Showing papers on "Elasticity (economics) published in 2001"

C 2 F , BN, and C nanoshell elasticity from ab initio computations

Abstract: Two-dimensional lattices of carbon, boron-nitride, and fluorine-carbon compositions are treated with ab initio methods in order to evaluate and compare their mechanical properties in a uniform fashion. The demonstrated robustness of continuum elasticity up to very small length-scale allows one to define and compute the in-plane stiffness and flexural rigidity moduli of the representative nanoshells of C, BN, and ${\mathrm{C}}_{x}\mathrm{F}$ $(xl~2).$ While only small deviations from linear elasticity are observed for C and BN, fluorination causes significant spontaneous shell folding. We discover that spontaneous curvature in fluorinated nanotubes shifts the energy minimum from a plane sheet towards the very small diameter tubes of (4,4) and even (3,3) indexes. Moreover, their equilibrium cross sections are distinctly polygonal, due to curvature self-localization, with an equilibrium angle of $71\ifmmode^\circ\else\textdegree\fi{}$ at each fluorine row attachment. Our analysis yields a simple physical model coupling the mechanical strain with chemical transformation energies.

Handbook of Linear Partial Differential Equations for Engineers and Scientists

Abstract: Includes nearly 4,000 linear partial differential equations (PDEs) with solutionsPresents solutions of numerous problems relevant to heat and mass transfer, wave theory, hydrodynamics, aerodynamics, elasticity, acoustics, electrodynamics, diffraction theory, quantum mechanics, chemical engineering sciences, electrical engineering, and other fieldsO

Classical and Computational Solid Mechanics

Abstract: Tensor analysis stress tensor analysis of strain conservation laws elastic and plastic behaviour of materials linearized theory of elasticity solutions of problems in linearized theory of elasticity by potentials two-dimensional problems in linearized theory of elasticity variational calculus, energy theorems, Saint-Venant's principle Hamilton's principle, wave propagation, applications of generalized co-ordinates elasticity and thermodynamics irreversible thermodynamics and viscoelasticity thermoelasticity viscoelasticity large deformation incremental approach to solving some nonlinear problems finite element methods mixed and hybrid formulations finite element methods for plates and shells finite element modelling of nonlinear elasticity, viscoelasticity, plasticity, viscoplasticity and creep.

Endothelium-Derived Nitric Oxide Regulates Arterial Elasticity in Human Arteries In Vivo

Abstract: Arterial elasticity is determined by structural characteristics of the artery wall and by vascular smooth muscle tone. The identity of endogenous vasoactive substances that regulate elasticity has not been defined in humans. We hypothesized that NO, a vasodilator released constitutively by the endothelium, augments arterial elasticity. Seven healthy young men were studied. A 20-MHz intravascular ultrasound catheter was introduced through an arterial sheath to measure brachial artery cross-sectional area, wall thickness, and intra-arterial pressure. After control was established, indices of elasticity (pressure-area relationship, instantaneous compliance, and stress-strain, pressure-incremental elastic modulus (Einc), and pressure-pulse wave velocity relationships) were examined over 0 to 100 mm Hg transmural pressure obtained by inflation of an external cuff. Thereafter, the basal production of endothelium-derived NO was inhibited by N G -monomethyl-L-arginine (L-NMMA) (4 and 8 mg/min). Finally, nitroglycerin (2.5 and 12.5 g/min), an exogenous donor of NO, was given to relax the vascular smooth muscle. Elasticity was measured under all of these conditions. L-NMMA (8 mg/min) decreased brachial artery area (P0.016) and compliance (P0.0001) and increased Einc (P0.01) and pulse wave velocity (P0.0001). Nitroglycerin (12.5 g/min) increased brachial artery area (P0.001) and compliance (P0.001) and decreased pulse wave velocity (P0.02). NO, an endothelium-derived vasodilator, augments arterial elasticity in the human brachial artery. Loss of constitutively released NO associated with cardiovascular risk factors may adversely affect arterial elasticity in humans. (Hypertension. 2001;38:1049-1053.)

