Showing papers on "Elasticity (economics) published in 1987"

On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects

Abstract: A fully three-dimensional finite-strain viscoelastic model is developed, characterized by: (i) general anisotropic response, (ii) uncoupled bulk and deviatoric response over any range of deformations, (iii) general relaxation functions, and (iv) recovery of finite elasticity for very fast or very slow processes; in particular, classical models of rubber elasticity (e.g. Mooney-Rivlin). Continuum damage mechanics is employed to develop a simple isotropic damage mechanism, which incorporates softening behavior under deformation, and leads to progressive degradation of the storage modulus in a cyclic test with increasing amplitude (Mullins' effect). A numerical integration procedure is proposed which trivially satisfies objectivity and bypasses the use of midpoint configurations. The resulting algorithm can be exactly linearized in closed form, and leads to symmetric tangent moduli. Quasi-incompressible response is accounted for within the context of a three-field variational formulation of the Hu-Washizu type.

The Effects of Pin Elasticity, Clearance, and Friction on the Stresses in a Pin-Loaded Orthotropic Plate

Abstract: The effects of pin elasticity, clearance, and friction on the stresses in a pin loaded orthotropic plate are studied. The effects are studied by posing the problem as a planar contact elasticity problem, the pin and the plate being two elastic bodies which interact through contact. Coulomb friction is assumed, the pin loads the plate in one of its principal material directions, and the plate is infinite in extent. A collocation scheme and interaction, in conjunction with a complex variable series solution, are used to obtain numerical results. The contact region between the plate and pin is unknown and must be solved for as part of the solution. The same is true of the region of friction induced no slip. Two pin stiffnesses, two clearance levels, two friction levels and two laminates, a (0/+ or - 45/90)s and a (02/+ or - 45)s, are studied. The effects of pin elasticity, clearance, and friction on the load capacity of the plate are assessed by comparing the load capacity of the plate with the capacity when the pin is rigid, perfectly fitting, and frictionless.

Calculation of elasticity and high pressure instabilities in corundum and stishovite with the Potential Induced Breathing Model

Abstract: Direct calculation of elasticity in the Potential Induced Breathing (PIB) model is developed. This allows calculation of elastic constants and acoustic velocities of oxides and silicates without any experimental data other than the values of fundamental constants, such as Planck's constant. The PIB model allows for spherical charge relaxation in response to the long-range electrostatic potential. This feature is not present in any other lattice dynamical model, and leads to many-body forces that break the Cauchy conditions for centrosymmetric crystals (i.e. C44=C12) without the introduction of explicit angle bending forces. The elastic properties are calculated here for corundum and stishovite. High pressure elastic instabilities are found for both corundum (α-Al2O3) and stishovite (SiO2). Softening of C44 for corundum is calculated to begin at approximately 120 GPa. This may require reconsideration of the ruby fluorescence pressure scale and recent ultra-high pressure diamond cell experiments. The high pressure instability in stishovite leads to a low pressure dependence for the aggregate shear wave velocity.

Matrix method for determining steps most rate‐limiting to metabolic fluxes in biotechnological processes

Abstract: The metabolic control theory developed by Kacser, Burns, Heinrich, and Rapoport is briefly outlined, extended, and transformed so as optimally to address some biotechnological questions. The extensions include (i) a new theorem that relates the control of metabolite concentrations by enzyme activities to flux ratios at branches in metabolic pathways; (ii) a new theorem that does the same for the control of the distribution of the flux over two branches; (iii) a method that expresses these controls into properties (the so-called elasticity coefficients) of the enzymes in the pathway; and (iv) a theorem that relates the effects of changes in metabolite concentrations on reaction rates to the effects of changes in enzyme properties on the same rates. Matrix equations relating the flux control and concentration control coefficients to the elasticity coefficients of enzymes in simple linear and branched pathways incorporating feedback are given, together with their general solutions and a numerical example. These equations allow one to develop rigorous criteria by which to decide the optimal strategy for the improvement of a microbial process. We show how this could be used in deciding which property of which enzyme should be changed in order to obtain the maximal concentration of a metabolite or the maximal metabolic flux.

