Elastic Heterogeneity Research Articles

Tunable elastic heterogeneity caused by deformation-induced magnetization in flexible metallic glass

In this letter we explore the magnetization effect on mechanical properties of a ductile Fe83C1B11Si2P3 metallic glass (MG). We firstly demonstrate that magnetic anisotropy can be systematically created by plastic deformation using high-load Berkovich indentation, and then provide compelling evidence by subsequent spherical nanoindentation which reveals tunable magnetization-induced submicron elastic heterogeneity. A new mechanism of magnetomechanical interaction, different from the alteration of “flow defect”, is proposed for explaining the apparent softening in the region without plastic deformation. Our studies have significance for modification and controlling of the microstructure and mechanical properties of MGs with respect to magnetic effect.

The Impact of Immigration: Why Do Studies Reach Such Different Results?

We classify the empirical literature on the wage impact of immigration into three groups, where studies in the first two groups estimate different relative effects, and studies in the third group estimate the total effect of immigration on wages. We interpret the estimates obtained from the different approaches through the lens of the canonical model to demonstrate that they are not comparable. We then relax two key assumptions in this literature, allowing for inelastic and heterogeneous labor supply elasticities of natives and the "downgrading" of immigrants. “Downgrading” occurs when the position of immigrants in the labor market is systematically lower than the position of natives with the same observed education and experience levels. Downgrading means that immigrants receive lower returns to the same measured skills than natives when these skills are acquired in their country of origin. We show that heterogeneous labor supply elasticities, if ignored, may complicate the interpretation of wage estimates, and particularly the interpretation of relative wage effects. Moreover, downgrading may lead to biased estimates in those approaches that estimate relative effects of immigration, but not in approaches that estimate total effects. We conclude that empirical models that estimate total effects not only answer important policy questions, but are also more robust to alternative assumptions than models that estimate relative effects.

Relation of vibrational excitations and thermal conductivity to elastic heterogeneities in disordered solids

In crystals, molecules thermally vibrate around the periodic lattice sites. Vibrational motions are well understood in terms of phonons, which carry heat and control heat transport. The situation is notably different in disordered solids, where vibrational excitations are not phonons and can be even localized. Recent numerical work has established the concept of elastic heterogeneity: disordered solids show inhomogeneous local mechanical response. Clearly, the heterogeneous nature of elastic properties strongly influences vibrational and thermal properties, and it is expected to be the origin of anomalous features, including boson peak, vibrational localization, and temperature dependence of thermal conductivity. These are all crucial long-standing problems in materials physics, which we address in the present work. We have considered a toy model able to stabilize different states of matter, by introducing an increasing amount of size disorder. The phase diagram generated by molecular dynamics simulations encompasses the perfect crystalline state with a spatially homogeneous elastic moduli distribution, multiple defective phases with increasing moduli heterogeneities, and eventually a series of amorphous states. We have established clear correlations among the heterogeneous local mechanical response, vibrational states, and thermal conductivity. We provide evidence that elastic heterogeneity controls both vibrational and thermal properties, and is a key concept to understand the anomalous puzzling features of disordered solids.

Coseismic deformation due to the 2011 Tohoku-oki earthquake: influence of 3-D elastic structure around Japan