Dynamic nonlinear elasticity in geomaterials

Abstract: 2

A model of crystal plasticity based on the theory of continuously distributed dislocations

Abstract: This work represents an attempt at developing a continuum theory of the elastic–plastic response of single crystals with structural dimensions of ∼100 μm or less, based on ideas rooted in the theory of continuously distributed dislocations. The constitutive inputs of the theory relate explicitly to dislocation velocity, dislocation generation and crystal elasticity. Constitutive nonlocality is a natural consequence of the physical considerations of the model. The theory reduces to the nonlinear elastic theory of continuously distributed dislocations in the case of a nonevolving dislocation distribution in the material and the nonlinear theory of elasticity in the absence of dislocations. A geometrically linear version of the theory is also developed. The work presented in this paper is intended to be of use in the prediction of time-dependent mechanical response of bodies containing a single, a few, or a distribution of dislocations. A few examples are solved to illustrate the recovery of conventional results and physically expected ones within the theory. Based on the theory of exterior differential equations, a nonsingular solution for stress/strain fields of a screw dislocation in an infinite, isotropic, linear elastic solid is derived. A solution for an infinite, neo-Hookean nonlinear elastic continuum is also derived. Both solutions match with existing results outside the core region. Bounded solutions are predicted within the core in both cases. The edge dislocation in the isotropic, linear theory is also discussed in the context of this work. Assuming a constant dislocation velocity for simplifying the analysis, an evolutionary solution resulting in a slip-step on the boundary of a stress-free crystal produced due to the passage and exit of an edge dislocation is also described.

Nonlinear elasticity : theory and applications

Abstract: Preface 1. Elements of the theory of finite elasticity R. W. Ogden 2. Hyperelastic Bell materials: retrospection, experiment, theory M. F. Beatty 3. Universal results in finite elasticity G. Saccomandi 4. Equilibrium solutions for compressible nonlinearly elastic materials C. O. Horgan 5. Exact integrals and solutions for finite deformations of the incompressible Varga elastic materials J. M. Hill 6. Shear Ph. Boulanger and M. Hayes 7. Elastic membranes D. M. Haughton 8. Elements of the theory of elastic surfaces D. J. Steigmann 9. Singularity theory and nonlinear bifurcation analysis Y.-C. Chen 10. Perturbation methods and nonlinear stability analysis Y. B. Fu 11. Nonlinear dispersive waves in a circular rod composed of a Mooney-Rivlin material H.-H. Dai 12. Strain-energy functions with multiple local minima: modeling phase transformations using finite thermo-elasticity R. Abeyaratne, K. Bhattacharya and J. K. Knowles 13. Pseudo-elasticity and stress softening R. W. Ogden.

High-pressure elastic properties of major materials of Earth's mantle from first principles

