Showing papers on "Elasticity (economics) published in 1997"
681 citations
15 Aug 1997
TL;DR: A closed form solution to the problem based on a Dugdale force-separation law is outlined and used to construct the map, and errors introduced by the Dugdale approximation are assessed by comparison with numerical solutions using the Lennard-Jones force law.
Abstract: Several continuum mechanics models of the adhesion between elastic spheres have found application to compliant materials such as rubber and to fine particles in the air or in colloidal suspension. More recently they are being used in connection with experimental techniques such as the surface force apparatus and the atomic force microscope. The appropriate model to use depends on the conditions: the size and elasticity of the spheres and the load to which they are subjected. To guide this choice a map has been constructed with nondimensional coordinates m and P, where the elasticity parameter m can be interpreted as the ratio of elastic deformation resulting from adhesion to the effective range of surface forces and the load parameter P is the ratio of the applied load to the adhesive force. A closed form solution to the problem based on a Dugdale force-separation law is outlined and used to construct the map. The errors introduced by the Dugdale approximation are assessed by comparison with numerical solutions using the Lennard-Jones force law. Copyright 1997Academic Press
549 citations
TL;DR: In this article, a meta-analysis is used to determine if there are factors that systematically affect price elasticity estimates in studies of residential water demand in the United States, and an econometric model is estimated, using price estimates from previous studies as the dependent variable.
Abstract: Meta-analysis is used to determine if there are factors that systematically affect price elasticity estimates in studies of residential water demand in the United States. An econometric model is estimated, using price elasticity estimates from previous studies as the dependent variable. Explanatory variables include functional form, cross-sectional versus time series, water price specification, rate structure, location, season, and estimation technique. Inclusion of income, rainfall, and evapotranspiration are all found to influence the estimate of the price elasticity. Population density, household size, and temperature do not significantly influence the estimate of the price elasticity. Pricing structure and season are also found to significantly influence the estimate of the price elasticity.
496 citations
TL;DR: In this article, a nonlinear theory of elastic boundary coating (or reinforcement) of an elastic solid is developed for plane strain deformations, which is applied to the analysis of the equilibrium of a finitely deformed halfplane consisting of compressible elastic material coated along its edge.
Abstract: In this paper, a nonlinear theory of elastic boundary coating (or reinforcement) of an elastic solid is developed for plane strain deformations. The coating consists of a material curve endowed with intrinsic elastic properties associated with extensibility and bending stiffness bonded to part, or all, of the bounding curve of the elastic body. The equations describing the equilibrium of the coated body when subject to finite deformation are derived using a variational method. The incremental equations describing a small departure from an equilibrium configuration are then derived and used to investigate the stability of a deformed configuration and the possibility of bifurcation.
The theory is applied to the analysis of the equilibrium of a finitely deformed half-plane consisting of compressible elastic material coated along its edge. The influence of the coating on the bifurcation behaviour of the half–plane is assessed against known results for an uncoated half–plane. Numerical results are used to illustrate the influence of certain material parameters on bifurcation.
290 citations
TL;DR: In this article, the authors investigated the temperature dependence of the mechanical properties of a filler-loaded tread compound experimentally and proposed a physically based method to represent this behaviour in the framework of non-linear continuum thermomechanics.