We investigated the effects of elastic heterogeneity on coseismic deformation associated with the 2011 Tohoku-oki earthquake, Japan, using a 3-D finite element model, incorporating the geometry of regional plate boundaries. Using a forward approach, we computed displacement fields for different elastic models with a given slip distribution. Three main structural models are considered to separate the effects of different kinds of heterogeneity: a homogeneous model, a two-layered model with crust–mantle stratification, and a crust–mantle layered model with a strong subducting slab. We observed two counteracting effects: (1) On large spatial scales, elastic layering with increasing rigidity with depth leads to a decrease in surface displacement. (2) An increase in rigidity from above the slab interface to below causes an increase in surface displacement, because the weaker hanging wall deforms to accommodate coseismic slip. Results for slip inversions associated with the Tohoku-oki earthquake show that slip patterns are modified when comparing homogeneous and heterogeneous models. However, the maximum slip only changes slightly: It increases from 38.5 m in the homogeneous to 39.6 m in the layered case and decreases to 37.3 m when slabs are introduced. Potency, i.e., the product of slip and fault area, changes accordingly. Layering leads to inferred slip distributions that are broader and deeper compared to the homogeneous case, particularly to the south of the overall slip maximum. The introduction of a strong slab leads to a reduction in slip around the slip maximum near the trench. We also find that details of the vertical deformation patterns for heterogeneous models are sensitive to the Poisson’s ratio. While elastic heterogeneity does therefore not have a dramatic effect on bulk quantities such as inferred potency, the mechanical response of a layered medium with a slab does lead to a systematically modified slip response, and such effects may bias studies of mega-thrust earthquakes.

Correlation between local elastic heterogeneities and overall elastic properties in metallic glasses

The common notion suggests that metallic glasses (MGs) are a homogeneous solid at the macroscopic scale; however, recent experiments and simulations indicate that MGs contain nano-scale elastic heterogeneities. Despite the fundamental importance of these findings, a quantitative understanding is still lacking for the local elastic heterogeneities intrinsic to MGs. On the basis of Eshelby's theory, here we develop a micromechanical model that correlates the properties of the local elastic heterogeneities, being very difficult to measure experimentally, to the measurable overall elastic properties of MGs, such as shear/bulk modulus and Poisson's ratio. Our theoretical modeling is verified by the experimental data obtained from various MGs annealed to different degrees. Particularly, we revealed that upon annealing, the Poisson's ratio decreases if shear softening dominates the behavior of local soft regions or increase if pressure softening becomes dominant in MGs. Our results provide quantitative insights into the structural mechanism of the Poisson's ratio criterion on the ductility long established for MGs. Finally, The correlation between the Poisson's ratio of a glass and the fragility of its corresponding liquid is also discussed.

Anomalous phonon scattering and elastic correlations in amorphous solids.

A major issue in materials science is why glasses present low-temperature thermal and vibrational properties that sharply differ from those of crystals. In particular, long-wavelength phonons are considerably more damped in glasses, yet it remains unclear how structural disorder at atomic scales affects such a macroscopic phenomenon. A plausible explanation is that phonons are scattered by local elastic heterogeneities that are essentially uncorrelated in space, a scenario known as Rayleigh scattering, which predicts that the damping of acoustic phonons scales with wavenumber k as kd+1 (in dimension d). Here we demonstrate that phonon damping scales instead as - kd+1 lnk, with this logarithmic enhancement originating from long-range spatial correlations of elastic disorder caused by similar stress correlations. Our work suggests that the presence of long-range spatial correlations of local stress and elasticity may well be the crucial feature that distinguishes amorphous solids from crystals.

Sound velocity fluctuations in confined granular materials: Coarse-graining lengths and elastic heterogeneities

We measure the consequences of elastic heterogeneities in confined granular layers using long-wavelength sound velocity determination. By progressively decreasing the coarse-graining length w, which is determined here by the sample size L, we measure the standard deviation of the longitudinal sound velocity and the packing density ϕ, normalized by their ensemble-averaged values. We find that the relative fluctuations in VL and ϕ increase when w is decreased. Importantly, we observe that decreasing the confining pressure P or using nonspherical particles leads to an important increase of the fluctuations in . We conduct simulations of sound propagation in 2D hexagonal packings with contact-stiffness disorder to mimic the inhomogeneous contact networks. The sound velocity fluctuations of coherent longitudinal waves increase either with decreasing the sample size or with increasing the elastic disorder related to confining pressure, in consistency with the experiments. Our experimental observations thus support the scenario of a pressure-dependent mesoscopic length (at ), below which the continuum elasticity breaks down, likely due to the large spatial fluctuation of the shear modulus .

