Elasto-plastic coupling within a thermodynamic strain space formulation of plasticity

Elasto-plastic coupling is studied within a general thermodynamic train space formulation of rate-independent plasticity by means of plastic internal variables. The strain space formulation offers a unified approach in treating both stable and unstable material behavior simultaneously. The conditions on elasto-plastic coupling are imposed by the second law of thermodynamics and the consistency equation in the strain space formulation, and are expressed by two inequalities. This is further illustrated by specific examples where explicit necessary and sufficient conditions on the elastic moduli and their change with plastic deformation are derived for the two inequalities to be satisfied.     

Experimental investigation of flow in a trench

An experimental investigation was made of the flow of a viscous incompressible liquid in a trench of square transverse cross section, using a laser Doppler velocimeter. The investigation was made with two values of the Reynolds number Re, corresponding to laminar and turbulent flow conditions in the channel. The experimental data show that a core with a constant vorticity is formed in the trench, that a jet propagates near the walls of the trench, and that there are secondary eddies in the corners of the trench. The motion of a viscous liquid in a trench of rectangular cross section is part of a broad class of breakaway flows. Experimental data on the investigation of flow in trenches are extremely few. A majority of the existing information is limited to visual observations [1–4]. In [2, 5, 6] the question of the unstable character of flow in trenches was discussed. Quantitative measurements of stable eddy flows in trenches were made in [7–9] using a thermoanemometer, and in [7] measurements were made of the pressure at the bottom and walls of trenches; there are data on the distribution of the velocity in the middle sections of trenches. In [8] the mean velocity, the intensity of the turbulence, and the stress of the turbulent flow were obtained in several sections parallel to the side walls of the trench, In [9] a measurement was made of the velocities also in two cross sections of a trench in which one component of the velocity prevails. A brief analysis of the existing experimental results shows that these data are insufficient to form a detailed representation of the character of flow in a trench.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 76–86, March–April, 1976.     

Explorative study of costs, effects and savings of screening for female fragile X premutation and full mutation carriers in the general population

OBJECTIVE: Evaluation of the costs, effects and savings of three strategies for female fragile X premutation and full mutation carrier screening in the general population. METHODS: We calculated the costs, effects and savings by using a general model for prenatal, preconceptional, and school carrier screening. Assumptions were based on literature data, expert opinions, prices and tariffs. RESULTS: Prenatal screening will detect most carriers and will lead to the highest number of avoided fragile X syndrome patients. The costs per detected carrier are quite similar for all screening programmes (around USD 45,000). All screening strategies have a favourable cost-savings balance (USD 14 million for prenatal screening, USD 9 million for preconceptional screening and USD 2 million for school screening). CONCLUSIONS: From an economic point of view, there is no obstacle to fragile X screening. The decision to screen or not can (and should) therefore concentrate on discussion of medical, social, psychological and ethical considerations.     

Tomographic reconstruction of shock layer flows

The tomographic reconstruction of supersonic flows faces two challenges. Firstly, techniques used in the past, such as the direct Fourier method (DFM) (Gottlieb and Gustafsson in On the direct Fourier method for computer tomography, 1998; Morton in Tomographic imaging of supersonic flows, 1995) or various backprojection (Kak and Slaney in Principles of computerized tomographic imaging, vol. 33 in Classics in Applied Mathematics, 2001) techniques, have only been able to reconstruct areas of the flow which are upstream of any opaque objects, such as a model. Secondly, shock waves create sharp discontinuities in flow properties, which can be difficult to reconstruct both in position and in magnitude with limited data. This paper will present a reconstruction method, matrix inversion using ray-tracing and least squares conjugate gradient (MI-RLS), which uses geometric ray-tracing and a sparse matrix iterative solver (Paige and Saunders in ACM Trans. Math. Softw. 8(1):43–71, 1982) to overcome both of these challenges. It will be shown, through testing with a phantom object described in tomographic literature, that the results compare favourably to those produced by the DFM technique. Finally, the method will be used to reconstruct three-dimensional density fields from interferometric shock layer images, with good resolution (Faletič in Tomographic reconstruction of shock layer flows, 2005). This paper was based on work that was presented at the 3rd International Symposium on Interdisciplinary Shock Wave Research, Canberra, Australia, March 1–3, 2006.     

Analytical approximation to large-amplitude oscillation of a non-linear conservative system

This paper deals with non-linear oscillation of a conservative system having inertia and static non-linearities. By combining the linearization of the governing equation with the method of harmonic balance, we establish analytical approximate solutions for the non-linear oscillations of the system. Unlike the classical harmonic balance method, linearization is performed prior to proceeding with harmonic balancing, thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations. Hence, we are able to establish analytical approximate formulas for the exact frequency and periodic solution. These analytical approximate formulas show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation.     

