Elastic Heterogeneity Research Articles

Effect of the elastic coefficient heterogeneity and crystallography on the grain growth stagnation

Effect of the elastic coefficient heterogeneity and crystallography on the grain growth stagnation

Using Price Elasticities of Water Demand to Inform Policy

This survey distills recent work on the price elasticity of demand for urban and agricultural water and outlines how it can inform the design of market-based approaches to manage increasingly scarce water resources. We offer a brief description of the water sector, including the primary users, main water sources, and market failures in the allocation and use of surface water and groundwater. A review of recent empirical research on the price elasticities of agricultural and urban water demand shows the progress made in our understanding of user response to prices and reveals substantial heterogeneity in the price response. We apply what we have learned about elasticities to surface water markets and price-based groundwater management. Heterogeneity in price elasticities suggests that water transfers may lead to large efficiency gains, but that their magnitude is site specific. Groundwater pricing may cost-effectively manage groundwater and fund the development of alternative water supplies, but heterogeneity in elasticity estimates highlights that the conservation and revenue generated are basin specific.

Understanding the scaling of boson peak through insensitivity of elastic heterogeneity to bending rigidity in polymer glasses

Amorphous materials exhibit peculiar mechanical and vibrational properties, including non-affine elastic responses and excess vibrational states, i.e., the so-called boson peak (BP). For polymer glasses, these properties are considered to be affected by the bending rigidity of the constituent polymer chains. In our recent work [Tomoshige, et al 2019, Sci. Rep. 9 19514], we have revealed simple relationships between the variations of vibrational properties and the global elastic properties: the response of the BP scales only with that of the global shear modulus. This observation suggests that the spatial heterogeneity of the local shear modulus distribution is insensitive to changes in the bending rigidity. Here, we demonstrate the insensitivity of elastic heterogeneity by directly measuring the local shear modulus distribution. We also study transverse sound wave propagation, which is also shown to scale only with the global shear modulus. Through these analyses, we conclude that the bending rigidity does not alter the spatial heterogeneity of the local shear modulus distribution, which yields vibrational and acoustic properties that are controlled solely by the global shear modulus of a polymer glass.

Strong discontinuity FE analysis for heterogeneous materials: The role of crack closure mechanism

We present a Finite Element model, which is devoted to describing the failure mechanics of quasi-brittle materials (e.g. concrete), such as the stiffness recovery effect at the transition from tension to compression, and the cyclic behavior with a low number of cycles. The material is studied at the meso-scale, and thus considered as a heterogeneous medium. The model is formulated within the framework of the strong discontinuity analysis and implemented using the Enhanced Finite Element Method (E-FEM). The key point is to locally embed the discontinuities inside the finite elements. Here, we take advantage of this strategy for two kinds of discontinuities. On the one hand, strong discontinuities aim to model cracks, at fine scale, that can open along mode-I. On the other hand, weak discontinuities are used to describe the elastic heterogeneity. In addition to the initiation and propagation of cracks, our main contribution is to add a closure mechanism. We show the ability of the model to simulate some of the well-known characteristics of such materials at macroscale, such as the unsymmetrical tension/compression behavior, the stiffness recovery effect, and hysterical load/displacement curve.

In situ monitoring of microstructure evolution during thermal processing of uranium-zirconium alloys using laser-generated ultrasound

