The relaxation of linear flexible polymers which are slightly poly-disperse

The relaxation of slightly poly-disperse linear flexible polymers has been expressed in a simplified blending rule which is presumed to be a weighted linear superposition of the relaxation spectra of mono-disperse components which constitute the blend. Discrete components are characterized by their molecular weight M _i,weight fraction w _i,and relaxation time spectrum H _i(). ). In contrast to broadly distributed blends in which the small molecules mobilize the large ones and vice versa, we introduce the term slightly polydisperse for blends with molecular weight distributions narrow enough to have very little change in the longest relaxation times of each molecular weight component. The properties of this blending rule are analyzed and dynamic data is calculated for slightly poly-disperse polystyrene. As an application, the blending rule is used to determine the characteristic mono-disperse parameters (BSW parameters) of two materials, poly (vinyl methyl ether) and polycarbonate, for which we could not determine their BSW parameters directly since they were not available in nearly monodisperse form. The proposed blending rule can only be applied to systems in which all components are above the entanglement molecular weight, i.e. M _iM _c.Dedicated to the memory of Professor Tasos C. Papanastasiou     

A critical review of some damage models with unilateral effect

The concern here is the macroscopic modeling of the brittle damage unilateral effect (due to the opening-closure of microcracks). Several formulations have been proposed in recent years to solve the problems pointed out by Chaboche (Int. J. Damage Mech. 1 (1992) 148). In this paper, we examine precisely two of these new formulations (Int. J. Damage Mech. 2 (1993) 311; Int. J. Damage Mech. 5 (1996) 384) and show that they still exhibit some major inconsistencies.     

On the eccentricity factor in the progressive crushing of tubes

The analysis of an axially compressed circular tube deforming in progressive axisymmetric folds carried out by Wierzbicki et al. [(1992) Int. J. Solids Structures 29, 3269–3288] assumes an eccentricity factor relating the inward and outward parts of the folds. This factor was arbitrary and was not derived from the analysis. The present work re-examines the problem and produces a value for the eccentricity factor which conforms with the experimental findings. Values of the critical angles required for the formation of the inward and outward folds obtained from the analysis were substantiated by those obtained from experiments.     

Two phase boundary layers in laminar film boiling

The laminar film boiling is analyzed by means of an integral procedure. The method treats the film boiling as a two phase boundary layer problem; thereby the effect of the interfacial shear on the heat transfer rate can be investigated. The problem is attacked by simultaneously solving the vapor and liquid boundary layer equations. An extensive comparison of the predicted results with the exact solutions substantiates the validity of the present integral procedure. Even the details of the velocity and temperature profiles turn out to be in close agreement with the exact solutions.     

Zur analytischen Behandlung des nichtlinearen aeroelastischen Galloping-Problems

Übersicht Es wird ein graphisch-numerisches Verfahren zur Lösung der nichtlinearen Galloping-Differential- gleichung dargelegt. Die Einzelheiten des Lösungsverfahrens werden beschrieben und an Hand eines typischen Beispiels näher erläutert.

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Summary A graphical-numerical method for the solution of the non-linear Galloping differential equation is presented. The details of the analytical procedure are discussed and explained by means of a typical example.

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Diese Arbeit entstand im Rahmen eines einjährigen Stipendiums der Alexander von Humboldt-Stiftung. Der Stipendiat Dr.-Ing. V. Manea ist Mitarbeiter im Institut de Mecanica Fluidelor si Constructii Aerospatiale, Bukarest.     

A photomechanics material for elastoplastic stress analysis

The object of this investigation was to develop a technique or method for elastoplastic stress analysis using the optical effects of transparent materials. Of paramount importance was the selection and characterization of a suitable model material. In particular, it was desirable that the material be able to undergo large plastic strains while, at the same time, exhibiting a suitable level of optical response. A mixture of flexible and rigid polyester resins was found suitable, i.e., the mixture exhibited large strains and good optical response. It was found that unload birefringence (fringe order immediately upon removal of load) could be used to determine strain for a uniaxial-stress field. In particular, it provided a means for evaluating stress- and strain-concentration factors. Comparisons with other methods showed that the proposed method was reliable and gave results that are similar to those by other means. The usefulness of the material and method for two- and three-dimensional problems awaits further study.     

On anti-symmetric waves in an unbounded piezoelectric plate with axisymmetric electrodes

In this paper we consider an unbounded piezoelectric plate with electrodes at its surfaces, which are axisymmetric with respect to an axis normal to the plate. The electromechanical waves in this plate are assumed to have an electric potential which is symmetric with respect to the middle plane of the plate. The electric field outside the plate will appear to be important. This external electric field is investigated, particularly in connection with the resonances of the plate.     

Bending stresses in out-of-round uni- and multi-axial internally pressurized strength specimens

A derivation is presented for the bending stresses in internally pressurized slightly elliptical tubular or ring specimens used in the testing of uni- and multiaxial strength. The solution obtained shows that the bending stresses are directly proportional to Young's modulus of elasticity of the material being tested. A numerical example applicable to strength testing of aluminum oxide demonstrates, that a slight out-of-round-ness can result in bending stresses which are an appreciable percentage of the observed values of the fracture strength. It is concluded that strength testing by means of the internal pressurization of tubular or ring specimens requires close dimensional control in specimen manufacture.     

Über die Anwendung von Liapunovs direkter Methode auf Stabilitätsprobleme kontinuierlicher,nichtkonservativer Systeme

Übersicht Es wird gezeigt, daß das klassische Energiekriterium für die Stabilität eines kontinuierlichen zweidimensionalen Systems eine eingeschränkte Aussagekraft hat, da es die Kleinheit der interessierenden Größen meist im quadratischen Mittel sichert. Ferner ergibt es sich, daß das klassische Energiekriterium für gewisse nichtkonservative Probleme, bei denen mitgehende Lasten vorkommen, hinreichend bleibt. Für diese nichtkonservativen Probleme ist die Stabilität unter tangential mitgehenden Lasten zudem größer als sie es bei denselben Problemen unter konservativen, richtungstreuen Lasten ist.

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Summary It is shown that the classical energy criterion for the stability of a continuous two-dimensional system is of a restricted value, since mostly the smallness in the mean-square of deflection and its derivatives can be guaranteed. Furthermore it results that the classical energy criterion for stability remains sufficient for certain nonconservative problems with follower forces. Besides, such nonconservative systems, subject to tangential forces, prove to be more stable as the same systems subject to conservative, unidirectional forces.

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Herrn Professor Dr. H. Ziegler in tiefer Verehrung zum 60. Geburtstag gewidmet.

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Die Arbeit wurde vom National Research Council of Canada unter Grant No. A 7297 unterstützt.