Showing papers on "Elasticity (economics) published in 1975"

Advanced strength and applied elasticity

Abstract: This exploration of stress analysis focuses on techniques for analysis in realistic settings. It provides coverage of mechanics of materials, theory of elasticity methods, and computer-oriented numerical methods-all supported with a broad range of fully worked-out examples.

A state space approach to elasticity

Abstract: The two-dimensional, plane stress problem of linear elasticity is analyzed within a state space framework The medium considered is homogeneous and isotropic Vlasov's mixed formulation of elasticity is used throughout The field equations are derived in closed form, thus avoiding Vlasov's intermediate infinite series solution Finally, all the properties of the transfer matrix are shown to follow directly from embedding the problem into a state space setting

On the elasticity and stability of perfect crystals at finite strain

Abstract: The concept of ideal strength of perfect crystals as an instability phenomenon is critically reviewed in the context of generalized moduli associated with arbitrary measures of stress and strain. Further aspects of elastic response to finite strain are discussed in relation to the classical model of an atomic lattice.

Out-of-Plane Fluctuations of Lipid Bilayers

Abstract: It is shown that out-of-plane fluctuations of two-dimensonally fluid membranes may lead to a decrease in effective area and affect stretching elasticity.

The elastic free energy and the elastic equation of state: Elongation and swelling of polydimethylsiloxane networks

Abstract: The elastic free energy for a tetrafunctional network is here expressed as where λ1, etc., are the principal extension ratios relative to the state of reference (wherein 〈r2〉 = 〈r2〉0), and C1, C2, and m are arbitrary parameters. The free energy of a swollen system is taken to be the sum G = Gmix + Gel of Gel and the free energy of mixing . Stress-strain relations and the chemical potential μ1 are derived from G as functions of the elasticity parameters C1, C2, and m, and of the thermodynamic interaction parameter χ or of . The dilation of the semi-open system subject to deformation when exposed to diluent at fixed activity is derived as the sum of the dilation at fixed composition and the dilation due to absorption of diluent. Experiments are reported on the dependence of the equilibrium retractive force on elongation for cross-linked polydimethylsiloxanes (PDMS) exposed to benzene or hexamethyldisiloxane vapor at regulated activities. Volume fractions of samples covered the range v2 = 1.00 to v2 ≈ 0.30. With the choice of m = ½ the elastic behavior of a given polymer is well represented by one combination of values for C1 and C2 at all dilutions by either diluent. The dependence of the Mooney-Rivlin (C2) term on volume is thus established, at least for PDMS, and the scope of the semi-empirical free energy expression and its consequents is greatly enlarged. Values of χ deduced from the equilibrium swelling of the unstrained networks exposed to benzene at various activities are in excellent agreement with those obtained previously from vapor pressures and osmotic pressures on linear PDMS. The results of Allen, Kirkham, Padget, and Price on the elastic behavior of natural rubber are discussed, with particular reference to the coefficients of dilation with elongation which they determined at fixed composition. The present results lend strong support to the principle of additivity of the free energies attributable to the network and to the bulk liquid system, respectively. This principle is fundamental to the analysis of rubber elasticity.

Covariant elasticity for smectics A

Abstract: 2014 A theory of static deformations of smectics A is presented, taking into account the large curvature deformations of the layers, but assuming that the variation in the thickness of the layers is small. The director n(r) and the layer phase function 03A6(r) (03A6 is constant on a given layer) are chosen as independent variables, but they have to be related by a relation, to which corresponds a Lagrange multiplyer. Permeation is taken into account. With the help of these variables, the bulk and boundaries equilibrium equations can be expressed simply, and the physical meaning of the Lagrange multiplyer is straightforward. The formulation is applied to the case of the stability of a cylindrical structure. It is found that the cylinders are unstable versus certain helical and sinusoidal deformations. LE JOURNAL DE PHYSIQUE TOME 36, JUILLET-AOÛT 1975, Classification Physics Abstracts 7.130

