Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session S30: Origin of Rigidity and YieldingFocus

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Sponsoring Units: DSOFT GSNP Chair: Sriram Ramaswamy, Indian Institute of Science Room: 502 
Thursday, March 5, 2020 11:15AM  11:51AM 
S30.00001: A statistical mechanical theory for the origin of rigidity in crystalline solids Invited Speaker: Surajit Sengupta It is known that if local atomic rearrangements leading to exchange of neighbours are allowed, no crystalline solid can be rigid in the thermodynamic limit. The usual rigid, elastic, response to shape changes, a defining character of a crystalline solid, arises because the time needed for such rearrangements diverge as the magnitude of deformation approaches zero. Starting from these general considerations, we had shown that crystal rigidity arises as a consequence of a first order phase transition in an expanded parameter space [1]. The solid is subjected to not only elastic deformation but also to a fictitious external field, which penalises rearrangements, with the understanding that properties of real crystals are recovered by first taking the thermodynamic limit and then letting this field go to zero. Within this picture, we obtain a first order phase transition between a rigid crystal, N, and a crystal, M, where atoms rearrange to eliminate internal stress for any given deformation while maintaining crystalline order. The NM phase boundary, in the thermodynamic limit, passes through the origin, where both field and deformation is zero. This picture gives us a fundamentally new viewpoint on the phenomenon of yielding, i.e. the loss of rigidity of a crystal when deformed beyond a limit, viz. the yield point. The phenomenon of yielding is now simply the nucleation of bubbles of the thermodynamically stable M phase within the metastable, rigid N crystal. An outcome of this theory is that the yield point is always a weak function of the rate of deformation and vanishes in the true quasistatic limit. The analytic form derived by us for the yield point as a function of the rate of deformation is able to explain experimental data over 15 orders of magnitudes in time [2]. We also discuss several details of yielding in Lennard Jones solids in 2 and 3 dimensions. 
Thursday, March 5, 2020 11:51AM  12:03PM 
S30.00002: Critical Scaling of Avalanches with Strain Rate in Athermal, Disordered Solids Mark Robbins, Joel Clemmer, Kenneth Salerno Molecular dynamics simulations are used to study critical behavior in slowly sheared disordered solids that are modeled as a bidisperse LennardJones glass. The mean flow stress rises as strain rate to the power 1/β. Finitesize scaling is used to determine β and the exponent ν describing the divergence of the correlation length. The system length L varies from 55 to 1753 particle diameters in d=2 and 20 to 163 in d=3. Fluctuations in the stress and kinetic energy per particle scale as L^{d/2}, implying that the largest avalanche scales as L^{α} with α < d/2. Temporal correlations are used to measure the dynamical exponent z relating the duration of an avalanche to its linear dimension. In contrast to lattice models, we find z>1, as required by causality. New scaling laws are derived for exponents describing the power law decay of the noise power spectrum with frequency and tested using finitesize scaling. 
Thursday, March 5, 2020 12:03PM  12:15PM 
S30.00003: Bauschinger effect in model glasses Sylvain Patinet, Armand Barbot, Ismail El Korde, Matthias Lerbinger, Damien Vandembroucq, Anaël Lemaître Once a material has experienced a significant plastic deformation, it it generally exhibits a softer stress response under reverse loading than under reloading in the original direction. The origin of this socalled Bauschinger effect, observable in various classes of materials remains poorly understood. We present here recent results obtained on twodimensional model glasses at atomistic and mesoscopic scales. Using a numerical method developed in [1] we perform measurements of the local plastic thresholds in the steady state flow of a 2D model glasses under athermal quasistatic (AQS) deformation. Our results show evidence for the development of a forwardreverse asymmetry of the distribution of the residual strengths that can be directly connected with the Bauschinger effect [2]. 
Thursday, March 5, 2020 12:15PM  12:27PM 
S30.00004: Shear banding transition in granular materials under uniform and boundary shear Yiqiu Zhao, Jonathan Bares, Hu Zheng, Joshua Socolar

Thursday, March 5, 2020 12:27PM  12:39PM 
S30.00005: Strain localization and shear band formation during tensile tests of disordered floating granular monolayers Hongyi Xiao, Robert Ivancic, Ge Zhang, Robert Riggleman, Andrea JoWei Liu, Douglas Durian Understanding and predicting strain localization and shear band formation during deformation of amorphous solids is an ongoing challenge. In this study, quasistatic tensile experiments were performed using a model disordered solid consisting of a monolayer of polydisperse granular spheres with capillary attractions floating on an airoil interface. Under tensile deformation, the strain in the monolayer gradually localizes into an inclined shear band, upon which failure occurs. The ductility of the monolayer can be tuned by using different particle sizes compared to the capillary length, which sets the interaction range. Using machine learning methods, we developed a scalar field, softness, that relates the local structure around particles and particlelevel dynamics. We found that softness tends to increase around particles that have rearranged. Furthermore, planes that develop into shear bands tend to have higher than average softness prior to deformation and become even softer as the shear band forms. These results reveal the relation between structure and dynamics that leads to strain localization, which could potentially apply to a broad range of amorphous solids. 