Laser-generated ultrasound was used to monitor microstructure evolution during thermal processing of as-cast, polycrystalline binary uranium-zirconium metallic fuel alloys with compositions of U-20wt.%Zr (U-20Zr), U-50wt.%Zr (U-50Zr) and U-80wt.%Zr (U-80Zr). Ultrasonic waveforms were recorded during heating and cooling the samples from room temperature to >973 K and back. A phase transition temperature for all three compositions was estimated from the temperature at which an abrupt and rapid reduction in ultrasonic velocities was observed. Microstructural features on the length scale of tens of micrometers were inferred from the observation of scattering of ultrasonic waves by elastic heterogeneities above ~823 K in U-20Zr, while a hysteresis in the ultrasonic velocities of U-80Zr upon cooling was attributed to a partial retention of the high temperature phase following thermal annealing. The U-50Zr alloy exhibited a reversible viscoelastic response above 933 K, as evidenced by the observation of high frequency attenuation of the shear component of the waveforms at high temperature. Ultrasonic measurements were supplemented by in situ transmission electron microscopy (TEM). The TEM images revealed that the δ-U-Zr matrix in the three compositions underwent a spinodal decomposition above ~823 K into nanoscale regions. The ultrasonic measurements revealed larger, micron-scale structure evolution in the U-20Zr alloy at the same temperature. This large-scale structure is associated with heterogeneous regions having different Zr content. Our findings show the potential heating rate dependence of microstructural evolution in U-Zr alloys and highlight differences in the thermomechanical response and associated length scales during thermal annealing between single- and dual-phase compositions. These results demonstrate the utility of laser ultrasonics to rapidly and efficiently scan phase boundaries and monitor micrometer-scale structure evolution in metallic fuel alloys.

Scale of operations of MNCs and heterogeneity: a multi-country analysis

ABSTRACT This paper examines the relationship between the productivity of parent firms and the scale of their subsidiaries in foreign markets. The empirical exam is based on a large sample of firms from 32 different countries. The average elasticity estimated for the baseline sample is 0.34; i.e. a 1% increase in labour productivity increases the scale of subsidiaries by 0.34%. For TFP, the elasticity is slightly lower, 0.23. The relationship is much stronger for manufacturing firms than for firms in the service sector. The paper also analyzes the degree of heterogeneity of elasticities estimated across countries. We find differences in the magnitude of elasticities but confirm the positive relationship between scale and parent firm productivities for a large fraction of countries. It also addresses the issue of potential endogeneity of productivity. The positive relationship between scale and productivity is confirmed when controlling for this.

A 3D Full Stress Tensor Model for Oklahoma

AbstractThe stress tensor is an important property for upper crustal studies such as those that involve pore fluids and earthquake hazards. At tectonic plate scale, plate boundary forces and mantle convection are the primary drivers of the stress field. In many local settings (10–100 s of km and <10 km depth) in tectonic plate interiors, we can simplify by assuming a constant background stress field that is perturbed by local heterogeneity in density and elasticity. Local stress orientation and sometimes magnitude can be estimated from earthquake and borehole‐based observations when available. Modeling of the local stress field often involves interpolating sparse observations. We present a new method to estimate the 3D stress field in the upper crust and demonstrate it for Oklahoma. We created a 3D material model by inverting multiple types of geophysical observations simultaneously. Integrating surface‐wave dispersion, local travel times and gravity observations produces a model of P‐wave velocity, S‐wave velocity, and density. The stress field can then be modeled using finite element simulations. The simulations are performed using our simplified view of the local stress field as the sum of a constant background stress field that is perturbed by local density and elasticity heterogeneity and gravitational body forces. An orientation of N82°E, for the maximum compressive tectonic force, best agrees with previously observed stress orientations and faulting types in Oklahoma. The gravitational contribution of the horizontal stress field has a magnitude comparable to the tectonic contribution for the upper 5 km of the subsurface.

The role of nano-scale elastic heterogeneity in mechanical and tribological behaviors of a Cu–Zr based metallic glass thin film

Despite its significance in fundamentally understanding mechanical behaviors of metallic glasses, the effect of elastic heterogeneity on plastic deformation and thereby nanotribological behavior of metallic glass thin films (MGTFs) remains an open question. By a combination of nano-scratch, nano-DMA and nanoindentation tests, we have investigated in the present work the room-temperature inhomogeneous plastic deformation behavior and nanotribological properties of Cu–Zr based MGTFs obtained by magnetron sputtering with different substrate temperatures. It is revealed that while the studied MGTF experiences a moderate rise of both hardness and Young's modulus with the elevating substrate temperature from 300 K to 473 K, its wear resistance significantly increases during the nano-scratch under a ramping load. More interestingly, through systematically studying the serration dynamics during the nano-scratch for MGTFs with different thermal history, we found that the increase of critical length scale for shear banding, which is well accompanied by the reduction of nano-scale elastic heterogeneity, tends to make shear banding more difficult in the amorphous structure, and thus enhance the wear resistance of the tested MGTFs. The current findings may provide a useful guidance to develop MGTFs with a superior mechanical and tribological properties via tuning their nanoscale elastic heterogeneity.

