Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session N28: Continua, Networks, & Earthquakes |
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Sponsoring Units: GSNP Chair: Oscar Lopez-Pamies, University of Illinois at Urbana-Champaign Room: 336 |
Wednesday, March 20, 2013 11:15AM - 11:27AM |
N28.00001: Earthquakes in the Laboratory: Continuum-Granular Interactions Robert Ecke, Drew Geller, Carl Ward, Scott Backhaus Earthquakes in nature feature large tectonic plate motion at large scales of 10-100 km and local properties of the earth on the scale of the rupture width, of the order of meters. Fault gouge often fills the gap between the large slipping plates and may play an important role in the nature and dynamics of earthquake events. We have constructed a laboratory scale experiment that represents a similitude scale model of this general earthquake description. Two photo-elastic plates (50 cm x 25 cm x 1 cm) confine approximately 3000 bi-disperse nylon rods (diameters 0.12 and 0.16 cm, height 1 cm) in a gap of approximately 1 cm. The plates are held rigidly along their outer edges with one held fixed while the other edge is driven at constant speed over a range of about 5 cm. The local stresses exerted on the plates are measured using their photo-elastic response, the local relative motions of the plates, i.e., the local strains, are determined by the relative motion of small ball bearings attached to the top surface, and the configurations of the nylon rods are investigated using particle tracking tools. We find that this system has properties similar to real earthquakes and are exploring these ``lab-quake'' events with the quantitative tools we have developed. [Preview Abstract] |
Wednesday, March 20, 2013 11:27AM - 11:39AM |
N28.00002: Extreme statistics of avalanches near the depinning transition Michael LeBlanc, Luiza Angheluta, Karin Dahmen, Nigel Goldenfeld Near the depinning transition, motion proceeds by avalanche fluctuations with power law distributed sizes and durations. We derive exact exponents and scaling functions for the statistics of maximum avalanche velocities in a mean field theory of the transition. We find a power law regime in the maximum velocity distribution with an exponent that agrees with the distribution of peak amplitudes observed in acoustic emission experiments of crystal plasticity. Our results should be applicable to the study of a number of systems considered to be in the mean field interface depinning universality class, ranging from magnets to earthquakes. [Preview Abstract] |
Wednesday, March 20, 2013 11:39AM - 11:51AM |
N28.00003: Acoustic-Friction Networks and the Evolution of Shear Ruptures in Laboratory Earthquakes H.O. Ghaffari, R.P. Young The evolution of shear rupture fronts in laboratory earthquakes are analysed with the corresponding functional networks, constructed over photo-elastic, real-time contacts and acoustic emission friction-patterns. We show that the mesoscopic and transport characteristics of networks follow the same trends for the same type of the shear ruptures in terms of rupture speed, while also comparing the results of four different friction experiments. The classified fronts--obtained from a saw-cut fault and natural faulted Westerly granite - regarding friction network parameters show a clear separation into two groups, indicating two different rupture fronts. With respect to the scaling of local ruptures' durations with the networks' parameters, we show that the gap is related to the possibility of a separation between slow and regular fronts. Based on our results, we develop a statistical based method to model the evolution of functional damage networks while we consider that any rupture flows in a critical plane with two main fixed points. [Preview Abstract] |
Wednesday, March 20, 2013 11:51AM - 12:03PM |
N28.00004: Forecasting large earthquakes using small-quake correlations Braden Brinkman, Michael LeBlanc, Yehuda Ben-Zion, J.T. Uhl, Karin Dahmen It has long been speculated that periodic stress variations, such as the tides, may trigger earthquakes, and hence tide-earthquake correlations could be used as signals for predicting large earthquakes prior to failure. We developed a simple probabilistic model of earthquake triggering which we used to simulate series of earthquake events in a fault subjected to external periodic stresses of amplitudes and frequencies representative of tidal or seasonal stress variations. By analyzing correlations between small events and periodic stress cycles, we compute the probability that a large event will occur. We find that seasonal stresses are better predictors of impending large earthquakes. In addition, our results also apply to many other sheared frictional stick-slip systems which display small slips, such as rock interfaces or granular matter. [Preview Abstract] |
Wednesday, March 20, 2013 12:03PM - 12:15PM |
N28.00005: Critical Scaling of Avalanche Dynamics in Sheared Amorphous Solids with Inertia K. Michael Salerno, Craig Maloney, Mark O. Robbins We present results from molecular-dynamics simulations of model disordered solids~under quasi-static, steady-state shear in two and three dimensions.~~Plastic deformation occurs through intermittent ``avalanches'' of local rearrangements. As in other slowly-driven systems from magnets to geologic faults, avalanches exhibit critical scaling behavior. Results for the avalanche statistics, duration and power spectrum are analyzed with finite-size scaling. The exponents describing the power law distribution of avalanches and the relation between their size and duration are independent of dimension, suggesting that mean field behavior extends to two dimensions. In contrast, the scaling exponents depend on the degree of inertia or damping, with distinct universality classes in the underdamped and overdamped limits [1]. The same universality classes are observed with Galilean-invariant and non-Galilean-invariant thermostats, but the crossover between these limits will be contrasted. The implications for different experimental systems will be discussed.~ [1] PRL 109, 105703 (2012). [Preview Abstract] |
