Session A49: Understanding Amorphous Matter Through Modeling and Simulation I

Yielding and shear banding of amorphous materials

Many processes in nature and technology are governed by the dynamical transition via which a material in an initially solid-like state then yields plastically when subject to an imposed deformation. Key unresolved questions concern whether any material will yield smoothly via ductile behaviour or fail catastrophically via brittle behaviour; the roles of sample annealing, disorder and shear banding in the onset of yielding and failure; and whether any impending failure can be anticipated before it occurs. We address these questions by studying the yielding of slowly sheared amorphous materials, within minimal mesoscopic models.   

Thermal effects and scaling theory for the yielding transition in amorphous solids

The yielding transition in amorphous solids has been thoroughly studied in the athermal-quasistatic (AQS) limit. Finite temperature and driving rate introduce new, competing timescales to the problem that create new scaling behavior. We investigate these effects by adding thermal noise to a mesoscopic elastoplastic model (EPM). By studying low-temperature and low driving, we retain a clear separation of timescales between avalanches and loading. We principally study the distribution of weak sites p(x) and the scaling of the avalanche size distributions p(s) and develop a mean-field scaling theory for these distributions based on a random-walker description. This mean-field theory satisfactorily collapses results from a thermal 2-dimensional elastoplastic model and predicts three distinct finite-scaling regimes: an AQS regime below a critical temperature, a trivial molten state above another critical temperature, and an intermediate regime with non-trivial scaling.  In addition to the scaling theory, we also find the appearance of temperature dependent stress-localization and characterize the resulting stress-overshoot.   

Plasticity in amorphous solids is mediated by topological defects in the displacement field

The microscopic mechanism by which amorphous solids yield plastically under an externally applied stress or deformation has remained elusive in spite of enormous research activity in recent years. Most approaches have attempted to identify atomic-scale structural "defects" or spatio-temporal correlations in the undeformed glass that may trigger plastic instability. In contrast, here we show that the topological defects which correlate with plastic instability can be identified, not in the static structure of the glass, but rather in the nonaffine displacement field under deformation. These dislocation-like topological defects (DTDs) can be quantitatively characterized in terms of Burgers circuits (and the resulting Burgers vectors) which are constructed on the microscopic non-affine displacement field. We demonstrate that (i) DTDs are the manifestation of incompatibility of deformation in glasses as a result of violation of Cauchy-Born rules (nonaffinity); (ii) the resulting average Burgers vector displays peaks in correspondence of major plastic events, including a spectacular non-local peak at the yielding transition, which results from self-organization into shear bands due to the attractive interaction between anti-parallel DTDs; (iii) application of Schmid's law to the DTDs leads to prediction of shear bands at 45 degrees for uniaxial deformations, as widely observed in experiments and simulations.     

Structural change, plasticity and avalanches in cyclically sheared silica

Strong glasses are often characterized by strong directional interactions and  present a completely different behaviour with respect to their fragile counterpart. Under cyclical deformation they are known to display a sharply defined yielding transition with a discontinuous jump from an absorbing to a diffusive state similar to fragile glasses. In this work, we show that silica as a prototypical strong glass former under athermal quasi static cyclic deformation exhibits nontrivial plastic rearrangements. In contrast to mean-field predictions, the statistics of avalanches reveals significant qualitative change in their scaling behaviour. Across the yielding transition system exhibits a qualitative structural change which can be attributed to the crucial role of 5-fold coordination defects of silicon atoms. Such defects facilitate the strain localization in a densified shear-banded region above the yield strain.   

Jamming Transition of Sheared Athermal System With Pins

Currently, the jamming transition in granular media is well supported by theory and there is a broad understanding of the applicability as well. Using molecular dynamics simulations, we study the jamming transition of a two dimensional sheared granular system. Shearing is implemented via freezing the top and bottom of the binary mixture to create a wall that can be sheared at a constant velocity. The system is a 50:50 binary mixture with purely repulsive harmonic interactions of size ratio 1:1.4. We will present preliminary results on the influence of the jamming transition due to a shear and the addition of non-moving "pins". The size ratio of pins:small:large is 0.004:1:1.4 and pins are located on a square lattice. We investigate pressure and shear stress, as well as force distributions, and heat maps of the local shear stress.   

