Showing papers on "Elasticity (economics) published in 1984"

PEERS: A new mixed finite element for plane elasticity

Abstract: A mixed finite element procedure for plane elasticity is introduced and analyzed. The symmetry of the stress tensor is enforced through the introduction of a Lagrange multiplier. An additional Lagrange multiplier is introduced to simplify the linear algebraic system. Applications are made to incompressible elastic problems and to plasticity problems.

Theory of nonlocal elasticity and some applications

Abstract: : Constitutive equations of finite nonlocal elasticity are obtained. Thermodynamic restriction are studied. The linear theory is given for anisotropic and isotropic solids. The physical and mathematical properties of the nonlocal elastic moduli are explored through lattice dynamics and dispersive wave propagations. The theory is applied to the problems of surface waves, screw dislocation and a crack. Excellent agreements with the results known in atomic lattice dynamics and experiments display the power and potential of the theory.

Elasticity and Damping of Porous Materials and Impregnated Materials

Abstract: Earlier, a method was developed by the present author which predicts the elastic moduli of isotropic two-phase materials with arbitrary phase geometry. The primary scope of the present article is to demonstrate how this method works when used to predict elasticity (Young's modulus) and damping (loss tangent) of porous materials and impregnated materials made of elastic and/or viscoelastic Components. Simple equations are developed which are directly applicable to practical situations. Their qualities are tested successfully against a number of experimental data.

Elasticity of single‐crystal orthoferrosilite

Abstract: The elastic moduli of a synthetic single crystal of pure FeSiO3, orthoferrosilite, have been measured at 1 bar and 20°C by Brillouin spectroscopy. The moduli are (in megabars) c11 = 1.98, c22 = 1.36, c33 = 1.75, c44 = 0.59, c55 = 0.58, c66 = 0.49, c12 = 0.84, c13 = 0.72, c23 = 0.55. A comparison of the pyroxene crystal structure with elasticity data shows that distortion of the tetrahedral chains parallel to c is related to c33 Straight or extended chains increase c33, and highly kinked chains weaken the structure. However, the ferrosilite data show that beyond a certain degree of distortion the tetrahedral chains are essentially passive. Previous models of pyroxene elasticity have indicated that c11 should be most sensitive to composition. This is supported by the current study and is reflected in the elasticity data via a positive linear correlation of c11 with the size of the M1 octahedron, as measured by the average M1-0 distance. The average longitudinal modulus c¯11 ((c11 + c22 + c33)/3) varies linearly with composition in the system orthoenstatite-orthoferrosilite, whereas the average shear moduli c¯¯44 and c¯¯12 are constant for Fe contents of at least 20%. By comparison, data for the solid solution forsterite-fayalite are consistent with a linear variation of modulus versus composition between the end-members for all three average moduli. We suggest that this difference between orthopyroxene and olivine is due to a strong preference of Fe2+ for the M2 octahedral site in pyroxene. The isotropic shear modulus μ is 30% lower for ferrosilite than enstatite. Despite a similar contrast in end-member values of μ, the olivine data are consistent with a linear variation of μ between Fo100 and Fa100. At high temperatures, Fe and Mg in orthopyroxene will be randomly distributed, and a linear variation of μ with molar content of Fe is expected. A comparison of laboratory elasticity data with observed mantle properties shows that Vp, Vs, and ρ of the upper mantle are satisfied by pure olivine. However, the data strongly suggest that without the coexistence of a garnet phase, no more than 10% orthopyroxene may be present in a model mantle assemblage. Ca-clinopyroxene increases the upper limit on mantle garnet content but does not greatly affect constraints on the quantity of orthopyroxene in the upper mantle.

Viscoelastic properties of erythrocyte membranes in high-frequency electric fields.

Abstract: The high deformability of erythrocytes which is essential for their transport through the capillaries depends critically on their discoid shape and on the elasticity of the plasma membrane, which may be determined by interactions of the cytoskeleton, the lipid/protein leaflet and the glycocalyx. Although techniques exist for measurement of the static elastic properties of erythrocytes, the cells are continuously deformed in vivo, the stress varying within periods of a few seconds. Thus dynamic elastic behaviour is essential for their physiological function. We present here a novel means of measuring the dynamic elastic constants of the red cell based on the transient deformation of individual cells in an inhomogeneous high-frequency (HF) electric field. By microscopy it is possible to record cellular elongations as small as 200 nm occurring within time scales of 1 ms. A main advantage is that the cellular response is linear and thus can be more readily interpreted theoretically. We have observed a creep function consisting of two exponentials with response times of 0.1 s and 1 s, which can be described in terms of a simple viscoelastic model. A remarkable temperature dependence of the membrane elasticity between 25 degrees C and 15 degrees C is observed for freshly drawn cells but not for trypsinized ones.