Abstract: This essay investigates the temperature dependence of the mechanical properties of a filler-loaded tread compound experimentally and proposes a physically based method to represent this behaviour in the framework of non-linear continuum thermomechanics. To this end, we realise a series of monotonic and cyclic strain controlled tests on cylindrical specimens in tension at different temperature levels. The experimental data show the isothermal mechanical behaviour to be mainly influenced by non-linear elasticity in combination with non-linear rate dependence and weak equilibrium hysteresis. We observe that the rate sensitivity of the material depends strongly on the temperature : at low temperature levels, the rate sensitivity is essentially higher than at high temperatures. The elastic properties of the material depend comparatively less on the temperature. Nevertheless, higher temperature levels lead to higher equilibrium stresses. In order to represent the material behaviour, we start with a multiplicative split of the deformation gradient into a mechanical and a thermal part as proposed by Lu and Pister (1975). Physically, this idea corresponds to a stress-free thermal expansion followed by an isothermal stress-producing deformation. We suppose the thermal part of the deformation gradient to be isotropic. As a consequence of this, the velocity gradient decomposes additively into a pure thermal and a pure mechanical part. By using these elements, we exploit the Clausius Duhem inequality and assume the so-called ‘mechanical second Piola Kirchhoff stress tensor’ to be a functional of the ‘mechanical Green's strain tensor’. In a further step, we define this functional by a system of constitutive equations which are based on a rheological model. The evolution equations for the internal variables are formulated by using the concept of dual variables proposed by Haupt and Tsakmakis (1989, 1996). The rate sensitivity is modelled by a stress and temperature dependent viscosity function. The elastic part of the equilibrium stress is described by entropy elasticity in combination with a modified Mooney Rivlin strain energy function. The equilibrium hysteresis effects are represented by rate independent plasticity in arclength representation as proposed by Valanis (1971). The constitutive model is compatible with the dissipation principle of thermodynamics and describes the general trend of the experimental data fairly well.
249 citations
TL;DR: It is concluded that elastocalcinosis induces destruction of elastic fibers, which leads to arterial stiffness, and the latter may be involved in the development of left ventricular hypertrophy in a normotensive model.
Abstract: We tested the hypothesis that a simple change in wall composition (medial calcium overload of elastic fibers) can decrease aortic elasticity. Calcium overload was produced by hypervitamino...
190 citations
TL;DR: In this paper, the complete sets of elastic constants of 4H and 6H silicon carbide single crystals were determined by Brillouin scattering, and the compressibility, 4.5×10−3 GPa, is about 3-5 times smaller than those reported for polycrystalline SiC materials.
Abstract: The complete sets of elastic constants of 4H and 6H silicon carbide single crystals were determined by Brillouin scattering. The elastic constants of 6H SiC are C11=501±4, C33=553±4, C44=163±4, C12=111±5, and C13=52±9 GPa; the corresponding ones of 4H SiC are the same within experimental uncertainties. The compressibility, 4.5×10−3 GPa, is about 3–5 times smaller than those reported for polycrystalline SiC materials.
187 citations
TL;DR: In situ synchrotron x-ray scattering experiments show that the amount of lateral molecular order increases upon stretching of collagen fibers, and a new molecular model for collagen elasticity is proposed, which reproduces this linearity and gives a simple explanation for the form of the stress-strain curve of collagen.
168 citations
TL;DR: A new pseudo strain energy function is used to examine the stress-strain relationship of the blood vessel and it is found that for the canine aorta, the degree of nonlinearity varies from 5% to 30%, depending on the magnitude of the strains in the physiological range.
Abstract: Blood vessel elasticity is important to physiology and clinical problems involving surgery, angioplasty, tissue remodeling, and tissue engineering. Nonlinearity in blood vessel elasticity in vivo is important to the formation of solitons in arterial pulse waves. It is well known that the stress–strain relationship of the blood vessel is nonlinear in general, but a controversy exists on how nonlinear it is in the physiological range. Another controversy is whether the vessel wall is biaxially isotropic. New data on canine aorta were obtained from a biaxial testing machine over a large range of finite strains referred to the zero-stress state. A new pseudo strain energy function is used to examine these questions critically. The stress–strain relationship derived from this function represents the sum of a linear stress–strain relationship and a definitely nonlinear relationship. This relationship fits the experimental data very well. With this strain energy function, we can define a parameter called the degree of nonlinearity, which represents the fraction of the nonlinear strain energy in the total strain energy per unit volume. We found that for the canine aorta, the degree of nonlinearity varies from 5% to 30%, depending on the magnitude of the strains in the physiological range. In the case of canine pulmonary artery in the arch region, Debes and Fung [Debes, J. C. & Fung, Y. C.(1995) Am. J. Physiol. 269, H433–H442] have shown that the linear regime of the stress–strain relationship extends from the zero-stress state to the homeostatic state and beyond. Both vessels, however, are anisotropic in both the linear and nonlinear regimes.
