Superposition of finite deformations in Mooney-Rivlin materials

Six controllable states are known to exist for all homogeneous, isotropic, incompressible, elastic bodies. It is shown that certain pairs of these controllable states may be superposed in Mooney-Rivlin materials thereby constructing new controllable states for these materials.

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Zusammenfassung Es gibt sechs kontrollierbare Zustände für alle homogenen, isotropischen, inkompressiblen, elastischen Körper. Es ist gezeigt dass gewisse Paare dieser kontrollierbaren Zustände geschichtet werden können in Mooney-Rivlin Materialen und dadurch neue kontrollierbare Zustände für diese Materialen geschaffen werden.

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This work was carried out while both authors were associated with the Department of Aerospace Engineering and Engineering Mechanics at The University of Texas at Austin and was supported by U.S. National Science Foundation Grant GK-37367 to that institution.     

A torsional creep apparatus

Summary This paper describes a torsional creep apparatus for the determination of the creep compliance in shear as a function of time. The instrument is suitable for the measurement of compliances below 5·10^–8 m²/N, in the time range between 1 and 10⁵ seconds. Within five minutes and with an accuracy of 1 C, the temperature of the specimen can be adjusted to any value between –175 and –200 C. From the torsional creep measurements can be calculated the dynamic shear modulus and the corresponding damping. The lowest damping, determined in this way, is several times 10^–3.

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Zusammenfassung Ein Apparat zur Messung des Torsions-Kriechverhaltens wird beschrieben. Das Instrument ist zur Bestimmung von Nachgiebigkeiten kleiner als 5·10^–5 m²/N im Zeitbereich zwischen 1 und 10⁵ Sekunden geeignet. Die Temperatur der Probe läßt sich innerhalb 5 Minuten und mit einer Genauigkeit von 1 C auf jeden Wert zwischen –175 und –200 C einstellen. Aus der gemessenen Kriechfunktion können der dynamische Schubmodul und die dynamische Dämpfung berechnet werden. Eine untere Grenze für die Dämpfung, die man auf diese Weise noch bestimmen kann, ist einige Male 10^–3.

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The work was partly sponsored by the Office of Naval Research, Washington, D. C., under contract number N 62558-3884.     

Experimental and theoretical determination of frequencies of elastic toroids

Experiments are described which determine natural frequencies of five toroidal models whose major diameters are of 10 in. and whose minor diameters vary from 0.25 to 2 in. The experimentally determined frequencies are compared with the theoretical frequencies derived using the elementary theories for the in-plane and out-of-plane vibrations of circular rings of R. Hoppe and J. H. Michell, as well as the method of internal constraints. The comparative results for the frequencies are presented in tabular form.     

Magnetohydrodynamic mixed convection in a vertical channel

The problem of combined free and forced convective magnetohydrodynamic flow in a vertical channel is analysed by taking into account the effect of viscous and ohmic dissipations. The channel walls are maintained at equal or at different constant temperatures. The velocity field and the temperature field are obtained analytically by perturbation series method and numerically by finite difference technique. The results are presented for various values of the Brinkman number and the ratio of Grashof number to the Reynolds number for both equal and different wall temperatures. Nusselt number at the walls is determined. It is found that the viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. It is also found that the analytical and numerical solutions agree very well for small values of ε.     

Phase split of liquid–liquid two-phase flow at a horizontal T-junction

This paper provides data on the split of liquid/liquid two-phase flow at a horizontal T-junction. Phase maldistribution was measured for kerosene–water flow at the T-junction with equal pipe diameters of 67.4 mm. Data were taken with both stratified flow with a mixture at interface and dispersed flows approaching the junction. The degree of phase maldistribution was not very great but preferential emergence of either phase from the side-arm was observed depending on the flow rates of the two-phases. There are similarities with the limited split data from liquid/solid flows and the degree of separation is seen to depend on the dispersed/continuous phase density ratio. The data were compared to predictions from the correlation by Seeger et al. The Seeger equation gives but reasonable agreement.     