Thursday, March 5, 2020 12:39PM  1:15PM 
S30.00006: Yielding and mechanical failure in (amorphous) solids Invited Speaker: Juergen Horbach Recently, a Monte Carlo simulation study [1] has shown that yielding in crystalline solids is associated with an underlying quasistatic firstorder phase transition. As a consequence, in the limit of a deformation with sufficiently low strain rate, the rigid response of a crystal due to a shape change of its boundaries corresponds to a metastable state that transforms to a stable state where internal stresses are eliminated, maintaining the crystalline order. A nucleation theory based on these findings predicts the yield point as a function of strain rate and shows agreement with data from experiment and molecular dynamics (MD) simulations over 15 orders of magnitude [2]. In the case of amorphous solids (glasses), a MD simulation study, using an athermal quasistatic (aqs) deformation protocol [3], have found a sharp stress drop in the stressstrain relation that marks the transition from an elastic response of the glass to plastic flow. In Ref. [3], this stress drop has been 
Thursday, March 5, 2020 1:15PM  1:27PM 
S30.00007: Unjamming and reentrant jamming of dense systems in the extreme active limit Deshpreet Bedi, Pinaki Chaudhuri, Chandan Dasgupta, Bulbul Chakraborty Simulations of dense, athermal assemblies of selfpropelled soft particles with infinite persistence time display intriguing mechanical properties as a function of the strength of the active propulsion force and the packing fraction of the system. Applying active propulsion to an initial, passivelyjammed state results in unjamming and subsequent flow of the system. We find that there is a threshold force above which the system remains fluid indefinitely but below which the system experiences reentrant jamming, and that this threshold force increases as the density of the system is increased. Interestingly, we find that the average coordination numbers of both fluid and rejammed states under active propulsion are larger than those of the passivelyjammed states for a given packing fraction. 
Thursday, March 5, 2020 1:27PM  1:39PM 
S30.00008: States of selfstress in disordered solids Shang Zhang, Leyou Zhang, Vishwas Vasisht, Emanuela Del Gado, Xiaoming Mao We investigate the interplay between the mechanical responses of disordered solids and their states of selfstress (SSSs), which are equilibrium stress distributions in a mechanical network with force balanced on any component. SSSs are determined by the geometry of the network (they span the null space of the network's equilibrium matrix) and govern loadbearing abilities of this network. On the other hand the mechanical load changes the geometry and feedback to the SSSs. By presenting our results on SSSs in disordered solids generated by molecular dynamics simulations as well as jamming protocols, we explore the relation between SSSs in a disordered solid and the memory of how the mechanical network is prepared, as well as how they yield under stress. 
Thursday, March 5, 2020 1:39PM  1:51PM 
S30.00009: Local order and structural rearrangement in twodimensional jammed systems under oscillatory shear Erin Teich, Larry Galloway, Paulo Arratia, Danielle Bassett Amorphous, jammed systems are abundant in nature and utilized often in manmade materials. The way in which their disordered structure evolves under the application of shear stress is an area of active investigation with consequences in contexts ranging from earth science to cancer research. Identifying local structural characteristics that influence macroscopic dynamics in these materials remains an ongoing challenge, and previous work has indicated generally that particles with ordered local environments are less likely to dynamically rearrange under shear. Here, we expand on this preliminary conclusion, and quantify it concretely in a twodimensional colloidal jammed system subject to oscillatory shear. We analyze local crystallinity and identify crystal grains in these systems. We track structural correlations over time, and find that crystalline particles that are more interior within grains are less likely to rearrange. Moreover, propensity to rearrange occurs in a hierarchy according to the degree to which particles are “protected” within the grains. In addition, structural correlations qualitatively change at strain amplitudes above yield, where elasticity and viscosity become comparable, implying a transition in structural memory in the system. 
Thursday, March 5, 2020 1:51PM  2:03PM 
S30.00010: Yielding and transient shear banding in soft jammed solids Vishwas Vasisht, Emanuela Del Gado We have designed 3D numerical simulations of a soft spheres model, with size polidispersity and in athermal conditions, to study the transient shear banding that occurs during yielding of jammed soft solids. We have analyzed the effects of different types of drag coefficients used in the simulations and compare the results obtained using LeesEdwards periodic boundary conditions with the case in which the same model solid is confined between two walls. While load curves and velocity profiles obtained in different conditions displays some differences, the presence of a stressovershoot and a related transient banding phenomenon are a robust feature for overdamped systems and large enough samples. We use this computational approach to investigate the microscopic origin of the flow inhomogeneities and the role played by the confinement. 
Thursday, March 5, 2020 2:03PM  2:15PM 
S30.00011: Strain dependent hysteresis in nanoparticle aggregate dispersions visualized to explain origin of the Payne Effect and Spectral Hole Burning in crosslinked filled rubber Zach Gault, Zsolt Terdik, Peter James Lu, Joerg Werner, David A Weitz Filled rubbers are composite materials containing two interpenetrating phases: crosslinked elastomers, and a ‘filler’ consisting of nanoparticle particle aggregates. The nanoparticle aggregates form a systemspanning subnetwork that reinforces the elastomer network and introduces a new energy loss mechanism at low strains of only 15%. This loss mechanism, known as the Payne Effect, is one of the mechanical hallmarks of filled rubbers and is a major contributor to rolling friction in tires. We create a transparent model system to study the strain dependent hysteresis of nanoparticle aggregates. With this system we can directly observe microstructural changes of filler particle aggregates during in situ shear deformation. We complement these observations with bulk rheological tests, including spectral hole burning, to gain new insight into the microscopic structural changes that occur during cyclic deformation. 
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