Showing papers on "Elasticity (economics) published in 1990"

Nonlinear elasticity and pressure-dependent wave speeds in granular media

Abstract: Following is an analysis of the small-strain nonlinear elasticity of granular media near states of zero stress, as it relates to the pressure-dependent incremental linear elasticity and wave speeds. The main object is elucidation of the p ½ dependence of incremental elastic moduli on pressure p , a dependence observed in numerous experiments but found to be at odds with the p ½ scaling predicted by various micromechanical models based on hertzian contact. After presenting a power-law continuum model for small-strain nonlinear elasticity, the present work develops micromechanical models based on two alternative mechanisms for the anomalous pressure scaling, namely: (1) departures at the single-contact level from the hertzian contact, due to point-like or conical asphericity; (2) variation in the number density of hertzian contacts, due to buckling of particle chains. Both mechanisms result in p ½ pressure scaling at low pressure and both exhibit a high-pressure transition to p ½ scaling at a characteristic transition pressure p *. For assemblages of nearly equal spheres, a non-hertzian contact model for mechanism (1) and percolation-type model for (2) yield estimates of p * of the form p * = c μ ˆ ∝ 3 . Here c is a non-dimensional coefficient depending only on granular-contact geometry, while α ≪ 1 is a small parameter representing spherical imperfections and μ ˆ is an appropriate elastic modulus of the particles. Then, with R representing particle radius and h a characteristic spherical tolerance or asperity height, it is found that α = ( h / R ) ½ for mechanism (1) as opposed to α = h / R for (2). Limited data from the classic experiments of Duffy & Mindlin on sphere assemblages tend to support mechanism (1), but more exhaustive experiments are called for. In addition to the above analysis of reversible elastic effects, a percolation model of inelastic ‘shake-down’ or consolidation is given. It serves to describe how prolonged mechanical vibration, leading to the replacement of point-like or inactive contacts by stiffer Hertz contacts may change the pressure-scaling behaviour of particulate media. The present analysis suggests that pressure-dependence of elasticity may provide a useful means of characterizing the state of consolidation and stability of dense particulate media.

Molecular theory of curvature elasticity in surfactant films

Abstract: We develop a microscopic‐level formulation for the curvature elasticity of monolayer and bilayer systems of typical surfactant molecules. It is argued that both the bending and saddle‐splay force constants k and k are determined primarily by the conformational entropy of the flexible hydrocarbon chain rather than by the electrostatic interactions associated with hydrophilic head groups. A priori estimates of the chain contributions are made for the first time, without the use of any adjustable parameters. Both k and k are shown to be calculable wholly from the conformational statistics describing the planar film. In particular, these constants are expressed in terms of the derivatives and moments of the lateral pressure profile characterizing chain packing in the unbent layers. By considering the dependence of the curvature elasticity on chain length, area per molecule, and composition in mixed films, we are able to account for the order‐of‐magnitude variations in k observed in a variety of different surfactant systems. The replacement of long chain molecules by short ones is shown to be especially efficient in lowering the bending energy from 10’s of kBT to kBT. The effect of ‘‘free’’ vs ‘‘blocked’’ exchange are also presented and contrasted with the case of fixed area‐per‐molecule bending deformation. Finally, monolayer vs bilayer results are compared and the calculated signs and magnitudes of k and k are discussed in the context of planar bilayer stability.

Application of the Trefftz method in plane elasticity problems

Abstract: Direct and indirect approximations using sets of non-singular, complete Trefftz functions, i.e. the complete systems of solutions, have been successfully applied to harmonic problems.1 In this paper, the procedure is applied to a more complex situation—plane elasticity problems. The examples show that the present method can avoid the difficulties relating to singular integration and has good accuracy compared with traditional boundary elements.

A mechanical model for elastic fiber microbuckling

Abstract: A two-dimensional mechanical model is presented to predict the compressive strength of unidirectional fiber composites using technical beam theory and classical elasticity. First, a single fiber resting on a matrix half-plane is considered. Next, a more elaborate analysis of a uniformly laminated, unidirectional fiber composite half-plane is presented. The model configuration incorporates a free edge which introduces a buckling mode that originates at the free edge and decays into the interior of the half-plane. It is demonstrated that for composites of low volume fraction (<0.3), this decay mode furnishes values of buckling strain that are below the values predicted by the Rosen (1965) model. At a higher volume fraction the buckling mode corresponds to a half wavelength that is in violation of the usual assumptions of beam theory. Causes for deviations of the model prediction from existing experimental results are discussed.