Wednesday, March 20, 2013 12:15PM - 12:27PM |
N28.00006: Phase-Field Crystal Models and Elastic Excitations Vili Heinonen, Cristian Achim, Ken Elder, Tapio Ala-Nissil\"a Phase Field Crystal (PFC) models and their amplitude expansions are a novel attempt to bridge the gap between atomistic and continuum models in materials modeling. The studied quantity is the atomic density field that varies in time and space. Not only do these new models allow longer length scales but also longer time scales: many interesting phenomena happen over diffusive time scales that are beyond the reach of classical molecular dynamics or Monte Carlo methods. As with Dynamic Density Field theory a local equilibrium in the system is assumed leading into diffusive dynamics. This implies that the time scale under study is lot slower than time scale of elastic excitations in the system. In other words, we are assuming that phonon modes die out instantaneously. However, it turns out that the system exhibits elastic excitations that have to be relaxed separately. We propose a physical constraint to the time evolution of the density field, which ensures elastic equilibrium at all times. [Preview Abstract] |
Wednesday, March 20, 2013 12:27PM - 12:39PM |
N28.00007: Strain recovery in dual cross-linked polymer grafted nanoparticle networks Balaji Iyer V S, Victor Yashin, Isaac Salib, Tomasz Kowalewski, Krzystof Matyjaszewski, Anna Balazs Via computational modeling, we investigate the mechanism of strain-recovery in dual cross-linked polymer grafted nanoparticle networks. The individual nanoparticles are composed of a rigid core and a corona of grafted polymers that encompass reactive end groups. With the overlap of the coronas on adjacent particles, the reactive end groups form permanent or labile bonds, and thus form a ``dual cross-linked'' network. We consider the strain recovery of the material after it is allowed to relax from the application of the tensile force. We apply multiple cycles of tension and relaxation and determine how the stress-strain curves change in the course of these repetitive deformations. Notably, the existing labile bonds can break and new bonds can form in the course of deformation. Hence, a damaged material could be ``rejuvenated'' both in terms of the recovery of strain and the number of bonds, if the relaxation occurs over a sufficiently long time. We show that this rejuvenation depends on the fraction of permanent bonds, strength of labile bonds, and maximal strain. [Preview Abstract] |
Wednesday, March 20, 2013 12:39PM - 12:51PM |
N28.00008: ABSTRACT WITHDRAWN |
Wednesday, March 20, 2013 12:51PM - 1:03PM |
N28.00009: An analytical method for determining material parameters from inflation tests of thick nonlinear materials Theresa K. Tonge, Thao D. Nguyen The inflation test is a widely used method for applying a biaxial stress state to polymers and biological tissues. The stress response is determined by assuming the inflated specimen can be modeled as a membrane. However, neglecting the effect of bending can generate large errors for thick specimens and in particular for those exhibiting highly nonlinear material behavior. We have developed a novel thin shell method to analytically determine material properties from the inflation test while accounting for bending. The method assumes a linear strain gradient from bending to calculate the in-plane stress resultants from the constitutive relations for the stress response. These stress resultants are fit to the experimentally determined stress resultants calculated from the applied pressure and measured local curvatures. We have applied the method to fit an anisotropic constitutive model to inflation tests of human skin tissue. We have used Finite Element Analysis to validate the method as well as the resulting material parameters for the constitutive model. This thin shell method is sufficiently general to be applied to determine material properties for other thick, nonlinear materials such as aortic valves or gastrointestinal tissues. [Preview Abstract] |
Wednesday, March 20, 2013 1:03PM - 1:15PM |
N28.00010: Solvent-driven shape-memory effects for amorphous networks Rui Xiao, Thao Nguyen The swelling-induced shape memory behavior in polymers has inspired interest for their implications for biomedical applications. For amorphous polymers, the behavior is caused by a large decrease in the glass transition temperature caused by the absorption of a small amount of solvent. In this work, we present a theoretical model of the effect of low solvent concentration on the glass transition behavior of the materials. Specifically, the presence of solvent increases the configurational entropy; thus altering the temperature-dependence of the molecular mobility. The model was implemented numerically for finite element simulation. The computational model also considers the effect of diffusion process to describe more accurately the time-dependent effects of solvent-induced shape recovery behavior. To validate the model, we performed isothermal uniaxial tension tests on both the dry and fully saturated materials. Shape recovery performance was investigated by observing the shape change of an initially deformed sample in an isothermal water bath by using digital image tracking. Comparison between experimental data and simulations shows good agreement. [Preview Abstract] |