Homogenized moment tensor and the effect of near‐field heterogeneities on nonisotropic radiation in nuclear explosion

AbstractWe investigate the effect of small‐scale heterogeneities close to a seismic explosive source, at intermediate periods (20–50 s), with an emphasis on the resulting nonisotropic far‐field radiation. First, using a direct numerical approach, we show that small‐scale elastic heterogeneities located in the near‐field of an explosive source, generate unexpected phases (i.e., long period S waves). We then demonstrate that the nonperiodic homogenization theory applied to 2‐D and 3‐D elastic models, with various pattern of small‐scale heterogeneities near the source, leads to accurate waveforms at a reduced computational cost compared to direct modeling. Further, it gives an interpretation of how nearby small‐scale features interact with the source at low frequencies, through an explicit correction to the seismic moment tensor. In 2‐D simulations, we find a deviatoric contribution to the moment tensor, as high as 21% for near‐source heterogeneities showing a 25% contrast of elastic values (relative to a homogeneous background medium). In 3‐D this nonisotropic contribution reaches 27%. Second, we analyze intermediate‐periods regional seismic waveforms associated with some underground nuclear explosions conducted at the Nevada National Security Site and invert for the full moment tensor, in order to quantify the relative contribution of the isotropic and deviatoric components of the tensor. The average value of the deviatoric part is about 35%. We conclude that the interactions between an explosive source and small‐scale local heterogeneities of moderate amplitude may lead to a deviatoric contribution to the seismic moment, close to what is observed using regional data from nuclear test explosions.

Fully Coupled Resolution of Heterogeneous Elastic–Plastic Contact Problem

The recent development of semi-analytical methods (SAM) has led to numerous improvements in their capabilities in terms of phenomena that can be accounted for and numerical efficiency. They now allow to perform fast and robust simulations of contact between inelastic—with either elastic–plastic or viscoelastic behavior—and anisotropic or heterogeneous materials. All effects may be combined, with either coating, inclusions, cavities, or fibers as inhomogeneities. The coupling between local and global scales remains numerically difficult. A framework is proposed here for contact problems considering the effect of elastic heterogeneities within an elastic–plastic matrix. The mutual interactions among heterogeneities and their surrounding plastic zone as well as the interactions between them and the contact surface through which the load is transmitted should be accounted for. These couplings are outside the validity domain of the Eshelby’s equivalent inclusion method (EIM) that assumes a uniform stress field in an infinite space far from the inhomogeneity. In the presence of heterogeneities close to the surface or located at the Hertzian depth, the yield stress can be reached locally due to the additional stress it generates, whereas the stress and strain state would remain purely elastic for a matrix without inclusion. It is well known that for rolling element bearing and gear applications, the ruin of components is often linked to cracks initiated in the vicinity of large or hard inclusions that act as stress raisers. It turned out that plastic strains tend to reduce the stress generated by the contact pressure while hard heterogeneities will increase it. As plastic strain accumulation can provide the basis for fatigue damage criteria, the second half of the paper will illustrate how the method can be used to identify and rank geometrical and material parameters that influence the location and magnitude of the maximal plastic strain.

Spatial Distributions of Local Elastic Moduli Near the Jamming Transition

Recent progress on studies of the nanoscale mechanical responses in disordered systems has highlighted a strong degree of heterogeneity in the elastic moduli. In this contribution, using computer simulations, we study the elastic heterogeneities in athermal amorphous solids--composed of isotropic static sphere packings--near the jamming transition. We employ techniques based on linear response methods that are amenable to experimentation. We find that the local elastic moduli are randomly distributed in space and are described by Gaussian probability distributions, thereby lacking any significant spatial correlations, that persist all the way down to the transition point. However, the shear modulus fluctuations grow as the jamming threshold is approached, which is characterized by a new power-law scaling. Through this diverging behavior we are able to identify a characteristic length scale, associated with shear modulus heterogeneities, that distinguishes between bulk and local elastic responses.