Heat transfer measurements and correlations for air–water flow of different flow patterns in a horizontal pipe

Heat transfer coefficients were measured and new correlations were developed for two-phase, two-component (air and water) heat transfer in a horizontal pipe for different flow patterns. Flow patterns were observed in a transparent circular pipe using an air–water mixture. Visual identification of the flow patterns was supplemented with photographic data, and the results were plotted on the flow regime map proposed by Taitel and Dukler and agreed quite well with each other. A two-phase heat transfer experimental setup was built for this study and a total of 150 two-phase heat transfer data with different flow patterns were obtained under a uniform wall heat flux boundary condition. For these data, the superficial Reynolds number ranged from 640 to 35,500 for the liquid and from 540 to 21,200 for the gas. Our previously developed robust two-phase heat transfer correlation for a vertical pipe with modified constants predicted the horizontal pipe air–water heat transfer experimental data with very good accuracy. Overall the proposed correlations predicted the data with a mean deviation of 1.0% and an rms deviation of 12%.     

Mechanics Applied to Skeletal Ontogeny and Phylogeny

The musculo-skeletal system serves the mechanical function of creating motion and transmitting loads. It is made up mainly of four components: bone, cartilage, muscle and fibrous connective tissue. These have evolved over millions of years into the complex and diverse shapes of the animal skeleton. The skeleton, however, is not built to a static plan: it can adapt to mechanical forces during growth, it can remodel if the forces change, and it can regenerate if it is damaged. In this paper, the regulation of skeletal construction by mechanical forces is analyzed from both ontogenetic and phylogenetic standpoints. In the first part, models of biomechanical processes that act during skeletal ontogenesis – tissue differentiation and bone remodeling – are presented and, in the second, the evolution of the middle ear is used as an example of biomechanical change in skeletal phylogenesis. Because the constitutive laws for skeletal tissues are relatively well understood, and because the skeleton is preserved in the fossil record, application of mechanics to skeletal evolution seems to present a good opportunity to explore the relationships governing ontogenetic adaptations and phylogenetic change.     

Large frequency bands viscoelastic properties of honey

Honey is a viscoelastic material which presents a crystallization phase transition at low temperatures. This phase transition limits the studies of dynamic behavior at high frequencies from the classical rheometry using time–temperature superposition (TTS). In order to characterize the viscoelastic properties of honey at high frequencies, we have developed a multiple ultrasonic reflection device (MUR). The viscoelastic properties of honey were measured by MUR and classical rheometry at high and low frequencies, respectively, between 13.1 and 31.3 °$°$C. Matching both results, we built the master curve over a frequency range covering nine decades, from which we determined the main rheological parameters of honey. Finally, from an inverse approach, we extracted from this master curve, the acoustical parameters for frequencies inaccessible by the ultrasonic methods.     

Application of Uniform Asymptotics to the Second Painlevé Transcendent

In this work we propose a new method for investigating connection problems for the class of nonlinear second‐order differential equations known as the Painlevé equations. Such problems can be characterized by the question as to how the asymptotic behaviours of solutions are related as the independent variable is allowed to pass towards infinity along different directions in the complex plane. Connection problems have been previously tackled by a variety of methods. Frequently these are based on the ideas of isomonodromic deformation and the matching of WKB solutions. However, the implementation of these methods often tends to be heuristic in nature and so the task of rigorising the process is complicated. The method we propose here develops uniform approximations to solutions. This removes the need to match solutions, is rigorous, and can lead to the solution of connection problems with minimal computational effort. Our method relies on finding uniform approximations of differ ential equations of the generic form as the complex‐valued parameter . The details of the treatment rely heavily on the locations of the zeros of the function F in this limit. If they are isolated, then a uniform approximation to solutions can be derived in terms of Airy functions of suitable argument. On the other hand, if two of the zeros of F coalesce as , then an approximation can be derived in terms of parabolic cylinder functions. In this paper we discuss both cases, but illustrate our technique in action by applying the parabolic cylinder case to the “classical” connection problem associated with the second Painlevé transcendent. Future papers will show how the technique can be applied with very little change to the other Painlevé equations, and to the wider problem of the asymptotic behavio ur of the general solution to any of these equations. (Accepted May 15, 1997)     

Use of caged fluorescent dyes for the study of turbulent passive scalar mixing

The non-intrusive initialization of a flow field with distinct and spatially segregated scalar components represents a significant experimental difficulty. Here a new technique is described which makes possible the non-intrusive initialization of a spatially binary passive scalar field in a laminar or turbulent flow field. This technique uses photoactivatable (caged) fluorescent dyes dissolved in the flow medium. The scalar field within the flow field is tagged or initialized by uncaging the appropriate regions with an ultraviolet excimer laser. Mixing between the tagged and untagged regions is quantified using standard laser induced fluorescence techniques. The method is currently being used to study mixing in a turbulent pipe flow.