Dispersed Two‐Phase Flow of Viscoelastic Polymeric Melts in a Circular Tube

Abstract: An experimental study on the dispersed two‐phase flow of visco‐elastic polymeric melts has been carried out. For the study, blends of two incompatible polymers, polystyrene and high‐density polyethylene, were extruded through a circular tube having an L/D ratio of 20. Mixing was achieved by the combined use of a single‐screw extruder and a Static Mixer (Kenics Corp., Thermogenizer). The state of dispersion of one polymer in another was determined from microphotographs taken of extrudate samples. The variables investigated in order to better understand the mechanism of drop formation, were the blending ratio of a mixture, its flow rate, and its melt temperature. In the present study, measurements were taken of wall normal stresses along the longitudinal direction of a capillary die, permitting one to determine both the viscous and elastic properties of the material investigated. It has been found that the viscosity of the blend goes through a minimum and then through a maximum at certain blending ratios, and that the elasticity of the blend goes through a maximum and then through a minimum at certain blending ratios. Interestingly enough, it has been observed that the minimum viscosity occurs at approximately the same blending ratio which gives rise to the maximum elasticity, and that the maximum viscosity occurs at approximately the same blending ratio which gives rise to the minimum elasticity. A phenomenological argument is presented to explain the physical origin of the observed viscoelastic properties of dispersed two‐phase polymer systems.

Isothermal elastohydrodynamic lubrication of point contacts. 1: Theoretical formulation

Abstract: The isothermal elastohydrodynamic lubrication (EHL) of a point contact was analyzed numerically by simultaneously solving 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. In the numerical analysis of the Reynolds equation, a phi analysis (where phi is equal to the pressure times the film thickness of the 3/2 power) was used to help the relaxation process. The EHL point contact analysis is applicable for the entire range of elliptical parameters and is valid for any combination of rolling and sliding within the contact.

A three-element model describes excised cat papillary muscle elasticity.

Abstract: The three-element model for skeletal muscle has been widely applied to cardiac muscle. It consists of an active contractile element (CE) that represents the muscle's response to stimulation, in ser...

High‐density polyethylene melt elasticity—some anomalous observations on the effects of molecular structure

Abstract: The die swell behavior of polymeric melts is a manifestation of melt elasticity of these materials and is of considerable commercial as well as fundamental importance. Hence, knowledge of the effect of such molecular variables as molecular weight (MW) and molecular weight distribution (MWD) on melt elasticity is important from both commercial and basic rheological points of view. The effect of these variables on melt elasticity of broad-distribution polymers in the shear rate region of commercial interest is not unambiguously known, with most published theory and experiment being applicable to the low-shear behavior of narrow-distribution polymers and blends thereof. There is indication that die swell increases with increasing MW and broadening MWD. However, the current investigation of carefully characterized broad-distribution HDPE materials prepared specifically to examine the effects of various molecular variables on melt elasticity does not support this contention and, in fact, provides consistent evidence for the opposite result, i.e., decreasing die swell with increasing MW or broadening distribution. The various samples studies were prepared by fractionation removal or addition of component molecular species or by polymerization designed to provide systematic variation of molecular species or by polymerization designed to provide systematic variation of molecular parameters. Overall MWD's of the samples were characterized, and die swell behavior was determined at 200°C over a wide shear rate region in a high L/D capillary both with and without annealing of extrudates. The results are presented showing effects of specific molecular variables.

The modulus of elasticity of human cortical bone: an in vivo measurement and its clinical implications.

Abstract: The modulus of elasticity was derived by combining the velocity of ultrasound measurements and photon absorption (Norland-Cameron method) in human cortical bone (proximal radius) in vivo. The results compare favorably with published values of the elasticity modulus obtained in vitro. Values obtained for a heterogeneous group of patients with bone and joint complaints differed from those of normal volunteers.

Inequalities of Korn and Friedrichs in elasticity and potential theory

Abstract: Integral inequalities for quadratic functionals arising in plane elasticity and two-dimensional potential theory are discussed and related. Information on the optimal constants (which depend on the domain geometry) is obtained through consideration of associated eigenvalue problems.

Evaluation of the Theories of Rubberlike Elasticity Using Swollen Networks Crosslinked at Different Degrees of Dilution

Abstract: A recently reported study described the preparation of elastomeric networks by crosslinking poly(dimethylsiloxane) chains in both the undiluted state and in solution. Measurements of the moduli of these networks in the unswollen state gave results supporting the theory of rubberlike elasticity developed by Flory and coworkers, rather than the corresponding theory due to James and Guth. These results were not entirely unambiguous, however, because of complications due to departures (“2C2 corrections”) from the expected elastic equation of state. Much of this uncertainty has now been removed by measurements of the moduli of such networks in the swollen state, a condition under which the effects of the 2C2 contributions are known to be minimized. These new results strongly support the earlier conclusion that the Flory theory is the more nearly correct. Nonequilibrium effects, as well as the 2C2 corrections, diminish upon incorporation of a diluent into the crosslinked network; similar decreases occu...