Linear elasticity theory of pentagonal quasicrystals

Abstract: Presentation de solutions generales aux equations elastiques lineaires inhomogenes pour des quasi-cristaux pentagonaux. Ces equations sont celles obtenues en minimisant l'energie elastique harmonique qui inclut un couplage entre les variables de deplacement et les phasons. Presentation des solutions en termes de fonctions de Green

Modeling impact dynamics for robotic operations

Abstract: The motion of an object to be manipulated is determined by the forces applied to the object. During a collision, impulsive forces may dominate all other forces, and determine the ultimate success or failure of a task. More effective planning and control of manipulators should be possible if the impact process, including the effects of friction and elasticity, is better understood. This paper explores the planar impact of two objects, and develops simple graphical methods for predicting the mode of contact, the total impulse, and the resultant motions of the objects. In the special case of a perfectly plastic collision, the fundamental motion of the object-whether an angular acceleration will occur, and if so in what direction-is the same as predicted in earlier work on quasi-static pushing.

Molecular structure and elastic behavior of poly(ethylene oxide) networks swollen to equilibrium

Abstract: Etude sur des reseaux obtenus par reaction d'α,ω-dihydroxy polyoxyde d'ethylene avec un pluriisocyanate. Gonflement dans le dioxanne et dans l'eau

Measuring Market Power in U.S. Industry

Abstract: Non-competitive conduct can be assessed by estimating the size of the markup or Lerner index achieved in a market. The markup implies a price elasticity of demand faced by the representative firm. For a given markup, non-competitive conduct is greater the more elastic is the market elasticity of demand. The ratio of the firm's to the market elasticity is a measure of non-competitive conduct that is insensitive to the value of the monopoly. To implement this measure, both the firm's and the market elasticities of demand must be estimated. Hall shows how to estimate the markup, and hence the elasticity faced by the firm, from the cyclical behavior of productivity. To estimate the market elasticity, an instrumental variables procedure exploiting a covariance restriction between productivity shocks and demand shocks is used. Results for broad sectors of private industry and for non-durable manufacturing industries display a wide range of monopoly power.

Transversely Isotropic Elasticity Tensors

Abstract: A representation formula for the elasticity tensor of a linearly elastic, transversely isotropic material is obtained, depending on eight constants. If, besides rotations about the axis of symmetry, reflections with respect to planes through that axis are also regarded as admissible symmetry transformations for the material, it is shown that the number of constants reduces to six. It is also shown that, no matter whether reflections belong to the collection of admitted symmetry transformations or not, only five constants are needed for hyperelastic materials.

Saint-Venant's problem

Abstract: The relaxed Saint-Venant problem.- Theory of loaded cylinders: The problems of Almansi and Michell.- Anisotropic materials.- Heterogeneous media.- Saint-Venant's problem for cosserat elastic bodies.

Elasticity and anharmonicity of potassium chloride at high temperature

Abstract: High temperature elasticity of single crystal potassium chloride has been studied by the Rectangular Parallelepiped Resonance (RPR) method up to 870 K (⋍ 3.8 times the Debye temperature, ϑ). The elastic stiffness moduli, C 11 and C 44, decrease linearly with temperature while C 12 increases slightly with temperature. The RPR method is particularly suited to measurements of elasticity at high temperatures, since no glues (which decompose at high temperature) are used to connect the transducers to a specimen. As a consequence, the measured spectrum closely approximates the theoretical spectrum of a specimen freely suspended in space with no external contact. The present elasticity data permits the investigation of the thermodynamic properties of potassium chloride far above the Debye temperature when used together with the previous zero-pressure data on thermal expansivity and heat capacity. The equation of state of potassium chloride is virtually unaffected by anharmonicity, even at T/ϑ=3.8. One result is that the thermal pressure for KCl above the Debye temperature linearly increases with temperature. There is also small dependence on volume, in contrast to NaCl where there is no dependence on volume.