Drying performance and surface forces of a pair of impinging radial jets

The drying performance and the forces generated by a pair of radial jets impinging on a plane surface are studied experimentally and compared with a pair of in-line (axial) jets. The reattachment rings of the radial jets are visualized by liquid-crystal-thermography. The results of the drying experiments are presented in terms of Sherwoodnumbers. The results of the surface force measurements are presented in terms of force coefficients. The effects of flow exit angle, exit velocity, horizontal nozzle spacing and vertical nozzle to surface distance on mass transfer and net surface force are discussed. Results show that drying performance of a pair of radial jets with an exit angle towards the surface of 10° is 18% higher than that of a pair of in-line jets. The surface force of impinging radial jets depends on the exit angle. A global pressure force on the surface is typical for jets directed towards the surface, while a global lifting force is found when the jet is initially directed away from the surface. Radial jets have a high potential in drying applications for force sensitive products and when high drying rates and/or small suction forces are of interest.     

Sinkviskosimeter zur Bestimmung der Viskosität von Kunststoffschmelzen unter hydrostatischem Druck

Zusammenfassung Es wird ein Sinkviskosimeter zur Messung der Viskosität von Polymerschmelzen unter hydrostatischem Druck beschrieben. Von zwei angefügten Meßbeispielen behandelt das eine die Druckabhängigkeit der Viskosität von Polystyrol- und Polyäthylenschmelzen, das andere die Viskosität von Polystyrolschmelzen mit niedermolek ularen Zusätzen.

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Summary A viscometer of the falling cylinder type for measuring the viscosity of polymer melts under pressure is described. The applicability of this viscometer is shown by measuring the influence of hydrostatic pressure and of blowing agents on the viscosity of polymer melts.

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Mit 8 Abbildungen und 2 Tabellen     

Single specimen determination of Young's and bulk moduli of polymers

Summary A new method is presented for the rapid and consecutive determination of theYoung's and bulk moduli of polymeric solids in compression loading. Usually these properties are determined by separate measurements. However, by using an undersized specimen in a standard bulk compressibility tester, it is possible to determine both moduli on the same specimen in a single test procedure. Initial loading of the undersized specimen results in a decrease in length and an increase in diameter. From these changes,Young's modulus may be calculated. Once the bore of the tester is filled, the application of additional pressure results in a decrease in the volume of the polymer from which the bulk modulus may be calculated. Both determinations may be made within minutes. The moduli values are in general agreement with published values and the calculated values for Poisson's ratio fall into the expected range.

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Zusammenfassung Es wird eine neue Methode vorgestellt für die schnelle und fortlaufende Bestimmung des Elastizitäts- und Kompressions-Modul us polymerer Festkörper bei einer Druckbelastung. Normalerweise werden diese Eigenschaften durch unterschiedliche Methoden bestimmt. Durch Benutzung einer unterdimensionierten Probe in einem Standard-Kompressionsprüfgerät ist es möglich, beide Moduln an der gleichen Probe in einem einzigen Versuch zu ermitteln. Die Anfangsbelastung einer unterdimensionierten Probe führt zu einer Längenabnahme und einer Zunahme des Durchmessers. Aus diesen Änderungen läßt sich der Elastizitätsmodul berechnen. Sobald die Bohrung des Gerätes gefüllt ist, führt die Erhöhung des Druckes zu einer Volumen-Abnahme des Polymers, aus dem sich der Kompressionsmodul berechnen läßt. Beide Bestimmungen können in wenigen Minuten durchgeführt werden. Die Modulwerte stimmen im allgemeinen mit veröffentlichten Werten überein, und die für dasPoisson-Verhältnis ermittelten Werte liegen in dem erwarteten Bereich.

     

The ductile fracture of polycarbonate

The fracture of a known ductile polymer (polycarbonate) is investigated. It is shown that polycarbonate obeys the Dugdale model of ductile yielding by comparing measured plastic-zone sizes and displacements to the theoretical predictions. Strain-energy release rates are calculated and the critical value is shown to be one or two orders of magnitude higher than critical values for brittle polymers. Photoelastic photographs of the fracture process are presented and it is shown that the photoelastic effect definitely enhances the definition of the yield zone. Microscopic photoelastic photographs are also presented which are used to give a new interpretation to the photoplastic effect. Finally, suggestions for future work are presented.