Transmission of Global Commodity Prices to Domestic Producer Prices: A Comprehensive Analysis

Utilizing a comprehensive dataset that includes a sample of 104 countries for corn, 54 countries for soybeans, 82 countries for wheat, and 77 countries for rice and covers the period from 1991 to 2013, we estimate a globally comprehensive but heterogeneous (country-specific) transmission elasticities between international prices and domestic producer prices. We mainly utilize the traditional two-step Engel-Grange cointegration model and the recently developed nonlinear autoregressive distributed lags (NARD) model to estimate the transmission elasticities. We find mixed evidence on the existence of long-run relationship between international and domestic price. For corn 66 out of 104, for soybeans 27 out of 54, for wheat 47 out of 82, and for rice 49 out of 77 countries, we fail to have a long-run relationship. For corn and soybeans, the long-run relationship is evident in top producing countries whereas the converse is evident for wheat and rice, particularly for rice. We also find that the pass-through of international to domestic prices is asymmetric in the majority cases — these asymmetries are negative, i.e., the domestic producer prices react less fully to an increase in international prices than to a decrease and are acute in the short-run than the long-run. We also estimate the crop-specific short-run global mean transmission elasticities, which vary from 0.358 (corn) to 0.524 (soybeans).

Molecular Mechanisms of Plastic Deformation in Sphere-Forming Thermoplastic Elastomers

Plastic deformation of sphere-forming triblock thermoplastic elastomers is studied with molecular dynamics simulations in order to elucidate microscopic mechanisms operative in nanostructured macromolecular materials. Phase separation of linear triblock copolymers is achieved by first equilibrating a melt using soft interactions that are subsequently replaced by a standard bead–spring model to obtain mechanical properties. We compare two deformation modes of both uniaxial stress and strain and vary the polymer chain length from unentangled to moderately entangled chains. Our simulations show that triblocks exhibit significant increase of strain hardening compared to homopolymer elastomers. We analyze several properties such as global chain deformation and local monomer motion, number and shape of spherical domains, and the evolution of the fraction of chains bridging between domains. Results confirm the notion of improved mechanical properties through effectively cross-linking chain ends. Void nucleation at different stages of deformation is observed to occur either at the interface between glassy and rubbery phases or immediately following the breakup of glassy domains and is therefore intimately related to the elastic heterogeneity of the material.

Quantitative analysis of rock stress heterogeneity: Implications for the seismogenesis of fluid-injection-induced seismicity

We compared elastic-rock heterogeneity measured by borehole logging to the occurrence of seismic events caused by hydraulic fracturing of the corresponding rock sections. Our observations made from two hydraulic fracturing case studies suggest that elastic-rock heterogeneity controls the occurrence of fluid-injection-induced seismicity. The seismic events occurred preferentially in rock sections characterized by low Poisson’s ratio and high Young’s modulus. Based on analytic solutions of stress fluctuations in elastically heterogeneous media in equilibrium to a homogeneous far-field stress, we quantified the relation between elastic-rock heterogeneity and stress changes leading to fracture opening and reactivation in two end member models of 1D and 3D heterogeneity. We found that significant fluctuations of rock stress originated from elastic rock heterogeneity. Moreover, we found that stress changes leading to fracture opening and reactivation in rocks undergo scale invariance spatial fluctuations. This gave a possible physical explanation for the observed scale invariance of seismogenic processes. We analyzed the physical meaning of a heterogeneity index of rocks, which indicated rock sections of high Young’s modulus and low Poisson’s ratio. We found that this index can be used to identify rock sections of high differential stress. In addition, our results suggest that it is related to the occurrence probability of brittle rock failure during hydraulic fracturing. Nevertheless, we found that fluctuations of Poisson’s ratio showed an even stronger correlation to critical stress changes which resulted in opening and reactivation of fractures in rocks. We obtained an analytic solution of stress fluctuations in vertical transverse isotropic layers such as shale deposits and applied it to a hydraulic fracturing case study of a shale gas reservoir. Also in this case, we observed strong relations between seismicity and fluctuations of stress in space.