165 citations
Patent•
15 Oct 1997
TL;DR: Examplary gelating films as mentioned in this paper are cross-linked and non-cross-linked granular and nongranular gelating sheets, typically including a plasticizer, and optionally including a cross-linking agent incorporated within or over one or more surfaces of the film.
Abstract: Examplary gelating films comprise cross linked and non-cross linked granular and non-granular gelating sheets, typically including a plasticizer, and optionally including a cross-linking agent incorporated within or over one or more surfaces of the film. The gelating films are dry, thin, and preferably meet certain pliability, elasticity, melting temperature, and other criteria. Methods are described for producing these films from collagen. Methods are further described for applying these films to tissue with and without the application of energy.
TL;DR: In this article, the elasticity of substitution between land and non-land inputs in the production of housing has been investigated, and it was shown that the substitution elasticity is higher than indicated in previous studies.
TL;DR: In this article, the authors derived the finite and incremental elasticity of a random packing of identical spheres using energy methods, and derived expressions for the third-order elastic constants as a function of confining pressure.
Abstract: The finite and incremental elasticity of a random packing of identical spheres is derived using energy methods. We consider different models for the contact forces between spheres, all of which are based upon or related to the fundamental Hertz theory; we consider only the special cases of perfect friction (no tangential slip) or no tangential friction. The existence of a strain energy function for the medium depends critically upon the type of contact. If the tangential contact stiffness is independent of the normal force, then the energy is well defined for all values of the macroscopic strain. Otherwise, the strain energy of the system is path dependent, in general. However, the concept of a quadratic strain energy function is always well defined for incremental motion superimposed on large confining stress and strain. For all models considered, we derive the changes in wave speeds due to incremental strains. For the models based upon an energy function we derive expressions for the third-order elastic constants as a function of confining pressure.
TL;DR: In this paper, a viscoelastic constitutive equation for liquid crystalline flows is presented in terms of tensor order parameter dynamics, which takes into account short range order, long range order (Frank elasticity), and flow effects.
Abstract: A viscoelastic constitutive equation for liquid crystalline flows is presented in terms of tensor order parameter dynamics. The presented equation takes into account short range order, long range order (Frank elasticity), and flow effects, and captures the spatio-temporal evolution of the tensor order parameter. The dimensionless parameters arising in the theory are the Deborah (De) number and Ericksen (Er) number, and their ratio is a new dimensionless number R which represent the ratio of short range elasticity to long range elasticity. At Er → ∞ the model converges to the Doi equation, and for De → 0 to the Leslie-Ericksen director equation; the consistency with the Doi theory is shown by the classical shear flow solutions: tumbling, oscillating, and steady state. The model is used to analyze rectilinear simple shear flow subjected to strong anchoring conditions. For the range of governing parameters studied in this paper it is found that for small Er, a spatially nonhomogenous steady state of the tensor order parameters exists. For De corresponding to the tumbling solutions of the Doi equation, the present theory predicts the presence of a composite three layer structure: (a) a center bulk region characterized by director tumbling; and (b) two director oscillating regions next to the bounding surfaces. The amplitude of the director oscillations decrease from a maximum at the boundaries between tumbling-oscillating modes to zero at the bounding surfaces. The boundary between the tumbling-oscillating mode is characterized by the time periodic emergence of an abnormal nematic state, which is characterized by a tensor order parameter with two equal eigenvalues on the shear plane. The emergence of the abnormal nematic state provides for a compatibility mechanism between oscillations and rotations. Thus, we have found through the use of computational modeling a new mechanism that explains the compatibility of Doi's tumbling solutions and fixed surface anchoring conditions. The new flow mechanism is independent of the type of strong anchoring conditions, and arises with planar, homeotropic, and any arbitrary director anchoring.