The coarsening kinetics of two misfitting particles in an anisotropic crystal

Abstract: We examine the influence of elastic stress on the Ostwald ripening kinetics of two elastically and diffusionally interacting, misfitting spherical particles in an anisotropic crystal. The coupled equations of elasticity and diffusion are solved analytically in series form in a bispherical coordinate system when the matrix supersaturation is small, local equilibrium obtains at the interface, particle and matrix possess the same cubic elastic constants, and the stress engenered by compositional inhomogeneity is negligible. Expressions are obtained for the matrix composition field, the local normal interfacial velocities of the particles, the isotropic particle growth rates, and the velocity of the particles' centers of mass. Inverse coarsening, or the growth of a smaller particle at the expense of a larger particle, is predicted for particle alignments along the elasticity soft 〈100〉 directions in nickel and for the 〈110〉 and 〈111〉 directions in molybdenum. Coarsening rates are often significantly enhanced for other particle orientations with respect to those of the stress-free case. The elastic stresses also change the functional dependence of the particle growth rate on particle size suggesting that the temporal exponents observed during classical ripening may not obtain in stressed systems. These predictions indicate that elastically-induced preferential coarsening strongly influences microstructural development in two-phase coherent alloys.

Garment for aquatic activities having increased elasticity and method of making same

Abstract: An aquatic garment, such as a wet suit or dry suit formed of a water-impervious material having a thickness dimension sufficient to provide thermal insulation for a user during aquatic activities. The garment includes stretch areas having an array of grooves with a depth dimension sufficient to significantly increase the elasticity of the garment transverse to the grooves while maintaining the mechanical integrity and thermal insulation in the stretch area. Variation in the elasticity and in the direction or orientation of enhanced elasticity can be achieved by varying the spacing and direction along which the grooves extend. A method for formation of grooved aquatic garments to enhance their stretchability also is disclosed.

The Elasticity of Export Demand for U.S. Cotton

Abstract: The conceptually relevant elasticity for policy analysis is the total export demand elasticity, which takes into account feedback effects of the U.S. price on other countries' prices. In this paper, a total export demand elasticity for U.S. cotton is estimated in an extended Armington framework. The results indicate that the export demand facing the United States is probably elastic; however, estimated total demand elasticities are considerably less elastic than the estimated direct demand elasticities, which do not account for feedback effects resulting from finite excess supply elasticities in the rest of the world. In designing agricultural policy, a knowledge of relevant elasticities is essential. Given the current economic climate characterized by volatile export markets and prices, the price elasticity of export demand has received considerable attention. Economists, however, have not reached a consensus about the magnitude of this parameter. In their review of studies of price elasticity of export demand for agricultural commodities, Gardiner and Dixit report seven estimates of the elasticity of export demand for U.S. cotton, ranging from -0.02 (Taylor and Collins) to -5.5 (Johnson). Because the policy recommendations based on the assumption of an elastic foreign demand could differ dramatically from those based on the assumption of inelastic foreign demand, further research in this area is warranted. The objective of this paper is to develop estimates of the elasticity of foreign demand for U.S. cotton. The Armington approach was used to formulate models for estimation because it is simple to formulate, is a powerful method for modeling U.S. crop exports (Sarris 1981, Thompson), and had not been used extensively in modeling cotton trade. The study differs from previous works by extending the Armington framework to estimate "total" elasticities of demand, in which feedback effects of U.S. price on the price of other countries' cotton is taken into account. Results from this paper should be useful in estimating the elasticity of export demand for U.S. cotton and in demonstrating the importance of estimating "total" export demand elasticities.

Equivalence of finite element methods for problems in elasticity

Abstract: Modifications of the Morley method for the approximation of the biharmonic equation are obtained from various finite element methods applied to the equations of linear isotropic elasticity and the stationary Stokes equations, by elimination procedures analogous to those used in the continuous case. Problems with Korn’s first inequality for nonconforming $P_1 $ elements and its implications for the approximation of the elasticity equations are also discussed.

Fabric reinforcement for plastic fuel tanks

Abstract: An improved plastic fuel tank for motor vehicle applications is disclosed The blow molded plastic fuel tank has at least one reinforcement insert encapsulated at a preselected area on the exterior surface of the fuel tank The reinforcement insert provides supplemental support, elasticity and fire resistance, or a combination thereof

Low-temperature properties of a model glass. I. Elastic dipole model.