Mechanical studies of sol-gel transition: Universal behavior of elastic modulus

Abstract: The critical behavior of the shear modulus of agarose gel was studied as a function of concentration and temperature. Experimental evidence is presented that the elasticity exponent agrees with the conductivity exponent of a percolating resistor network. It is found that the value of the elasticity exponent of agarose gel is independent of the path to the phase boundary. These results strongly suggest that the elastic behavior of gel in the critical region can be explained by the scalar elasticity model of percolation theory irrespective of the mechanism of gelation.

Deformation of single-mode optical fibers under static longitudinal stress

Abstract: The deformation of single-mode fibers resulting from a longitudinally applied static force has been measured experimentally by means of high resolution heterodyne interferometry and analyzed theoretically using the second-order theory of elasticity and the photoelastic effect. Both the elongation of the fiber and the phase change of light propagating through the fiber have been measured as a function of tensile force. The values of the elastic constants measured for fibers with pure silica core and B 2 O 3 doped cladding are E = 6.41 \times 10^{10} N/m2for the Young's modulus, \delta = -4.0 for the nonlinearity constant of the longitudinal strain, and \beta = -2.3 for the nonlinearity constant of the transverse strain. For unit elongations up to 0.3 percent, no creep, hysterisis, or relaxation effects have been observed within a resolution of one part in 104.

Rubber elasticity: a scaling approach

Abstract: A scaling analysis of the rubber-like elastic behavior of a cross-linked polymer network is presented which incorporates the two most salient contributions to the free energy of deformation: the chain connectivity of the segments and the restrictions on the chain configurations due to entanglements. The affine deformation of the junction points is assumed and a tube model is used to discuss the deformation dependence of the entanglement constraint parameter.

Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials

Abstract: We consider the equations of linear homogeneous anisotropic elasticity admitting the possibility that the material is internally constrained, and formulate a simple necessary and sufficient condition for the fundamental boundary value problems to be well-posed. For materials fulfilling the condition, we establish continuous dependence of the displacement and stress on the elastic moduli and ellipticity of the elasticity system. As an application we determine the orthotropic materials for which the fundamental problems are well-posed in terms of their Young's moduli, shear moduli, and Poisson ratios. Finally, we derive a reformulation of the elasticity system that is valid for both constrained and unconstrained materials and involves only one scalar unknown in addition to the displacements. For a two-dimensional constrained material a further reduction to a single scalar equation is outlined.

Stability of a rigid rotor supported on flexible oil journal bearings

Abstract: This investigation deals with the stability characteristics of oil journal bearings, including the effect of elastic distortions in the bearing liner. Graphical results are presented for (1) steady-state load, (2) stiffness and damping coefficients, and (3) the stability. These results are given for various slenderness ratios, eccentricity ratios, and elasticity parameters. The lubricant is first assumed to be isoviscous. The analysis is then extended to the case of a pressure-dependent viscosity. It has been found that stability decreases with increase of the elasticity parameter of the bearing liner for heavily loaded bearings.

Stress-strain relation for coated fabrics

Abstract: A constitutive relation is formulated for coated fabrics that exhibit both elastic and inelastic, but time-independent, responses The nonlinear orthotropic response is represented by an elastic portion related to yarn stretch and coating shear, and an inelastic part related to crimp interchange A method is proposed to compute the path-dependent inelastic strain and the elastic strain for any loading once material parameters are evaluated from uniaxial tests in the principal directions of elasticity

Theory of Fruit Firmness Sorting by Impact Forces

Abstract: THE impact forces of fruit striking a rigid surface were considered as a means for nondestructive determination of firmness. Impact forces were simulated with a simple elasticity model. Shape characteristics were evaluated as firmness predictors for variations in elasticity, mass, radius of curvature, and contact speed. The time characteristic (peak force)/(time to peak force squared) was sensitive to elasticity and relatively insensitive to fruit size. Frequency characteristics in the range 250 to 340 Hz exhibited a threshold relationship with elasticity and moderate sensitivity to size. All characteristics were sensitive to the speed at contact. Performance of several filter circuits to sense the designated frequency components was simulated. A Chebyshev filter gave better response than a biquad filter.