A direct approach to fiber and membrane reinforced bodies. Part II. Membrane reinforced bodies

The paper deals with membrane reinforced bodies with the membrane treated as a two-dimensional surface with concentrated material properties. The bulk response of the matrix is treated separately in two cases: (a) as a coercive nonlinear material with convex stored energy function expressed in the small strain tensor, and (b) as a no-tension material (where the coercivity assumption is not satisfied). The membrane response is assumed to be nonlinear in the surface strain tensor. For the nonlinear bulk response in Case (a), the existence of states of minimum energy is proved. Under suitable growth conditions, the equilibrium states are proved to be exactly states of minimum energy. Then, under appropriate invertibility condition of the stress function, the principle of minimum complementary energy is proved for equilibrium states. For the no-tension material in Case (b), the principle of minimum complementary energy (in the absence of the invertibility assumption) is proved. Also, a theorem is proved stating that the total energy of the system is bounded from below if and only if the loads can be equilibrated by a stress field that is statically admissible and the bulk stress is negative semidefinite. Two examples are given. In the first, we consider the elastic semi-infinite plate with attached stiffener on the boundary (Melan’s problem). In the second example, we present a stress solution for a rectangular panel with membrane occupying the main diagonal plane.     

A direct approach to fiber and membrane reinforced bodies. Part I. Stress concentrated on curves for modelling fiber reinforced materials

An approach is outlined to the equilibrium in fiber-reinforced materials in which the fibers are modeled as curves or lines with concentrated material properties. The system of forces representing the interaction of the fibers with the bulk matter is analyzed, and equilibrium of forces is derived from global laws. The displacements of the bulk matter are assumed to have continuous extension to the fibers. This forces the set of admissible deformations superquadratically integrable. This in turn forces the energy of the bulk of superquadratic growth. The material of the bulk matrix therefore cannot be linearly elastic. The energy of fibers can have a slower growth and can be quadratic. A formal set of assumptions is given under which an equilibrium state of minimum energy exists in the given external conditions. A weak form of equilibrium equations is derived for this equilibrium state. An explicitly calculable axisymmetric example is presented with an isotropic and quadratic energy of the matrix (linear elasticity) and linearly stretchable fiber. Since the superquadratic growth assumption is not satisfied, some peculiar features of the solution arise, such as the infinite limit of the radial displacement near the fiber. Nevertheless, from the obtained solution, we can compute the normal force in the fiber and the shear stress at the interface.     

High-resolution measurements of pressure self-broadening and shift for the metyl-cyanide rotational J=1−0 line

Summary The capabilities of the travelling-wave spectrometry in the field of high-resolution measurements of low-pressure gases at microwave frequencies are discussed. Some details about the main aspects of the experimental procedure and the data management, useful for the improvement of overall performances, are specified. A pressure broadening of (72.5±1.5) MHz/Torr and a pressure shift of (4.3±0.3) MHz/Torr are measured for theJ=1−0 rotational line of CH₃C¹⁴N. These results are more accurate than those previously reported and in better agreement with the theoretical predictions.

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Riassunto Si discutono le prestazioni di uno spettrometro a microonde ad onda progressiva nel campo della spettroscopia ad alta risoluzione in gas a bassa pressione. Sono in particolare considerati alcuni aspetti delle procedure sperimentali e dell'elaborazionedei dati che hanno portato a decisi miglioramenti nella sensibilità e nelle prestazioni complessive dell'apparato sperimentale. Sono stati misurati per la riga rotazionaleJ=1–0 di CH₃C¹⁴N un coefficiente di autoallargamento per pressione di (72.5±1.5) MHz/Torr e uno shift di (4.3±0.3) MHz/Torr. Queste misure risultano piú accurate di quelle precedentemente riportate e in migliore accordo con le previsioni teoriche.

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Резюме Обсуждаются возможности использования микроволнового спектрометра со скользящей волной для измерений с высоким разрешением в газах при низких давлениях. Рассматриваются основные аспекты экспериментальной процедуры и обработки данных, которые позволяют улучшить чувствительность аппаратуры. Измерены величины самоуширения с давлением (72.5±1.5) МГц/Тор и сдвига с давлением (4.3±0.3) МГц/Тор для ротационной линииJ=1–0 для CH₃C¹⁴N. Полученные результаты являются более точными, чем ранее опубликованные, и лучше согласуются с теоретическими предесказаниями.