TL;DR: In this paper, the authors used a high frequency single element focused transducer to track speckle motion in two dimensions with near unity correlation coefficients using a 50 MHz elasticity microscope.
Abstract: An elasticity microscope images tissue stiffness at fine resolution. Possible applications include dermatology, ophthalmology, pathology, and tissue engineering. In addition, if the resolution approaches cellular dimensions, then this system may be very useful in understanding tissue micromorphology. Elasticity images can be reconstructed from displacement and strain fields measured throughout the specimen during controlled external loading. High frequency ultrasound is used to obtain these images by tracking coherent speckle motion during deformation. In this paper, methods are presented to track speckle in two dimensions with near unity correlation coefficients using a high frequency, single element focused transducer. These techniques include improved means for speckle tracking. Procedures to control boundary conditions for consistent specimen deformation and scanning techniques required to obtain a plane-strain state in the imaging plane are also discussed. To test these methods, a 50 MHz elasticity microscope was constructed.
TL;DR: In this paper, the deformation of a single drop suspended in a medium under uniaxial elongational flow along the central axis of a converging conical channel made of Plexiglas is investigated.
Abstract: We report experimental results on the deformation of a single drop suspended in a medium under uniaxial elongational flow along the central axis of a converging conical channel made of Plexiglas. Both the drop and the continuous phases consist of constant viscosity elastic fluids, so-called Boger fluids. This study reveals several interesting features about the role played by both the drop and matrix elasticities on the drop deformability. In a given matrix fluid, the drop deformation decreases as its elasticity increases. For a given drop fluid, the matrix elasticity has the opposite effect: the drop deformation increases with increasing matrix elasticity. An empirical relation between the drop and matrix deformations is established as a function of the drop and matrix characteristic elastic times.
TL;DR: In this paper, the effects of ageing on the values of Euv and vuvh are discussed, and the caracteristiques de deformation of compacted well-graded sandy gravel are evaluated by measuring vertical and horizontal strains locally in very small amplitude cyclic tests on square prismatic specimens.
Abstract: Deformation characteristics at strains less than about 0·001% in compacted well-graded sandy gravel were evaluated by measuring vertical and horizontal strains locally in very small amplitude cyclic tests on square prismatic specimens. The very small strain Young's modulus Eu exhibits strong inherent anisotropy and stress-state-induced anisotropy. The very small strain Poisson's ratio vuvh is a function of stress ratio. Effects of ageing on the values of Euv and vuvh are discussed. On a evalue les caracteristiques de deformation d'un gravier sableux compacte et a granulome trie continue a des contraintes inferieures a 0,001 p. 100 environ, en mesurant les contraintes verticales et horizontales locales dans des essais cycliques a tres faible amplitude realises sur des eprouvettes prismatiques carrees. Le module de Young pour tres faibles contraintes E0 met en evidence une forte anisotropie inherente et une anisotropie provoquee par l'etat de contrainte. Le coefficient de Poisson pour tres f...
TL;DR: In this article, a tight-binding total energy model parametrized to first-principles linearized augmented plane-wave computations is applied to study elasticity and elastic anisotropy in Fe, Xe, and Si at high pressures.
Abstract: A tight-binding total-energy model parametrized to first-principles linearized augmented plane-wave computations is applied to study elasticity and elastic anisotropy in Fe, Xe, and Si at high pressures. We find that the model works well in reproducing the compression, electronic structure, phase relations, and elasticity in these diverse materials. In Xe, for example, the same parametrization works well over a fivefold compression range from a van der Waals solid to a dense metal. We find that the cubic close-packed structures are all more anisotropic than hexagonal close packed and that at high pressures the elastic anisotropy approaches that of any central force nearest-neighbor model. We find that long-range, nonorthogonal parametrizations are necessary for greatest accuracy.
