Session Y20: Understanding Glasses and Disordered Matter Through Computational Models III

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We aim to develop multiscale models of plastic flow and failure processes in amorphous solids, materials that exhibit a complete lack of crystalline order. We take metallic glass as an exemplar material and apply molecular dynamics simulation to examine the physics of deformation. We elate the evolution of the glass structure under shear to the “effective temperature” that characterizes the degree of glass disorder in building and seek to validate a constitutive model of plastic response. The constitutive model has been incorporated into a high-fidelity viscoplastic finite differencing scheme that adapts techniques originally developed for solving the Navier-Stokes equation. A novel machine learning algorithm then utilizes the atomistic data to guide the parameterization of the constitutive model so as to optimize the agreement between atomistic and continuum representations of the material. We see that a high level of agreement can be reached between the molecular dynamics data and the continuum result. In doing so we have begun to ask some fundamental questions about the coarse graining necessary to provide a rigorous connection between atomistic and continuum models, and the relation of this coarse graining to the concept of “effective temperature.”   

Live

Silicate glasses are widely applied in fields including medicine, optics, electronics, telecommunication and energy. These materials often fail due to their inherently brittle characteristics, while the relationships between atomic structure and the fracture nucleation process remain incompletely understood. Our team used classical ReaxFF molecular dynamics simulations to model fracture nucleation of silica-based glasses in aqueous environments. Developing structure-property relationships using this simulation method is computationally expensive, limiting the number of samples and making interpretation challenging. This project aims to use a recurrent neural network with the long-short term memory mechanism to learn the dynamic processes behind fracture nucleation and predict likely locations of fracture nuclei. We interpret the learned model to glean new physical insight into how local structure influences failure in this critical material.
Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
SAND2020-11508 A   

Live

The distribution of local proximity to yielding, p(x), governs the statistical properties of failure events in the yielding transition of amorphous solids. In the thermodynamic limit, p(x) has a pseudogap of the form p(x)∼x^θ. Using a mesoscopic model of amorphous plasticity under strain-controlled athermal quasistatic loading conditions, we show that for finite-systems p(x) has a previously unrecognized intermediate power-law deviating from the pseudogap exponent θ, before entering a terminal plateau with p(x«1)∼L^-p. We connect these regimes to finite-size effects originating in the mechanical noise and the drift velocity. There is a fundamental difference in the mechanical noise originating from large and small plastic events, and this gives rise to the intermediate power-law regime. We demonstrate that, although the extremal statistic x_min determines the global distance to instability and is located at the entrance to the intermediate power-law, this newly observed regime does not alter established scaling relations between the pseudogap exponent and the yielding exponents.   

Live

Bulk metallic glasses (BMG) are amorphous alloys with many desirable properties such as high yield strength and elasticity. Due to their disordered structure and complex response to applied stress, it is difficult to predict whether a given BMG sample will deform in a ductile or brittle manner. Using molecular dynamics simulations, we generated binary Lennard-Jones (LJ) glasses over a range of cooling rates. We then performed athermal quasistatic tension tests on these samples to obtain a wide range of force versus strain responses. To analyze and interpret this data, we developed a spring network model, where springs can break and reform based on atomic rearrangements. We calibrate the spring network model using the probability distribution that a spring of given length and angle relative to the pulling direction will break by measuring changes in the Voronoi neighbors as a function of strain in the LJ simulations. We find that the force versus strain curves from the spring model agree quantitatively with those from the LJ simulations. The spring network model gives insight into the important parameters that control the mechanical response of BMGs.   

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Modeling shear band formation of brittle amorphous solids under load is an ongoing challenge. In this study, a newly developed structuro-elasto-plasticity (StEP) model is used to capture the essential physics for brittle response. The local disordered structure is described by a machine learning-informed property, softness, which represents the propensity of a local region to rearrange. Softness interacts with the elastic strain and plastic rearrangements. Details of these interactions are measured from two particulate systems that exhibit shear band formation during deformation: quasi-static tensile experiments of particle rafts and computational simulations of tensile deformation of polymer nanopillars. Direct microscopic measurements capture the interplay between structure, dynamics and elasticity, such as a local increase of softness after rearrangements indicating structural weakening. Such effects are then incorporated into a lattice StEP model, which qualitatively captures the shear band formation process as well as brittle-to-ductile transitions when system variables (e.g. temperature) are changed.   