Abstract: The elasticity of materials is important for our understanding of processes ranging from brittle failure, to flexure, to the propagation of elastic waves. Seismologically revealed structure of the Earth's mantle, including the radial (one-dimensional) profile, lateral heterogeneity, and anisotropy are determined largely by the elasticity of the materials that make up this region. Despite its importance to geophysics, our knowledge of the elasticity of potentially relevant mineral phases at conditions typical of the Earth's mantle is still limited: Measuring the elastic constants at elevated pressure-temperature conditions in the laboratory remains a major challenge. Over the past several years, another approach has been developed based on first-principles quantum mechanical theory. First-principles calculations provide the ideal complement to the laboratory approach because they require no input from experiment; that is, there are no free parameters in the theory. Such calculations have true predictive power and can supply critical information including that which is difficult to measure experimentally. A review of high-pressure theoretical studies of major mantle phases shows a wide diversity of elastic behavior among important tetrahedrally and octahedrally coordinated Mg and Ca silicates and Mg, Ca, Al, and Si oxides. This is particularly apparent in the acoustic anisotropy, which is essential for understanding the relationship between seismically observed anisotropy and mantle flow. The acoustic anisotropy of the phases studied varies from zero to more than 50% and is found to depend on pressure strongly, and in some cases nonmonotonically. For example, the anisotropy in MgO decreases with pressure up to 15 GPa before increasing upon further compression, reaching 50% at a pressure of 130 GPa. Compression also has a strong effect on the elasticity through pressure-induced phase transitions in several systems. For example, the transition from stishovite to CaCl2 structure in silica is accompanied by a discontinuous change in the shear (S) wave velocity that is so large (60%) that it may be observable seismologically. Unifying patterns emerge as well: Eulerian finite strain theory is found to provide a good description of the pressure dependence of the elastic constants for most phases. This is in contrast to an evaluation of Birch's law, which shows that this systematic accounts only roughly for the effect of pressure, composition, and structure on the longitudinal (P) wave velocity. The growing body of theoretical work now allows a detailed comparison with seismological observations. The athermal elastic wave velocities of most important mantle phases are found to be higher than the seismic wave velocities of the mantle by amounts that are consistent with the anticipated effects of temperature and iron content on the P and S wave velocities of the phases studied. An examination of future directions focuses on strategies for extending first-principles studies to more challenging but geophysically relevant situations such as solid solutions, high-temperature conditions, and mineral composites.

Elasticity of iron at the temperature of the Earth's inner core

Abstract: Seismological body-wave(1) and free-oscillation(2) studies of the Earth's solid inner core have revealed that compressional waves traverse the inner core faster along near-polar paths than in the equatorial plane. Studies have also documented local deviations from this first-order pattern of anisotropy on length scales ranging from 1 to 1,000 km (refs 3, 4). These observations, together with reports of the differential rotation(5) of the inner core, have generated considerable interest in the physical state and dynamics of the inner core, and in the structure and elasticity of its main constituent, iron, at appropriate conditions of pressure and temperature. Here we report first-principles calculations of the structure and elasticity of dense hexagonal close-packed (h.c.p.) iron at high temperatures. We find that the axial ratio c/a of h.c.p. iron increases substantially with increasing temperature, reaching a value of nearly 1.7 at a temperature of 5,700 K, where aggregate bulk and shear moduli match those of the inner core. As a consequence of the increasing c/a ratio, we have found that the single-crystal longitudinal anisotropy of h.c.p. iron at high temperature has the opposite sense from that at low temperature(6,7). By combining our results with a simple model of polycrystalline texture in the inner core, in which basal planes are partially aligned with the rotation axis, we can account for seismological observations of inner-core anisotropy.

Elasticity of hollow polyelectrolyte capsules prepared by the layer-by-layer technique

Abstract: Osmotically induced deformations (invaginations) of polyelectrolyte capsules were observed in poly(styrene sulfonate, sodium salt) (PSS) solution since PSS of Mw 70 000 is excluded from the capsule interior. It was found that there is a critical osmotic pressure difference at which the initial spherical capsule shape becomes unstable and invaginations are formed. This critical osmotic pressure was obtained as a function of the wall thickness and the capsule size. A theoretical model is provided which describes the relationship between the critical osmotic pressure, the elasticity modulus, the capsule wall thickness, and the capsule radius. The model was verified by measuring the invagination onset as a function of particle radius and wall thickness. The elasticity modulus of the PSS/PAH (polyallylamine hydrochloride) polyelectrolyte multilayer was measured as a function of wall thickness and capsule diameter. The modulus ranges between 500 and 750 MPa, which indicates a relatively strongly interconnected polyelectrolyte multilayer structure. With higher molecular weight PAH the elasticity modulus of the PSS/PAH multilayer was slightly enhanced.