Abstract: Developpement d'un modele permettant d'expliquer les proprietes universelles a basses temperatures des verres, dans l'intervalle de temperatures 1

Surface interaction potentials in elasticity

Abstract: The problem of modelling body-environment interactions is a rather formidable one: neither is there a wealth of inspiring examples nor is the corpus of knowledge in mathematical analysis such as to allow indiscriminate generalization of the few well understood cases.

Non-linear spring

Abstract: A spring given elasticity by way of elastic portions formed between slits which are provided on a base material of, e.g. solid cylindrical shape, cylindrical pipe shape, etc. The slits are formed on an outer peripheral surface of the base material at different phase angles. They are arranged along the length of the material and parallel to each other. The elastic portions are disposed at different pitches along the length so that some of them have different elasticity from the others. The elasticity between some portions and the others may be varied by way of changing an inner diameter of a through hole formed in the spring. Thereby the spring has non-linear elasticity characteristics. The spring may have a through hole and a line of slit spirally extending about the axis and communicating with the through hole. A line of elastic portion is defined by the slit and also extends spirally about the axis of the spring. The width of the elastic portion is changed along the axis of the spring.

The structure of the distortion free-energy density in nematics: Second-order elasticity and surface terms

Abstract: By means of a phenomenological approach, we demonstrate that the mixed splay-bend elastic constantK 13 in the free energy density of nematic liquid crystals must be considered zero, unless the bulk contributions of the squares of the distortion second-order derivatives are taken into account, together with the squares of the first-order derivatives times the second-order derivatives, and with the fourth powers of the first-order derivatives. Such contributions just reduce to one in the presence of—and close to—a threshold. Furthermore, the saddle-splayK 24-term instead is shown always to play an essential role, as the bulk first-order elasticity, in determining the distortion free energy of nematics with weak anchoring subjected to spatial deformations. Finally, the new surfacelike elastic constants are shown to have a nilpotent character: thus they behave as well asK 24 from the point of view of the variational calculus.

Melamine resin moldings having increased elasticity

Abstract: Moldings, in particular foams and fibers, based on melamine/formaldehyde condensation products, in which from 0.1 to 70 mol % of the melamine have been replaced by melamine substituted by from 1 to 3 hydroxyoxaalkyl groups of the formula --(CH.sub.2 --CH.sub.2 --O).sub.n --CH.sub.2 --CH.sub.2 --OH n=1-5) have increased elasticity.

On the Relevant Elasticity Estimates for Cost Structure Analyses of the Trucking Industry

Abstract: The effects of output qualities on costs of trucking firms could be evaluated at a given number of ton-kilometers or at a given number of shipments. This note shows that false interpretations of potential output qualities effects could occur when these effects are evaluated at a given number of ton-kilometers. Copyright 1990 by MIT Press.

Curvature elasticity of ordered bicontinuous structures

Abstract: The curvature free energy of an interfacial membrane is used to predict the relative stability of cylindrical, lamellar and ordered, bicontinuous, saddle-shaped structures. Because they are surfaces of constant mean curvature, the saddle-shaped structures have a finite range of stability as a function of concentration even when the saddle-splay elastic constant < 0, favoring structures where the two radii of curvature have the same sign.

Lubricant elasticity and the performance of dynamically loaded short journal bearings

Abstract: A theoretical analysis is developed for flow of lubricants in a dynamically loaded short journal bearing. The upper convected Maxwell model is chosen to study the influence of lubricant elasticity on the motion of the shaft center within the bearing. An order of magnitude analysis reveals that the fluid relaxation time does not influence bearing performance for steady loads. For time varying loads, however, numerical calculations show that the pressure distribution, the minimum oil film thickness, the attitude angle, and the shaft orbit are all significantly affected by the presence of fluid elasticity.

Biaxial Extension Studies Using Inflation of Sheets of Unimodal Model Networks

Abstract: Measurements of uniaxial extension and compression were made on model poly(dimethylsiloxane) (PDMS) [−Si(CH3)2−O−]x networks to examine the molecular theories of rubber elasticity. The stress-strain isotherms showed that the Flory-Erman theory of rubber elasticity is in good agreement with experimental data from extension to compression (α−1: 0.3–13), while the Mooney-Rivlin relation is useful only in a specific region of extension ratio (α−1: 0.3–0.8). The experimental results strongly support the theory of Flory-Erman, rather than those of phantom and affine networks. It is thus evident that the Flory-Erman theory of rubber elasticity is the more nearly correct.