Live

We study the Anderson transition for three-dimensional (3D) N×N×N tightly bound cubic lattices where both real and imaginary parts of on-site energies are independent random variables distributed uniformly between -W/2 and W/2. Such a non-Hermitian analog of the Anderson model is used to describe random-laser medium with local loss and amplification. We employ eigenvalue statistics to search for the Anderson transition. For 25% smallest-modulus complex eigenvalues we find the average ratio r of distances to the first and the second nearest neighbor as a function of W. For a given N the function r(W) crosses from 0.72 to 2/3 with a growing W demonstrating a transition from delocalized to localized states. When plotted at different N all r(W) cross at W_c = 6.0 ± 0.1 (in units of nearest-neighbor overlap integral) clearly demonstrating the 3D Anderson transition. We find that in the non-Hermitian 2D Anderson model, the transition is replaced by a crossover.   

Live

Imposing an external driving, amorphous solids can flow via a succession of plastic rearrangement of localized particles. Numerous numerical and experimental studies have shown that loci of plastic instability in glasses are triggered by spatially localized soft spots in direct analogy with dislocations present in crystalline solids, although the population and microscopic structure of the former being significantly different from the latter. The detection and nature of such “amorphous defects” have received a lot of attention, one of the goals being to predict from the microscopic structure itself which regions are likely to undergo a rearrange upon deformation. In this study, we investigate plasticity in a model glass former driven via Athermal Quasistatic Shear. Using SWAP Monte Carlo, we are able to prepare equilibrium amorphous configurations from high to very low temperatures, which translates in controlling the crossover behavior from ductile to brittle glasses. We compute various structural indicators ranging from purely structural to highly non-linear methods that require the knowledge of the interactions between constituents. We fully quantify how well these metrics compete with each other for various glass stabilities and how far in the deformation (here the strain) do they perform in predicting plastic events. Moreover, we are capable of extracting estimates for the full spatial distribution of plastic defects both in quiescent glasses and across the yielding transition, allowing to microscopically characterize and draw a line between ductile and brittle materials.   

Live

The slow relaxation of disordered systems known as aging exhibits puzzling behavior when subjected to temperature shifts, leading to the rejuvenation effect, for example. When these effects are realized in mean field spin glasses, they are attributed to the hierarchical energy landscape of the spin glasses, a consequence of replica symmetry breaking (RSB). Here, we give a counterexample to demonstrate that, while hierarchical landscapes do produce rejuvenation effects, the dynamics are not necessarily governed by RSB. We introduce a toy model, the cluster model, developed based on the idea that aging is governed by record dynamics (RD)[1] in which rare events of record size allow a system to overcome energetic or entropic barriers, before reconfiguring into the next metastable state. Our numerical simulations of the cluster model show that even with the absence of RSB, the system still produces rejuvenation and memory effects. These effects can be explained with the timescales of the rare events as a reflection of the topology of the landscape.


[1] N. Becker et al 2014 J. Phys.: Condens. Matter 26 505102
https://doi.org/10.1088/0953-8984/26/50/505102   

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Disordered solids all yield at a common shear strain of about 3%, but the behavior beyond yield is different for different systems and for systems with different histories. Foams can deform indefinitely without fracturing, many systems exhibit crackling noise or avalanche behavior, and still others exhibit shear banding and brittle fracture. A phenomenological model capable of capturing and predicting these behaviors from microscopic properties and interactions has long been sought. We previously studied avalanches in an athermal, jammed packing of Hertzian particles that is sheared quasistatically, and disentangled the interplay between rearrangements, strain, and softness, a machine-learned structural descriptor that predicts the propensity of a particle to rearrange. We now use those microscopic results to construct a coarse-grained structuro-elasto-plasticity (StEP) model and explore its behavior.   

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The interplay of non-Hermiticity and disorder plays an important role in condensed matter physics. The 10-fold way classification becomes further enriched into a 38-fold way according to recent studies [1]. Here, we report the universal critical behaviors of Anderson transitions driven by non-Hermitian disorders in three-dimensional (3D) Anderson model [2] and 3D U(1) model, that belong to 3D class AI† and 3D class A in the 38 classes respectively. Based on the finite-size scaling analyses, critical exponents are estimated as ν =0.99 ± 0.05 for the class AI†, ν = 1.09 ± 0.05 for the class A. We further studied spectral rigidity and level spacing distribution at the critical point. These critical behaviors strongly support that non-Hermiticity changes the universal class of the Anderson transition.[1] K. Kawabata,et al., PRX, 9, 041015 (2019). R. Hamazaki, et al., PRR, 2, 023286 (2020). [2] Y. Huang, and B. I. Shklovskii, PRB, 101, 014204 (2020), 102, 064212 (2020).