The Geographical Scope of Multinational Firms and Heterogeneity

This paper offers an empirical assessment of the geographical scope of multinational activity at the world level. With this objective, we estimate scope elasticities, which is the relationship between the productivity of the parent firm and the probability of operating abroad in different markets through subsidiaries with the same main activity. Elasticities are estimated for a baseline cross-section of 35 home countries that represent more than 70% of total outward FDI investment at the world level. At the aggregate level, the results indicate quite consistently, through various estimation methods, that a 10% increase in the productivity of the parent firm increases the probability in a range between 0.8–1.0%. Elasticities for manufacturing more than double the elasticities for the service sector. The paper also explores the heterogeneity of scope elasticities across home countries and sectors. This heterogeneity is related to differences across bilateral home-host country characteristics such as the size of the potential host market, bilateral distance and other factors such as institutional quality of host countries and cultural closeness. The signs attached to some of these factors are in general consistent with the predictions of models of firm heterogeneity and FDI activity.

Sound damping in soft particle packings: the interplay between configurational disorder and inelasticity.

We numerically investigate sound damping in disordered two-dimensional soft particle packings. We simulate evolution of standing waves of particle displacements and analyze time correlation functions of particle velocities and power spectra. We control the strength of inelastic interactions between the particles in contact to show how the inelasticity affects anomalous sound characteristics of disordered systems: Increasing the strength of inelastic interactions, we find that (i) sound softening vanishes and (ii) attenuation coefficients exhibit a transition from the Rayleigh law to quadratic growth. We also report (iii) how the Ioffe-Regel limit frequencies depend on the strength of inelasticity as useful information for experiments and applications of the sound in disordered media. Our findings suggest that sound damping in soft particle packings is determined by the interplay between elastic heterogeneities and inelasticity.

Drivers of Participation Elasticities across Europe: Gender or Earner Role within the Household?

We compute participation tax rates across the EU and find that work disincentives inherent in tax-benefit systems largely depend on household composition and the individual's earner role within the household. We then estimate participation elasticities using an IV Group estimator that enables us to investigate the responsiveness of individuals to work incentives. We contribute to the literature on heterogeneous elasticities by providing estimates for different socioeconomic groups by country, gender and earner role within the household. Our results show an average elasticity of 0.08 for men and of 0.14 for women as well as a high degree of heterogeneity across countries. The commonly cited difference in elasticities between men and women stems predominantly from the earner role of the individual within the household and nearly disappears once we control for this factor.

Price Elasticity and Beyond: The Determinants of Residential Electricity Consumption in New York

The price elasticity of electricity demand has been the focus of an important literature, because of the potential impact it has on energy and economic policy. We contribute to it by looking at the state of New York case in an innovative way. We construct a three-dimensional (utility × county × year) panel dataset of electricity sales to residential consumers from 21 electric utilities in all 62 counties of state of New York over the years of 1994 to 2013 to estimate the price elasticity of residential electricity average demand (per household). Such data enables us to account for differences within a large jurisdiction, without having to rely on household-level data, which are difficult to obtain, especially over different years. We find that the short-run and intermediate-run price elasticity of demand are respectively in the vicinity of -0.04 and -0.07 and that the long-run elasticity is around -0.60. We also investigate how the price elasticity varies in different contexts, as described by time period, price level, income level, weather indicators, and other variables. We find that once we take into account the heterogeneity of contexts, the multiplicity of significant price elasticities of demand make it difficult to have a valid, global, interpretation of the impact of a price change upon households. There is such an heterogeneity of price elasticities across the different contexts that one should be cautious on its use for policy, as a single value may not represent any consumer at all.

