Effects of polydispersity and Isomorph Theory on shearing soft glassy materials 公开
Jiang, Yonglun (Spring 2022)
Abstract
My PhD work consists of two simulation projects. One is to study the effect of polydispersity on the dense 2D granular system under steady shear. We use the Durian bubble model together with Lees-Edwards boundary conditions to generate the shear on our systems with exponential size distributions with various size spans. Then we compare the results with conventional bidisperse system. Shear produces a mean affine flow, and nonaffine plastic deformations resulting from local rearrangements. We calculate the deviation from the affine flow to quantify the nonaffinity for individual particles. We also calculate the deviation from the local group affine motions to quantify the local plastic deformation. We find that both of them significantly depend on the particle size as well as the positions to other particles within the system. In contrast to bidisperse systems, the large particles in our simulations cause a new flow pattern for the relatively smaller particles. This flow pattern leads to more complicated ways of rearrangements that are the origins of the new behaviors we find. We further demonstrate a quantitative way to distinguish between “large” and “small” particles. Finally, we show how these results become increasingly important as the particle size distribution broadens. These findings are qualitatively different than previously found in bidisperse systems.
The other project is to apply the isomorph theory on the glassy simple system under simple shear. After cooling the Kob-Andersen binary Lennard-Jones system below the glass transition, we generate a so-called isomorph from the fluctuations of potential energy and virial in the NVT ensemble: a set of density, temperature pairs for which structure and dynamics are identical when expressed in appropriate reduced units. To access dynamical features, we shear the system using the SLLOD algorithm coupled with Lees-Edwards boundary conditions and study the statistics of stress fluctuations and the particle displacements transverse to the shearing direction in steady state. We find good collapse of the statistical data, showing that isomorph theory works well in this regime. The analysis of the distribution of stress fluctuations allows us to identify a clear signature of avalanche behavior in the form of an exponential tail on the negative side. This feature is also isomorph invariant. We then investigate further and turn our focus on the transient part of the stress and strain curve when the system yields. For the study here, we investigate a much larger density span over which the performance of various isomorph generating methods needs to be examined. Comparisons and comments on these methods are provided. We then shear the system along the identified isomorph. Here since the transient part depends on the thermal history, we shear the glassy samples generated by different cooing rates with different strain rates. Excellent collapsing quality again for steady state stress is verified. We notice however, that the peak stress at the transient part on the stress strain curve is not invariant, but decreases by a few percent for each ten percent increase in density, although the differences decrease with increasing density.
Table of Contents
1 Introduction
1.1 Amorphous materials and three control parameters
1.2 Yield of amorphous solid
1.3 Effect of polydispersity
1.4 Isomorph theory
2 Simulation method
2.1 Durian bubble model and Runge-Kutta method
2.2 Lees-Edwards boundary conditions
2.3 RUMD
3 Effects of Polydispersity on 2D dense soft particles under steady shear
3.1 Introduction
3.2 Simulation
3.3 Nonaffine motion
3.4 D2 min,i
3.5 Discussion
3.6 Conclusion
4 Isomorph theory on sheared glassy systems: Part I
4.1 Introduction
4.2 Methods to generate isomorph
4.3 Invariance of various quantities
4.3.1 Analysis of Stress-strain Curves
4.3.2 Particle Dynamics under Shear
4.4 Implication for Alternative Reduced Units
4.5 Conclusion
5 Isomorph theory on sheared glassy systems: Part II
5.1 Introduction
5.2 Simulation
5.3 Methods to generate isomorph
5.3.1 Integration using the density scaling exponent γ
5.3.2 Direct isomorph check
5.3.3 Stress-based direct isomorph check
5.3.4 Force method
5.3.5 Comparison of above methods
5.3.6 Matching the flow stress
5.4 Invariance of flow stress and peak stress
5.5 Invariance of pair structure and single-particle dynamics in the steady state
5.6 Investigation on the non-isomorphic peak stress
5.7 Conclusion
6 Conclusion
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