     

Materials with elastic range: A theory with a view toward applications. Part III: Approximate constitutive relations

Dedicated to Gianfranco Capriz, with gratitude for his continued encouragement and inspiration     

Dynamics of supercooled and glassy dipropyleneglycol dibenzoate as functions of temperature and aging: Interpretation within the coupling model framework

Dielectric relaxation measurements of a typical small molecular glassformer, dipropyleneglycol dibenzoate show the presence of two secondary relaxations. Their dynamic properties differ in the equilibrium liquid and glassy states, as well as the changes during structural recovery after rapid quenching the liquid to form a glass. These differences enable us to identify the slower secondary relaxation as the genuine Johari-Goldstein (JG) beta-relaxation, acting as the precursor of the primary alpha-relaxation. Agreement between the JG beta-relaxation time and the independent relaxation time of the coupling model leads to predicted quantitative relations between the JG beta-relaxation and the alpha-relaxation that are supported by the experimental data.     

Relaxation dynamics in tert-butylpyridine/tristyrene mixture investigated by broadband dielectric spectroscopy

We investigated, by means of dielectric spectroscopy, the relaxation dynamics of glass forming binary mixtures composed by the quite rigid polar molecules tert-butylpyridine dissolved in the apolar solvent tristyrene. By changing the relative concentration of the components we observed a transition from a relaxation scenario with a structural process and an excess wing to that with a structural process and a well resolved secondary process. Another relaxation process, slower than the latter, was observed, well below Tg. Our detailed analysis evidenced that the secondary relaxation with shorter relaxation time can be identified as the Johari-Goldstein relaxation for all the mixtures, whereas the new relaxation process was attributed to a different type of motion of tert-butylpyridine needing a larger amount of free volume for the molecular rotation.     

Influence of a reduced mobility layer on the structural relaxation dynamics of aluminum capped ultrathin films of poly(ethylene terephthalate)

The structural dynamics of ultrathin polymer films of poly(ethylene terephthalate) capped between aluminum electrodes have been investigated by dielectric relaxation spectroscopy. A deviation from bulk behavior, appearing as an increase of the relaxation time at a fixed temperature, is observed for films of thickness below 35 nm. The slowing down acts as a constant shift factor independent from the temperature, and the fragility is constant. The interfacial energy between aluminum and poly(ethylene terephthalate) is calculated to be 3 mJ/m2, confirming a strong interaction between polymer and substrate, which leads to the presence of a layer characterized by a reduced mobility at their interfaces. We proposed a mathematical schematization of a multylayer model that allowed qualitative reproduction of the observed thickness dependences of the static and dynamic properties. In terms of such a model, the upper limit for the thickness of the reduced mobility layer was estimated as 20 nm. The conditions to extend the proposed model to different observables are finally suggested.     

A laser extraction/combustion technique for in situ delta(13)C analysis of organic and inorganic materials

A CO(2) laser extraction system is described for in situ delta(13)C analysis of organic and inorganic materials. Carbonaceous compounds volatilized by the laser are quantitatively converted to CO(2) gas by a combustion furnace mounted after the sample chamber. Gases produced by the laser and combustion processes are swept by helium carrier gas and separated by a packed gas chromatography column prior to their introduction to an isotope ratio monitoring mass spectrometer. A sample of lentil bean was analyzed at a spatial resolution of 200 μm and yielded delta(13)C values with precision of +/- 0.3 per thousand. The accuracy of delta(13)C measurements was better than +/- 0.5 per thousand from NBS 22 (mineral oil), USGS 24 (graphite), and IAEA CO-1 (calcium carbonate). Copyright 1999 John Wiley & Sons, Ltd.     

Structural macromolecular parameters determining electroconductivity of oxidized poly-n-vinylpyrrole

The dependence of electroconductivity on conjugation length as well as the related basic mechanism was investigated by chemical (FeCl₃) oxidation of insulating polymers from N-vinylpyrrole (NVP) starting with different Fe/NVP ratios and different molecular weights. The results allow to establish that oxidation occurs mainly intrachain and that electroconductivity has a sharp increase for a conjugation length higher than ∼15 NVP-units.     

Rotational viscosity of uniaxial molecules

Non-equilibrium molecular dynamics (NEMD) are used to calculate the vortex or rotational viscosity of fluids composed of uniaxial molecules. It is shown that the NEMD homogeneous spin flow algorithm proposed by Edberg, R., Evans, D. J., and Moriss, G. P., 1987, Molec. Phys., 62, 1357 considerably underestimates the vortex viscosity. A modified version of this algorithm is proposed and applied to liquid chlorine and nitrogen. The results are in good agreement with previous work using equilibrium or other NEMD methods, and also show that at high spin rates the vortex viscosity decreases with increase in magnitude of the external torque used to drive the spin flow.