Protein elasticity based on conformations of sequential polypeptides: the biological elastic fiber

Abstract: Fibrous elastin of the biological elastic fiber is a cross-linked condensed state in which there is roughly one-half polypeptide and one-half water. The precursor protein tropoelastin, a chemical fragmentation product α-elastin, and a sequential polypeptide (l·Val1-l·Pro2-Gly3-l·Val4-Gly5) n , which is a prominent primary structural feature of tropoelastin, are each soluble in all proportions in water at 20°C. On heating to physiological temperatures, each undergoes aggregation and forms a dense viscoelastic phase, which as the fiber itself, is about 60% water. This reversible heat-elicited condensed phase is called the coacervate. Circular dichroism studies show coacervation to be a process of increasing intramolecular order. Electron microscopy (light, scanning, and transmission) shows coacervation to be a process of increasing order intermolecularly. Thus a rise in temperature between 20 and 40°C results in an increase in order of the polypeptide. Coacervation is an inverse temperature transition, and the condensed state is anisotropic at the molecular level. Thermoelasticity studies in water on bovine ligamentum nuchae fibrous elastin and on γ-irradiation cross-linked polypentapeptide coacervates show increases in elastomeric force,f, over the same 20–40°C temperature range in which the inverse temperature transition gives rise to the coacervate, and the constancy off/T with temperature, once the transition is effectively completed, suggests a high-entropy component to the elastomeric force. Thus the data argue for an anisotropic-entropic elastomer. Detailed conformational studies on the polypentapeptide result in the development of a β-spiral conformation in which there are regularly recurring β-turns in loose helical array (a structure that forms on raising the temperature) and in which there are recurring dynamic suspended segments that are the focal point of large, low-energy oscillatory motions called librations. The structure gives rise to a librational entropy mechanism of elasticity wherein the amplitudes of the rocking motions become damped on stretching. This perspective is substantiated by dielectric relaxation studies on the coacervate state and by characterization of synthetic analogs of the polypentapeptide. Dielectric relaxation studies on a concentrated state of about 60% water show the development of a regular structure over the same temperature range as for the development of the coacervate state, and the development of the regular structure with increasing temperature is seen to parallel the development of elastomeric force with increasing temperature. Increasing elastomeric force coincides with increasing regularity of structure! Synthetic analogs of the polypentapeptide, designed to interfere with the librational processes of the suspended segment, impair elastic function, and an analog that makes the β-turn more rigid results in increased elastic modulus. This development of a librational entropy mechanism for protein elasticity is a departure from the kinetic theory of rubber elasticity, the random network perspective that has dominated the traditional view of biological elasticity for the past several decades. The new perspective opens the way to insightful consideration of new elastomeric biomaterials with numerous biomedical applications.

Effective elasticity tensor of a periodic composite

Abstract: The effective elasticity tensor of a composite is defined to be the four-tensor C which relates the average stress to the average strain. We determine it for an array of rigid spheres centered on the points of a periodic lattice in a homogeneous isotropic elastic medium. We first express C in terms of the traction exerted on a single sphere by the medium, and then derive an integral equation for this traction. We solve this equation numerically for simple, body-centered and face-centered cubic lattices with inclusion concentrations up to 90% of the close-packing concentration. For lattices with cubic symmetry the effective elasticity tensor involves just three parameters, which we compute from the solution for the traction. We obtain approximate asymptotic formulas for low concentrations which agree well with the numerical results. We also derive asymptotic results for C at high inclusion concentrations for arbitrary lattice geometries. We find them to be in good agreement with the numerical results for cubic lattices. For low and moderate concentrations the approximate results of Nemat - Nasser et al., also agree well with the numerical results for cubic lattices.

Experimental Study of the Elastic Properties of a Percolating System

Abstract: Simultaneous measurement of the conductivity and the elasticity exponents in two dimensions for a percolating system made of metal and voids is reported. The elasticity exponent is $T=3.5\ifmmode\pm\else\textpm\fi{}0.4$, much larger than the conductivity exponent $t=1.2\ifmmode\pm\else\textpm\fi{}0.1$. This result is in excellent agreement with the theoretical prediction of Bergman.

Conservation laws in elasticity - II. Linear homogeneous isotropic elastostatics

Abstract: Application a l'elasticite statique lineaire, homogene isotrope. Determination des lois de conservation tridimensionnelles et bidimensionnelles

Experimental tests of entanglement models of rubber elasticity. 2. Swelling

Abstract: Les donnees experimentales de gonflement sont utilisees pour comparer les modeles theoriques de l'elasticite du caoutchouc... Des neuf modeles examines, seulement trois (modele de Gaylord et Mavrucci, modele de Graessley et le modele de Flory Erman) sont en accord avec le comportement observe

Elastohydrodynamic Lubrication of Line Contacts

Abstract: An isothermal elastohydrodynamically lubricated rectangular contact was evaluated numerically. This required the simultaneous solution of the elasticity and Reynolds equations. In the elasticity analysis the contact zone was divided into equal rectangular areas, and it was assumed that a uniform pressure was applied over each area. The elastohydrodynamic lubrication theory thus developed was used to investigate the influence of the dimensionless speed, load, and materials parameters on minimum film thickness. Ten cases were used in obtaining the minimum film thickness formula. Plots are shown that indicate the details of the pressure distribution, film shape, and flow. The characteristic pressure spike is clearly in evidence as is the parallel film shape through the central portion of the contact, with a minimum film thickness occurring near the outlet of the contact.