Modelling of elastic continua using a grillage of structural elements based on discrete element concepts

Abstract: A framework is described for modelling an elastic continuum using a grillage of beam-like structural elements derived from discrete element concepts. The beam element properties are derived in detail and implemented in a structural analysis code for validation against classical two-dimensional plane elasticity solutions. The framework offers the possibility of modelling the onset and propagation of fracture in materials that are initially continuous, without the need for specialized elements or remeshing in the context of traditional finite elements. Copyright © 2001 John Wiley & Sons, Ltd.

Cholesterol decreases the interfacial elasticity and detergent solubility of sphingomyelins.

Abstract: The interfacial interactions of cholesterol with sphingomyelins (SMs) containing various homogeneous acyl chains have been investigated by Langmuir film balance approaches. Low in-plane elasticity among the packed lipids was identified as an important physical feature of the cholesterol−sphingomyelin liquid-ordered phase that correlates with detergent resistance, a characteristic property of sphingolipid−sterol rafts. Changes in the in-plane elastic packing, produced by cholesterol, were quantitatively assessed by the surface compressional moduli (Cs-1) of the monolayer isotherms. Of special interest were Cs-1 values determined at high surface pressures (>30 mN/m) that mimic the biomembrane situation. To identify structural features that uniquely affect the in-plane elasticity of the sphingomyelin−cholesterol lateral interaction, comparisons were made with phosphatidylcholine (PC)−cholesterol mixtures. Cholesterol markedly decreased the in-plane elasticity of either SM or PC regardless of whether they wer...

Demand Specification for Municipal Water Management: Evaluation of the Stone-Geary Form

Abstract: To specify demand in most water allocation problems, researchers face a tradeoff between flexibility and parsimony. Flexible forms are less constraining on elasticity estimates, but require large parameter sets that tend to cause poor out-of-sample forecasts and computational difficulties. Using a five-year panel of Texas municipalities, the parsimonious Stone-Geary form yields estimated demand functions that are comparable to flexible form results. The Stone-Geary specification also provides an estimate of the portion of water use that may not be responsive to price, and is useful in analysing price structures and designing conservation policies.

Ultrasonic elasticity imaging

Abstract: In an ultrasound imaging system, a displacement vector is estimated for a pattern of samples throughout an imaged region of interest (ROI) by comparing two successive B-mode frames. The displacement vector is preferably estimated using block matching. Once displacement vectors are estimated for samples throughout the ROI, corresponding strain values are estimated, which indicate the degree of elasticity of the respective tissue portions. An image is then displayed showing the strain distribution within the ROI as it is stressed, for example, by the user pressing the ultrasound transducer against the patient's body. The invention allows for both real-time and post-processed generation of elasticity displays, even based on the same body of acquired frame data. The real-time display is preferably generated using lower quality block matching whereas the post-processed elasticity calculations are carried out using high-quality techniques. Different techniques are included for adjusting the size and location of the search region of the block matching based on different measures of reliability of current displacement estimates.

Magnetic resonance elastography using 3D gradient echo measurements of steady-state motion.

Abstract: Magnetic resonance elastography (MRE) is an important new method used to measure the elasticity or stiffness of tissues in vivo. While there are many possible applications of MRE, breast cancer detection and classification is currently the most common. Several groups have been developing methods based on MR and ultrasound (US). MR or US is used to estimate the displacements produced by either quasi-static compression or dynamic vibration of the tissue. An important advantage of MRE is the possibility of measuring displacements accurately in all three directions. The central problem in most versions of MRE is recovering elasticity information from the measured displacements. In previous work, we have presented simulation results in two and three dimensions that were promising. In this article, accurate reconstructions of elasticity images from 3D, steady-state experimental data are reported. These results are significant because they demonstrate that the process is truly three-dimensional even for relatively simple geometries and phantoms. Further, they show that the integration of displacement data acquisition and elastic property reconstruction has been successfully achieved in the experimental setting. This process involves acquiring volumetric MR phase images with prescribed phase offsets between the induced mechanical motion and the motion-encoding gradients, converting this information into a corresponding 3D displacement field and estimating the concomitant 3D elastic property distribution through model-based image reconstruction. Fully 3D displacement fields and resulting elasticity images are presented for single and multiple inclusion gel phantoms.