TL;DR: In this paper, the existence of SH surface waves in a half-space homogeneous material (i.e., antiplane shear wave motions which decay exponentially with the distance from the free surface) is shown to be possible within the framework of the generalized linear continuum theory of gradient elasticity with surface energy.
Abstract: The existence of SH surface waves in a half-space homogeneous material (i.e. anti-plane shear wave motions which decay exponentially with the distance from the free surface) is shown to be possible within the framework of the generalized linear continuum theory of gradient elasticity with surface energy. As is well-known such waves cannot be predicted by the classical theory of linear elasticity for a homogeneous half-space, although there is experimental evidence supporting their existence. Indeed, this is a drawback of the classical theory which is only circumvented by modelling the half-space as a layered structure (Love waves) or as having non-homogeneous material properties. On the contrary, the present study reveals that SH surface waves may exist in a homogeneous half-space if the problem is analyzed by a continuum theory with appropriate microstructure. This theory, which was recently introduced by Vardoulakis and co-workers, assumes a strain-energy density expression containing, besides the classical terms, volume strain-gradient and surface-energy gradient terms.
TL;DR: In this article, the general results from the theory of elliptic equations are applied in order to obtain the existence and uniqueness of the generalized solutions for the boundary value problems in elasticity of dipolar materials with voids.
TL;DR: In this article, the authors identify and map differences in the stiffness or elasticity of these ultrathin films at the very near surface (up to a few nm) by using the force modulation technique.
Abstract: Magnetic recording, microelectro mechanical systems, and other microelectronics industries use ultrathin continuous films as well as composite films. The motivation of this research was to identify and map differences in the stiffness or elasticity of these ultrathin films at the very near surface (up to a few nm) by using the force modulation technique. We have shown that this technique amplitudes on samples can yield quantitative elasticity data on samples with an elastic modulus up to a few tens of GPa. This technique provides an alternative to current elasticity measurements that require forces higher than 1 μN, and which can only make single point measurements. With this technique it is possible to make quantitative measurements with loads as low as a few tenths of a μN. By choosing tips that match the stiffness of the sample, the depth of the indentation during the elasticity measurement is kept small, thus eliminating significant plastic deformation of samples of any hardness and any stiffness. The...
TL;DR: In this article, the authors measured the adiabatic elastic moduli of single-crystal MgSiO 3 in the tetragonal garnet structure using Brillouin spectroscopy.
TL;DR: In this article, the bending elasticity of cylindrical, wormlike micelles in dilute solution was studied using a molecular-level model. But the authors focused on two structural-thermodynamic properties of the mouselles.
Abstract: Two structural−thermodynamic characteristics of cylindrical, wormlike micelles in dilute solution are studied using a molecular-level model: (a) the bending elasticity of the micelles and (b) thei...
TL;DR: In this paper, a constitutive law for the inelastic part of the stress is provided, in the form of an integro-differential equation, which involves the fractional order derivative of the internal variable.
Abstract: The short time and cyclic behavior of filled rubbers used in vibration isolation in the frequency range 10{sup {minus}2} to 10{sup 2} rad/s is examined. A form of the free-energy function consistent with the assumption of an additive stress decomposition is employed. A constitutive law for the inelastic part of the stress is provided, in the form of an integro-differential equation, which involves the fractional order derivative of the internal variable. It is assumed that the volumetric response of the material is elastic. The elasticity of rubber is modeled following classical models (e.g., Rivlin, Ogden), extended to include compressibility. Step-by-step integration of the constitutive law is performed. Simple shear experiments are used to assess the capability of the model to capture essential response characteristics, such as stiffness reduction under cyclic loading of increasing amplitude and the variation of dissipated energy with amplitude and frequency.
TL;DR: In this article, the local elastic compliance of organic monolayers (octadecyltriethoxysilane/mica and alkanethiol/gold) has been investigated with nanometer resolution by applying a force modulation technique to an atomic force microscope.