Elasticity of canine vocal fold tissue.

Abstract: Stress-strain curves were obtained from vocalis muscle tissue that was kept viable in an aerated Krebs-Ringer solution after excision of the larynx from live dogs. Results are compared to similar c...

Longitudinal surface waves for the study of dynamic properties of surfactant systems. II. Air-solution interface

Abstract: A recently developed longitudinal wave apparatus was employed to study the dynamic interfacial properties; the Gibbs elasticity, the diffusion parameter, the surface (excess) dilational viscosity, and the surface (excess) shear viscosity. The dynamic interfacial properties were calculated from the dispersion equation of the surface waves using the wave numbers and the damping coefficients of the longitudinal wave at different frequencies. The wave number and the damping coefficient were obtained by measuring, at different locations, the surface tension oscillations induced by the longitudinal wave. The system used in this study is the octanoic acid aqueous solution in a concentration range from 0.2 to 2.0 × 10 −6 mole/cm 3 . The Gibbs elasticity was observed to pass through a maximum, approximately 25 dyn/cm, at a concentration of 0.3 × 10 −6 mole/cm 3 . The diffusion parameter exhibited two apparent discontinuities. The results also indicate that the surface dilational viscosity is two orders of magnitude larger than the surface shear viscosity, corroborating with the previous findings.

Stability of the state sales tax income elasticity

Abstract: Revenue stability for a tax source is defined here as the situation where the income elasticity of revenues is countercyclical; that is, the elasticity rises in a recession and declines in an expan...

A National Micro-Data Based Model of Residential Electricity Demand: New Evidence on Seasonal Variation

Abstract: Building on earlier estimates of electricity demand, the author estimates elasticities by month to determine differences between heating and cooling seasons. He develops a three equation model of residential electricity demand that includes all the main components of economic theory. The model generates seasonal elasticity estimates that generally support economic theory. Based on the model using a national current household data set (monthly division), the evidence indicates there is a seasonal pattern for price elasticity of demand. While less pronounced, there also appears to be seasonal patterns for cross-price elasticity of alternative fuels, for the elasticity of appliance stock index, and for an intensity of use variable.

On local and global universal relations in elasticity

Abstract: Calcul, a l'aide de la methode de Hayes et Knops (1966), d'une relation universelle pour la deformation homogene consistant en un cisaillement simple superpose a une traction triaxiale. Calcul de la relation universelle de globale de Riolin a partir de la relation precedente. Application a un cylindre circulaire soumis a un cisaillement axial ou circonferenciel auquel se superpose une traction et un gonflement

Contact Between Plates and Unilateral Supports

Abstract: Etude de la tendance d'une plaque rectangulaire chargee lateralement a se desolidariser de ses supports. Dans le cas d'une plaque carree une transformation integrale finie convertit les equations en series duales resultant de l'approche de Levy-Nadai en une equation integrale singuliere qui peut etre resolue par des methodes standards. L'extension du contact ne depend que des proprietes geometriques et elastiques de la plaque

On the structure and the physical properties of micellar nematics

Abstract: Micellar nematic systems and some of their physical properties are reviewed. The effect of additives is demonstrated and discussed for selected surfactant systems with respect to phase stability and the induction of cholesteric states. Experimental results on physical properties of micellar nematics with emphasis on curvature elasticity are summarized and related to the micellar structure.

The sphere rheometer: I. Quasistatic measurements

Abstract: A new type of rheometer capable of measuring local viscosity as well as elasticity of translucent medium is described. This apparatus uses a magnetic sphere maintained in levitation by a magnetic field. The measurement of the reaction force exerted on the sphere when a straining field is induced around the sphere allows one to measure the rheological parameters of the medium with an accuracy of 3% for a large range of variation of elasticity and viscosity. Examples are provided for different classes of mediums.

On the role of lipid-bilayer elasticity for the lipid–protein interaction and the indirect protein–protein coupling

Abstract: The present paper deals with the curvature (or splay) elasticity of lipid bilayers and its possible consequences for the microscopic organization of membranes. Experimental studies of the microstructure of lipid-lipid and lipid-protein mixtures are reported and discussed in terms of this type of membrane elasticity. In particular, evidence is provided that the elastic distortion of lipid bilayers caused by the incorporation of proteins can lead to mechanisms of the indirect protein-protein interaction. Finally the question is discussed whether these mechanisms could also play a role for the formation of enzyme complexes in biological membranes.

Dynamic equations of the theory of elasticity of metals

Abstract: In pure metals at low temperatures, when the mean free path of conduction electrons is very large, the electron contribution to elastic forces becomes nonlocal. The forces that appear in the equations of motion of the lattice are then functionals of the electron distribution. The dynamics of conduction electrons, and the influence of the external magnetic field and of the self-consistent electric fields then become important. In this review, we examine the equations of elasticity, using the general assumptions of the modern theory of metals, based on the model-independent macroscopic approach. A detailed discussion is given of the deformation potential and its symmetry properties, and of the role of directional symmetry of the magnetic field. The effective interaction between electrons and sound waves and the role of electric fields accompanying an elastic wave are discussed as examples.