Wednesday, March 20, 2013 1:15PM - 1:27PM |
N28.00011: Distorted tetrahedral shapes of nematic vesicles Thanh Son Nguyen, Jonathan Selinger In membranes with internal orientational or crystalline order, there is a geometric coupling between 2D internal order and 3D shape. Nonuniformity in internal order tends to induce curvature, and curvature provides an effective potential acting on internal order. For a closed vesicle with nematic liquid-crystalline order, there must be a total topological charge of +2, which normally occurs as four defects of +1/2 each. Previous research has suggested that these four defects form a regular tetrahedron, leading to a tetrahedral shape of the vesicle, which may be useful in colloidal crystals for photonic applications. Here, we develop an explicit model to calculate energies of defect structures in nematic vesicles. When the liquid-crystal interaction energy is a purely 2D intrinsic interaction, we find that the perfect tetrahedral shape is stable only up to a maximum interaction strength (Frank constant), where it changes to an elongated rectangular configuration. When the interaction energy is a 3D extrinsic and intrinsic interaction, the perfect tetrahedral shape is never stable; the vesicle is a distorted tetrahedron for small Frank constant and a highly elongated rectangle for larger Frank constant. These results show the difficulty in designing tetrahedral structures. [Preview Abstract] |
Wednesday, March 20, 2013 1:27PM - 1:39PM |
N28.00012: Simple model for plastic deformation and slip avalanches in bulk metallic glasses Karin Dahmen, James Antonaglia, Junwei Qiao, Xie Xie, Peter Liaw, Jonathan Uhl Ductile bulk metallic glasses are known to deform under shear in an intermittent way with slip-avalanches detected as acoustic emission and serrations in the stress-strain curves. In many such materials, power laws govern the statistics of these avalanches. A basic micromechanical model for deformation of solids with only one tuning parameter is introduced. The model predicts the observed stress-strain curves, acoustic emissions, related power spectra, and power-law statistics of slip avalanches, including the dependence of the cutoff on experimental parameters with a continuous phase transition from brittle to ductile behavior. Material independent (``universal'') predictions for the power-law exponents and scaling functions are extracted using the mean-field theory and renormalization group tools. The results agree with recent experimental observations on deformed bulk metallic glasses. [Preview Abstract] |
Wednesday, March 20, 2013 1:39PM - 1:51PM |
N28.00013: Cavitation in Amorphous Solids Michael Falk, Pengfei Guan, Shuo Lu, Michael Spector, Pavan Valavala Molecular dynamics simulations of cavitation in a Zr50Cu50 metallic glass exhibit a waiting time dependent cavitation rate. On short time scales nucleation rates and critical cavity sizes are commensurate with a classical theory of nucleation that accounts for both the plastic dissipation during cavitation and the cavity size dependence of the surface energy. All but one parameter, the Tolman length, can be extracted directly from independent calculations or estimated from physical principles. On longer time scales aging in the form of shear relaxations results in a systematic decrease of cavitation rate. The high cavitation rates that arise due to the suppression of the surface energy in small cavities provide a possible explanation for the quasi-brittle fracture observed in metallic glasses. Analogous simulations of Fe80P20 reveal that segregation of P on the nanoscale leads to qualitatively different behavior that may be attributable to the idiosyncrasies of the interatomic potential. [Preview Abstract] |
Wednesday, March 20, 2013 1:51PM - 2:03PM |
N28.00014: Cavitation in rubber: An elastic instability or a fracture phenomenon? Oscar Lopez-Pamies In this presentation, I will confront a recently developed theory of cavitation for soft solids to a variety of cavitation experiments with the objective of establishing whether the phenomenon of cavitation is an elastic instability (and hence depends only on the elastic properties of the rubber), or, on the other hand, a fracture process (and hence depends on the fracture properties of the rubber). [Preview Abstract] |
Wednesday, March 20, 2013 2:03PM - 2:15PM |
N28.00015: Experimental realization of the zero temperature Random Field Ising Model : the condensation of $^4$He in aerogels Geoffroy Aubry, Laurent Guyon, Mathieu Melich, Panayotis Spathis, Florence Despetis, Pierre-Etienne Wolf Although widely studied, the effect of disorder on a first order phase transition is still highly debated. Numerical simulations of the $T=0$ Random Field Ising Model show that magnetization evolves by avalanches, the average size of which diverges below a critical disorder (Sethna et al., PRL 70 3347 (1993)). Nevertheless, experimental evidence is scarce up to now (Berger et al., PRL 85, 4176 (2000)). In the case of the liquid gas transition in disordered porous media, the same theoretical concepts can be applied (Detcheverry et al., PRE 72 051506 (2005)). We have studied experimentally this phase transition using $^4$He in silica aerogels. Optical and thermodynamical measurements show that the condensation is an out of equilibrium process. We clearly observe two filling regimes separated by a critical temperature $T^*$ : below $T^*$, filling is discontinuous (macro avalanche) whereas above $T^*$ it becomes continuous (micro avalanches). In addition, we have developed a speckle interferometry technique to detect single avalanches. We argue that our results support the disorder induced phase transition. [Preview Abstract] |
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