Abstract: Local elastic compliance of organic monolayers (octadecyltriethoxysilane/mica and alkanethiol/gold) has been investigated with nanometer resolution by applying a force modulation technique to an atomic force microscope. Systematic measurements were taken as a function of modulation frequency and amplitude, as well as the local environment surrounding the surface. The topography and local elasticity of the monolayers are contrasted to the bare substrate created by the tip of the atomic force microscope at high imaging force. Under ambient laboratory conditions, the Young's modulus of mica calculated from the elasticity images is lower than the organic monolayer. Soch an observation is not intuitive and can be explained by the thin film of water adsorbed on mica. Water adsorption can change the microscope tip surface interaction. As a result, mica appears as a softer surface than the organic layers. In addition, the elasticity is dramatically enhanced if the modulation frequency coincides with or is close to the natural resonance frequency of the tips of the atomic force microscope. Measurements taken under liquid provide more reproducible and accurate results because the resonance frequency is damped out and capillary interactions are avoided. The measured Young's modulus is also found to increase slightly with increasing modulation amplitude.
TL;DR: In this paper, an ultrasonic wave approach is presented for the optimal identification of the 21 independent elasticity constants of the most general linear homogeneous anisotropic elastic solid from wave speed measurements of obliquely incident ultrasonic bulk waves.
Abstract: An ultrasonic wave approach is presented for the optimal identification of the 21 independent elasticity constants of the most general linear homogeneous anisotropic elastic solid from wave speed measurements of obliquely incident ultrasonic bulk waves. Since the symmetry of acquisition planes is not taken into account, this inversion process is generalized to materials that do not possess three mutually orthogonal planes of symmetry. Minimization of an overdetermined system of nonlinear algebraic equations is solved by a constrained optimization method. Various classes of symmetry are considered. Several critical factors (initial guesses, scatter in experimental data) which can influence the accuracy of the elastic property reconstruction algorithm have been investigated by means of numerical examples that simulate in the best way a typical experiment. The sensitivity of the reconstruction algorithm to each identified elasticity constant is detected a posteriori by means of the estimation of a confidence...
TL;DR: In this paper, Cheng and He [Int. J. Engng Sci., 1995, 33, 389] showed that the micropolar Eshelby tensors are size-dependent both for the inside and for the outside of the circular cylinder.
TL;DR: In this article, the fundamental solution of anisotropic elasticity is given in terms of the eigenvectors and the generalized eigen vectors of the associated six-dimensional eigenvalue problem called Stroh's eigen value problem.
Abstract: A formula for the fundamental solution of anisotropic elasticity is given in terms of the eigenvectors and the generalized eigenvectors of the associated six-dimensional eigenvalue problem called Stroh's eigenvalue problem. From this formula an explicit closed form of the fundamental solution for transversely isotropic media can be obtained.
TL;DR: In this paper, the authors used a 50 MHz elasticity microscope to measure axial displacement and normal axial strain fields from a tissue mimicking a porcine epidermis.
Abstract: For pt.I see ibid., vol.44, no.6, pp.1304-19 (1997). Initial experimental results from a 50 MHz elasticity microscope are shown. Using methods discussed previously, we present measured displacement and normal axial strain fields from a tissue mimicking phantom. Results from this homogenous gel are compared to a finite element simulation of the deformation experiment. The spatial resolution is estimated to be approximately 52 /spl mu/m for axial displacements, and 71 /spl mu/m for normal axial strains. These estimates were further tested by imaging a phantom containing a hard cylindrical inclusion with cross-sectional diameter of 265 /spl mu/m. By examining the strain transition between regions in this image, the spatial resolution of the normal axial strain was verified to be at most 88 /spl mu/m. A typical experiment produces peak normal axial strain around 3%. These experiments demonstrate the potential of high frequency ultrasound as a means for elasticity microscopy. Preliminary deformation experiments are presented on porcine epidermis.