An effective medium theory for three-dimensional elastic heterogeneities

SUMMARY A second-order Born approximation is used to formulate a self-consistent theory for the effective elastic parameters of stochastic media with ellipsoidal distributions of small-scale heterogeneity. The covariance of the stiffness tensor is represented as the product of a onepoint tensor variance and a two-point scalar correlation function with ellipsoidal symmetry, which separates the statistical properties of the local anisotropy from those of the geometric anisotropy. The spatial variations can then be rescaled to an isotropic distribution by a simple metric transformation; the spherical average of the strain Green’s function in the transformed space reduces to a constant Kneer tensor, and the second-order corrections to the effective elastic parameters are given by the contraction of the rescaled Kneer tensor against the singlepoint variance of the stiffness tensor. Explicit results are derived for stochastic models in which the heterogeneity is transversely isotropic and its second moments are characterized by a horizontal-to-vertical aspect ratio η. If medium is locally isotropic, the expressions for the anisotropic effective moduli reduce in the limit η →∞ to Backus’s second-order expressions fora1-Dstochasticlaminate.ComparisonswiththeexactBackustheoryshowthatthesecondorder approximation predicts the effective anisotropy for non-Gaussian media fairly well for relative rms fluctuations in the moduli smaller than about 30 per cent. A locally anisotropic model is formulated in which the local elastic properties have hexagonal symmetry, guided by a Gaussian random vector field that is transversely isotropic and specified by a horizontal-toverticalorientationratio ξ.Theself-consistenttheoryprovidesclosed-formexpressionsforthe dependence of the effective moduli on 0 <ξ <∞ and 0 <η< ∞. The effective-medium parametrizations described here appear to be suitable for incorporation into tomographic modelling.

Young, Old, Conservative, and Bold: The Implications of Heterogeneity and Finite Lives for Asset Pricing

We study the implications of preference heterogeneity for asset pricing. We use recursive preferences in order to separate heterogeneity in risk aversion from heterogeneity in the intertemporal elasticity of substitution, and an overlapping-generations framework to obtain a non-degenerate stationary equilibrium. We solve the model explicitly up to the solutions of ordinary differential equations, and highlight the effects of overlapping generations and each dimension of preference heterogeneity on the market price of risk, interest rates, and the volatility of stock returns. We find that separating IES and risk aversion heterogeneity can have a substantive impact on the model's (qualitative and quantitative) ability to address some key asset pricing issues.

Exploring trade-offs in frequency allocation in a transit network using bus route patterns: Methodology and application to large-scale urban systems

Transit agencies seek to allocate their limited operational budget and fleet optimally to service routes in order to maximize user benefits. The Transit Network Frequency Setting Problem formulation developed in this study effectively captures the coupling between the routes and their prevailing patterns, which may have different subsets of stops visited at different times of the day. The number of riders is elastic to the prevailing number of bus trips at a given stop, which is the combination of different pattern dispatch frequencies. As a result, the study bridges the gap between the operator’s perspective where the decision unit is the pattern schedule, and the user’s perspective, which perceives frequencies at the route level. Two main formulations are introduced. The first one maximizes the number of riders and the total waiting time savings under budget, fleet, policy headway and bus loading constraints; the second minimizes the net cost under fleet, policy headway, bus loading, minimum ridership and minimum waiting time savings constraints. In both formulations, pattern headways are the decision variables. Spatial and temporal heterogeneity of ridership elasticity with respect to headway is captured. The formulations are applied to a large-scale test network for the Chicago area. The results show that a win–win solution is possible where both ridership and waiting time savings are increased, while the net cost is decreased.

Heterogeneous Viscoelasticity: A Combined Theory of Dynamic and Elastic Heterogeneity.

We present a heterogeneous version of Maxwell's theory of viscoelasticity based on the assumption of spatially fluctuating local viscoelastic coefficients. The model is solved in coherent-potential approximation. The theory predicts an Arrhenius-type temperature dependence of the viscosity in the vanishing-frequency limit, independent of the distribution of the activation energies. It is shown that this activation energy is generally different from that of a diffusing particle with the same barrier-height distribution, which explains the violation of the Stokes-Einstein relation observed frequently in glasses. At finite but low frequencies, the theory describes low-temperature asymmetric alpha relaxation. As examples, we report the good agreement obtained for selected inorganic, metallic, and organic glasses. At high frequencies, the theory reduces to heterogeneous elasticity theory, which explains the occurrence of the boson peak and related vibrational anomalies.