The Time-of-Day Travel Demand Elasticity Paradox

Driving demand and congestion are known to peak throughout the day, but temporal heterogeneity in travel demand elasticities is often overlooked. I estimate how the fuel economy elasticity of travel demand — a measure of the rebound effect from fuel economy standards — varies across peak and off-peak periods. The results present a paradox. Drivers are most elastic during peak demand periods. Mode switching for shorter commute trips appears to drive the heterogeneity, and the pollution benefits of fuel economy standards are shown to be more than offset by exacerbated congestion costs due to the timing of the rebound effect.

Globalization and labor demand elasticities: Do trading partners matter

This paper uses industrial level data across 41 developing and emerging economies over the period of 1993–2013, to analyze the impact of globalization on the elasticity of demand for labor. The use of both import penetration ratios and export intensity in our model allows for assessment of relative effectiveness of exports vis à vis imports in influencing the labor elasticities. Furthermore, the disintegration of exports and imports according to their trading partners helps explore a novel source of heterogeneity in labor elasticity originating as a result of trading relationship with developed and developing world. Using system-GMM approach, our results reveal that both exports and imports make labor demand more elastic, with imports leaving the labor demand more vulnerable to wage changes. Trading with developing countries renders labor demand more elastic and that too with respect to low-tech or labor intensive products, while trading with developed countries poses no effect. Overall, the results point towards developing countries encouraging greater exporting and importing ties with developed world to ease its impact on the elasticity of demand for labor. However, trading with developing countries need not be suspended rather labor protection programs need to be in place to counter any consequent adverse effects.

Effects of plasticity on the anisotropy of the effective fracture toughness

This paper investigates the effects of plasticity on the effective fracture toughness. A layered material is considered as a modelling system. An elastic-plastic phase-field model and a surfing boundary condition are used to study how the crack propagates throughout the material and the evolution of the effective toughness as a function of the layer angle. We study three idealized situations where only one of the properties among fracture toughness, Young’s modulus and yield strength is taken to be heterogeneous and the others are assumed to be uniform. We observe that in the case of toughness and strength heterogeneity, the material exhibits anomalous isotropy: the effective toughness is equal to the largest of the point-wise values for any layer angle except when the layers are parallel to the macroscopic direction of propagation. As the layer angle decreases, the crack propagates along the brittle-to-tough interfaces, whereas it goes straight when the layers have different yield strength but uniform toughness. We find that smooth deflections in the crack path do not induce any overall toughening and that the effective toughness is not proportional to either the cumulated fracture energy or the cumulated plastic work. In the case of elastic heterogeneity, the material is anisotropic in the sense of the effective toughness, as the latter varies as a function of the layer angle. Four toughening mechanisms are active: stress fluctuations, crack renucleation, plastic dissipation and plastic blunting. Finally, we consider a layered medium comprised of compliant-tough-weak and stiff-brittle-strong phases, as it is the case for many structural composites. We observe a transition from an interface-dominated to a plasticity-dominated failure regime, as the phase constituents become more ductile. The material is anisotropic in the sense of the effective toughness.

Analyzing carbon pricing policies using a general equilibrium model with production parameters estimated using firm data

Policy simulation results of Computable General Equilibrium (CGE) models largely hinge on the choices of substitution elasticities among key input factors. Currently, most CGE models rely on the common elasticities estimated from aggregated data, such as the GTAP model elasticity parameters. Using firm level data, we apply the control function method to estimate CES production functions with capital, labor and energy inputs and find significant heterogeneity in substitution elasticities across different industries. Our capital-labor substitution elasticities are much lower than the GTAP values while our energy elasticities are higher. We then incorporate these estimated elasticities into a CGE model to simulate China's carbon pricing policies and compare with the results using GTAP parameters. Our less elastic K-L substitution leads to lower base case GDP growth, but our more elastic energy substitution lead to lower coal use and carbon emissions. In the carbon tax policy exercises, we find that our elasticities lead to easier reductions in coal use and carbon emissions.