Topological derivatives of shape functionals for elasticity systems

Abstract: The exact form of topological derivative (TD) and the computational procedure for its calculation is derived for a class of shape functionals in 3D elasticity. The derivation is based on asymptotic expansion of solutions. TD is used numerical shape optimization and for solving shape inverse problems.

A Theory of Volumetric Growth for Compressible Elastic Biological Materials

Abstract: A general theory of volumetric growth for compressible elastic materials is presented. The authors derive a complete set of governing equations in the present configuration for an elastic material ...

Elasticity of six polycrystalline silicate garnets at pressure up to 3.0 GPa

Abstract: The elasticities of six polycrystalline silicate garnets (almandine, grossular, pyrope, uvarovite, andradite, and Prp 25 Alm 56 Spe 19 ) have been experimentally studied at pressures up to 3.0 GPa using a phase comparison method with an ultrasonic interferometer in a liquid cell piston-cylinder apparatus. Complete elasticity data sets (P- and S-wave velocities, bulk moduli K s , shear moduli G, and their first pressure derivatives K S ′ and G ′) have been obtained for all six garnets, and are used together with an up-to-date compilation of garnet elasticity data to examine composition-elasticity systematics of garnets. Our results suggest that pyralspite and ugrandite have different relationships between bulk sound velocity (V ϕ ) and mean atomic weight (M 0 ), between Poisson’s ratio (σ) and density (ρ), and between G / K s and K s /ρ ratios. A large error may occur when the systematics are applied across different garnet groups.

BEM for theomoelasticity and elasticity with body force : a revisit

Abstract: For thermoelasticity and elasticity with a body force, the regular boundary element method involves a domain integral. Special techniques have been devised to eliminate the domain integral by either exact treatment, or approximation using radial basis functions. This paper gives a unified presentation of these techniques. Body forces of gravity, centrifugal, gradient, harmonic, and arbitrary types are investigated. In the approximation by radial basis function, existing work is extended to include higher order basis functions of conical, spline, and polynomial types.

Analyse mathématique de la méthode Arlequin mixte

Abstract: Resume On analyse une formulation Arlequin mixte d'un probleme d'elasticite, fondee sur un raccord H 1 en «volume ». On montre, en continu et en discret (generalement non conforme), l'existence et l'unicite d'une solution ainsi qu'une majoration optimale d'erreur, moyennant une hypothese de compatibilite pour le choix des espaces de discretisation.

Rheological Model for the Study of Dilational Properties of Monolayers. Comportment of Dipalmitoylphosphatidylcholine (DPPC) at the Dichloromethane (DCM)/Water Interface under Ramp Type or Sinusoidal Perturbations

Abstract: The dilational properties of monolayers are analyzed using the classical linear approximation. In most cases, the observed interfacial behavior can be approached by a model corresponding to a two-dimensional viscoelastic solid. The monolayer is characterized by two dilational elasticity terms (Ee, equilibrium elasticity, and Ene, nonequilibrium elasticity) and by one relaxation time (τ). These three physical constants are obtained from the responses of a ramp type perturbation, or from the responses (as a function of the frequencies) after sinusoidal area variations. Using axisymmetric drop shape analysis experiments, a dipalmitoyl phosphatidylcholine (DPPC) layer at the dichloromethane/water interface is characterized. Measurements of the surface pressure variations as the response to linear or sinusoidal variations of surface area are performed. Identical rheological physical constants (equilibrium elasticity, nonequilibrium elasticity, and relaxation time) are obtained using both methods. Dilational be...