Characterization of non-affine displacement fields of amorphous solids in three dimensions

Amorphous solids exhibit large non-affine displacement fields in response to applied stress. In crystalline solids, topological defects cause non-affine displacements. However, the structural origins of the non-affine displacements in amorphous solids are difficult to identify due to the lack of long-range structural order. In previous studies, we employed Delaunay triangularization to characterize the non-affine displacement fields in two-dimensional binary Lennard-Jones solids undergoing athermal, quasistatic simple shear (AQS). We showed that quadrupolar displacement fields are most frequently observed and these are generated by pure shear defects of single Delaunay triangles. Here, we explore the structure and evolution of the displacement fields in binary Lennard-Jones solids undergoing AQS in three dimensions (3D) using Delaunay tetrahedralization. We find that quadrupolar and octopolar non-affine displacement fields occur in 3D. In addition, we identify the local strains of the single tetrahedra that give rise to these displacement fields.    

Using Delaunay triangularization to characterize non-affine displacement fields during athermal, quasistatic deformation of amorphous solids

We investigate the non-affine displacement fields that occur in two-dimensional Lennard-Jones models of metallic glasses subjected to athermal, quasistatic simple shear (AQS). During AQS, the shear stress versus strain displays continuous quasi-elastic segments punctuated by rapid drops in shear stress. We capture all information concerning the atomic motion during the quasi-elastic segments and shear stress drops by performing Delaunay triangularizations and tracking the deformation of each triangle. To understand the spatio-temporal evolution of the displacement fields, we follow minimal energy paths from the mechanically stable configuration immediately before to that after the stress drop.  We find that quadrupolar displacement fields form and dissipate both during the quasi-elastic segments and shear stress drops.  We then perform local perturbations to single triangles and demonstrate that local pure shear strains of triangular elements, which give rise to mostly quadrupolar displacement fields, are activated during AQS.  These results provide fundamental insights into the non-affine atomic motion that occurs in driven, glassy materials.   

A theory of supercooled-liquid dynamics based on machine-learned softness

Recent work has used machine learning to identify a local structural variable, the softness S, which is predictive of rearrangements in a variety of systems. In simulations of supercooled liquids and glasses, S has a simple interpretation in terms of local energy barriers to rearrangement, and is found to correlate well with the probability of particles to rearrange, both in and out of equilibrium.  Here we build a theory of the dynamics of supercooled liquids in terms of S.  By measuring the changes in S induced nearby when a particle rearranges in molecular dynamics simulations, we quantify facilitation. We describe a class of stochastic models which can incorporate these measurements, and show how time-reversal symmetry places strong restrictions on the parameters of the model.  This results in a theory of dynamics whose parameters are well-founded in microscopic measurements and which can be used to predict the growth of dynamical heterogeneity as the system is cooled.   

Markov state model for exploring the long-time dynamics of glass formers

Extensive efforts have been dedicated towards establishing robust links between the structural and dynamical heterogeneity found in amorphous materials at the nanoscale. Markov state models (MSMs) offer the attractive possibility of coarse-graining the dynamics of complex systems into a low-dimensional space, in which transitions occur with rates corresponding to the slowest modes of the system. We construct a two-state MSM of a binary Lennard-Jones mixture using Graph Dynamical Neural Networks in combination with the Variational Principle for Markov Processes. The transition timescale of the MSM is more than an order of magnitude larger than the conventional alpha-relaxation time, and reveals a fragile to strong crossover at the glass transition. The learned map of states assigned to the particles exhibits correlations of a few molecular diameters that, remarkably, are completely insensitive to temperature. We show that the MSM effectively constructs a map of scaled excess Voronoi volume, and the free energy difference between the two states is given exactly by the entropy of the these distributions. These results resonate with classic free volume theories of the glass transition and single out local packing fluctuations as the slowest relaxing features.