An atomic-level perspective of shear band formation and interaction in monolithic metallic glasses

Understanding the relationship between nanoscale structural heterogeneities or elastic fluctuations and strain localization in monolithic metallic glasses remains a long-standing underlying issue. Here, an atomic-level investigation of the correlation between elastic and structural heterogeneities and the mechanisms of shear banding in CuZr metallic glass is conducted using molecular dynamics simulations. The shear band formation and propagation processes and the intersection mechanism of multiple shear bands are evaluated by means of local entropy-based structural identification and von Mises stress calculation. The shear band follows the path of lower order and high entropy while shear deflection and branching occur when approaching regions of low entropy. The local von Mises stress calculation allows predictions on the shear band direction and the propensity for activation and propagation prior to yielding and sheds light on shear band branching and multiplication processes.

Price elasticities of residential electricity demand: Estimates from household panel data in Bangladesh

Abstract We collect a household level panel dataset to estimate the price elasticities of electricity demand for different types of urban households in Bangladesh. We use an instrumental variable estimation strategy which exploits exogenous variation in average electricity prices induced by a value-added-tax shock. The results indicate significant heterogeneity in price elasticities by electricity consumption levels. We conduct a number of simulations under alternative policy scenarios to illustrate how incorporating the heterogeneous nature of price elasticities into pricing policy can help decrease electricity demand-supply mismatch and inequality in electricity consumption. The results have important policy implications for developing countries aiming to address major energy issues by implementing tariff reforms.

Signature of local stress states in the deformation behavior of metallic glasses

The design of ductile heterogeneous metallic glasses (MGs) with enhanced deformability by purposely controlling the shear-band dynamics via modulation of the atomic-scale structures and local stress states remains a significant challenge. Here, we correlate the changes in the local atomic structure when cooling to cryogenic temperature with the observed improved shear stability. The enhanced atomic-level structural and elastic heterogeneities related to the nonaffine thermal contraction of the short-range order (SRO) and medium-range order (MRO) change the characteristics of the activation process of the shear transformation zones (STZs). The experimental observations corroborated by Eshelby inclusion analysis and molecular dynamics simulations disclose the correlation between the structural fluctuations and the change in the stress field around the STZ. The variations in the inclination axes of the STZs alter their percolation mechanism, affect the shear-band dynamics and kinetics, and consequently delay shear failure. These results expand the understanding of the correlation between the atomic-level structure and elementary plastic events in monolithic MGs and thereby pave the way for the design of new ductile metallic alloys.

Effect of heterogeneity on failure of natural rock samples

A carbonate sample extracted from the depth of about 10 kft was subjected to uniaxial loading while the confining stress remained constant. Post-experiment inspection of the sample showed an inclined crack at an angle less than 20° to the horizontal. This subhorizontal crack orientation was contrary to the expected 45° inclination, the plane of the maximum shear stress. Coincidentally, as shown by CT-scan prior to loading, there was a boundary between two layers of different density inside the sample located almost exactly where the crack appeared. This density difference has arguably translated into the contrast in the elastic properties at the boundary. The hypothesis is that because of this elastic heterogeneity, an incipient crack developed at the boundary due to the unavoidable tensile stressing of the sample as it was brought to the benchtop from its original state of high confining stress at depth. Controlled uniaxial compression made the sample slip along this crack, which then developed into a prominent feature. This assumption was corroborated by a numerical experiment showing a strong von Mises stress concentration at the elastic contrast boundary during hydrostatic tensile loading. Another sample, from the same formation, but without strong density heterogeneity, exhibited a classic 45° crack after uniaxial loading. These results provide a novel and important insight into the mechanics, breakage, and strength of natural rock.