers closer to the wall. The amplitude of these correlations, on the other hand, is found to be suppressed by the wall. While the former is connected to the effects of a hard boundary on the continuum mechanics scale, the latter is attributed to molecular scale wall effects on the size of the region (nearest neighbor cage), explored by particles on intermediate times scales.
We present a quantitative study of strain correlations in quiescent supercooled liquids and glasses. Recent two-dimensional computer simulations and experiments indicate that even supercooled liquids exhibit long-lived, long-range strain correlations. Here we investigate this issue in three dimensions via experiments on hard sphere colloids and molecular dynamics simulations of a glass forming binary Lennard Jones mixture. Both in the glassy state and in the supercooled regime, strain correlations are found to decay with a $1/r^{3}$ power-law behavior, reminiscent of elastic fields around an i…
Via molecular dynamics simulations of a generic glass former in the supercooled and normal liquid states, it is shown that spatial correlations of strain fluctuations exhibit a crossover from the well-established power-law $\sim 1/r^3$-decay at long wavelengths to an exponential behavior, $\sim \exp(-r/l_{\text {c}})$ at intermediate distances. The characteristic length of the exponential decay grows both with temperature and time via, $l_{\text {c}}^2 \propto D(T)\, t$, with $D(T)$ being the temperature-dependent diffusion coefficient. This suggests that the crossover between the power-law an…
We report observations of unusal \emph{first} plastic events in silica and metallic glasses in the shear startup regime at applied strain two orders of magnitude smaller than yield strain. The (non-Affine) particle displacement field during these events have complex real space structure with multiple disconnected cores of high displacement appearing at the \emph{same} applied strain under athermal quasistatic simple shear deformation, and identified by a ``cell based cluster analysis'' method. By monitoring the stress relaxation during the first plastic event by Langevin dynamics simulation, w…
Coarse-graining microscopic strains in a harmonic, two-dimensional solid and its implications for elasticity: non-local susceptibilities and non-affine noise
We show experimentally that both single and multiple mechanical memories can be encoded in an amorphous bubble raft, a prototypical soft glass, subject to an oscillatory strain. In line with recent numerical results, we find that multiple memories can be formed sans external noise. By systematically investigating memory formation for a range of training strain amplitudes spanning yield, we find clear signatures of memory even beyond yielding. Most strikingly, the extent to which the system recollects memory is largest for training amplitudes near the yield strain and is a direct consequence of…
We present a mathematical description of amorphous solid deformation and plasticity by extending the concept of instantaneous normal modes (INMs) to deformed systems, which allows us to retain the effect of strain on the vibrational density of states (VDOS). Starting from the nonaffine lattice dynamics (NALD) description of elasticity and viscoelasticity of glasses, we formulate the linear response theory up to large deformations by considering the strain-dependent tangent modulus at finite values of shear strain. The (nonaffine) tangent shear modulus is computed from the vibrational density o…
Rheological constitutive equation for model of soft glassy materials
我们精确地求解并详细地描述了泡沫、乳状液、泥浆等的低频剪切流变学的简化标量模型。Lequeux，P. Hebraud，M. E. Cates，Phys. Rev. Lett. 78，2020（1997）]。该模型将这种“软玻璃质材料”流变学的相似性归因于结构无序和亚稳性的共同特征。通过关注介观元素的动力学，它保留了一个通用的字符。相互作用由平均场噪声温度x表示，玻璃化转变发生在x=1（以适当的单位表示）。该模型的精确解采用将应力与应变历史相关联的本构方程的形式，从该本构方程可以导出所有流变性质。对于线性响应，我们发现储能模量G'和损耗模量G“都随频率ω^{x-1}（1<x<2）变化，在玻璃化转变附近变得平坦。在玻璃相，老化的模量预测。稳态剪切流动曲线显示x<2的幂律流体行为，玻璃相中具有非零屈服应力; Cox-Merz规则在该非牛顿状态下不成立。单阶和双阶应变进一步探讨了模型的非线性行为，这是不能很好地表示的BKZ关系。最后，我们考虑在有限应变幅γ下G'和G“的测量。在玻璃化转变附近，随着应变扫描中γ的增加，G“呈现最大值。由于非线性效应，它的值可能会被严重高估，即使当应力响应非常接近谐波时也会出现这种效应。在最大应变γ_c处，测量仍能探测到线性响应，这一点与频率无关。
We use large-scale simulations to investigate the dynamic fracture of silica and sodium-silicate glasses under uniaxial tension. The stress-strain curves demonstrate that silica glass is brittle whereas the glasses rich in Na show pronounced ductility. A strong composition dependence is also seen in the crack velocity which is on the order of 1800 m/s for glasses with low Na concentration and decreases to 700 m/s if the concentration is high. We find that during the fracture of Na-rich glasses very irregular cavities as large as 3-4 nm form ahead of the crack front, indicating the presence of …
As an extension of the isotropic setting presented in the companion paper [J. Phys. A 52, 144002 (2019)], we consider the Langevin dynamics of a many-body system of pairwise interacting particles in $d$ dimensions, submitted to an external shear strain. We show that the anisotropy introduced by the shear strain can be simply addressed by moving into the co-shearing frame, leading to simple dynamical mean field equations in the limit ${d\to\infty}$. The dynamics is then controlled by a single one-dimensional effective stochastic process which depends on three distinct strain-dependent kernels -…