Young, Old, Conservative, and Bold: The Implications of Heterogeneity and Finite Lives for Asset Pricing

We study the implications of preference heterogeneity for asset pricing. We use recursive preferences in order to separate heterogeneity in risk aversion from heterogeneity in the intertemporal elasticity of substitution and an overlapping-generations framework to obtain a nondegenerate stationary equilibrium. We solve the model explicitly up to the solutions of ordinary differential equations and highlight the effects of overlapping generations and each dimension of preference heterogeneity on the market price of risk, interest rates, and the volatility of stock returns. We find that separating intertemporal elasticity of substitution and risk aversion heterogeneity can have a substantive impact on the model’s (qualitative and quantitative) ability to address some key asset-pricing issues.

Acceleration of MPI mechanisms for sustainable HPC applications

Ultrascale computing systems are meant to reach a growth of two or three orders of magnitude of today computing systems. However, to achieve the performances required, we will need to design and implement more sustainable solutions for ultra-scale computing systems, understanding sustainability in a holistic manner to address challenges as economy-of-scale, agile elastic scalability, heterogeneity, programmability, fault resilience, energy efficiency, and scalable storage. Some of those solutions could be provided into MPI, but other should be devised as higher level concepts, less generalists, but adapted to applicative domains, possibly as programming patterns or or libraries. In this paper, we show some proposals to extend MPI trying to cover major domains that are relevant towards sustainability: MPI programming optimizations and programming models, resilience, data management, and their usage from applications.

SU‐E‐U‐01: Automatic Quantitative Analysis of Chronic Liver Disease Employing Shear Wave Ultrasound Elastography

Purpose:The purpose of this study was to quantify liver elastic heterogeneity in Shear Wave Elastography (SWE) by using textural features and evaluating their diagnostic performance on differentiating healthy from chronic liver disease patients, taking biopsy results as the gold standard.Methods:Clinical material includes 16 healthy (F0) and 15 with Chronic Liver Disease (F1,F2,F3,F4) patients according to the Metavir staging system. All exams were performed using the Aixplorer ultrasound system with a SuperCurved SC6‐1 transducer. From the SWE‐QBox the RGB displayed elasticity data of Young's modulus were transformed from RGB color space into an elasticity matrix of gray tones, whose values varied from zero to the maximum elasticity measurement. Every pixel with no RGB‐values was set to ‘−1’ due to non‐valid elasticity value for that pixel. From the elastogram map 185 textural features were computed (5 from the gray‐tone histogram, 26 second order statistic features, extracted from the co‐occurrence matrices and 10 features extracted from the run‐length matrices over four directions (00,450,900,1350) and distances of (d=1,3,5,7,9) pixels). Stepwise multi‐linear regression analysis was utilized to avoid feature redundancy leading to a feature subset feeding a Support Vector Machine (SVM) classifier. SVM‐model evaluation was performed by means of the leave‐one‐out method.Results:Maximum classification accuracy (93.5%) in distinguishing healthy from chronic liver disease patients was obtained employing three textural features (Standard Deviation, Sum‐Variance, Contrast) that describe the elastogram's contrast, variability and complexity. Sensitivity and specificity values were 93.3% and 94.0% respectively.Conclusion:The proposed classification scheme can provide reproducibility and reliability of liver SWE application in clinical practice. It can also assist the interpretation of SWE measurements which is considered as a difficult task due to absence of guidelines in the literature and to decrease the time/cost of diagnosis and the need for patients to undergo invasive examination.This research has been co‐financed by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program ’Education and Lifelong Learning’ of the National Strategic Reference Framework (NSRF) Research Funding Program: ARCHIMEDES III. Investing in knowledge society through the European Social Fund.