Crack kinking from an interface crack with initial contact between the crack lips

The authors recently theoretically studied crack kinking and opening from an initially closed crack (without friction) in some homogeneous medium. The same problem, but for an interface crack, is considered here. Comninou has shown that the asymptotic stress field prior to kinking is governed by a single, mode II stress intensity factor (SIF). Using this result, plus a homogeneity property of the problems of elastic fracture mechanics with unilateral contact envisaged, a change of scale, and two reasonable hypotheses, we establish the expression of the SIF at the tip of the small, open crack extension. It is shown that whatever the geometry of the external boundary and the crack and whatever the loading, these SIF depend solely upon the initial (mode II) SIF (in a linear way), the kink angle and Dundurs' parameters α and β. Using this result and Goldstein and Salganik's “principle of local symmetry” to predict the kink angle, one finds that it is independent of the loading but does depend upon Dundurs' parameters α and β. This contrasts with the case of an ordinary (initially closed) crack in some homogeneous medium, for which the kink angle was not only independent of the loading but an absolute constant. However, it is numerically found that the influence of the mismatch of elastic properties upon the kink angle is rather weak.     

Dynamic analysis of a multi-mass discrete-continuous layered system

Summary In the paper a one-dimensional discrete-continuous multi-mass layered system subject to an axial indirect kinematic excitation using the wave method is considered. Damping is taken into account by means of equivalent external and internal damping. The numerical analysis for specific cases of the discussed system mainly focusses on the determination of resonant displacements for the first and second frequency of free vibration in selected cross-sections of the system in dependence on the relative location of layers with various mechanical properties.

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Dynamische analyse eines geschichteten Körpers aus einzelmassen und massebehafteten Kontinua

Übersieht In diesem Beitrag wird ein eindimensionales Vielschichten-System aus Einzelmassen und massebehafteten Kontinua unter axialer, indirekter kinematischer Erregung mit der Wellengleichungsmethode untersucht. Dämpfung wird durch äquivalente äußere und innere Dämpfung berücksichtigt. Die numerische Behandlung spezieller Systeme konzentriert sieh auf die Bestimmung der Verschiebungen in ausgesuchten Querschnitten bei Resonanz mit der ersten und zweiten Eigenfrequenz, und zwar in Abhängigkeit von der relativen Anordnung von Schichten mit verschiedenen Materialeigenschaften.

     

Dynamic investigations of single gear transmission taking into account microcracks

Summary The paper concerns dynamic investigations of the model of gear transmission consisting of four rigid bodies and two torsion shafts. The shafts are assumed to contain microcracks which are taken into account by means of the equivalent shear modulus in accordance with the results of the papers [2, 3]. The influence of microcracks on the behaviour of the gear transmission in dynamic conditions is investigated for the first two frequencies of free vibrations and suitable amplitude-frequency curves. The investigations are carried out by means of two methods: the wave method which takes into account all the reflections of waves and the multibody system approach.

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Dynamische Untersuchungen eines einstufigen Getriebes mit Mikrorissen

Übersicht Vorgestellt werden dynamische Untersuchungen an einem Getriebemodell aus vier Starrkörpern und zwei Torsionswellen. Es wird angenommen, daß die Wellen Mikrorisse enthalten, die über einen äquivalenten Schubmodul nach [2, 3] berücksichtigt werden. Der Einfluß der Mikrorisse auf das dynamische Verhalten des Getriebes wird anhand der beiden ersten Eigenfrequenzen und der Amplituden-Erregerfrequenz-Beziehung untersucht. Benutzt werden zwei Methoden: die Methode der Wellenausbreitung, die alle Reflektionen berücksichtigt, und die Behandlung als Mehrkörpersystem.

     

Modèle électromagnétique d'objet dissimulé

We model propagation of electromagnetic waves in a medium, which is inhomogeneous with a rough layer, and which hides an object. We first get an effective medium, and then we solve the problem by integral equations.     

Size and sequence and the volume change of protein folding

The application of hydrostatic pressure generally leads to protein unfolding, implying, in accordance with Le Chatelier's principle, that the unfolded state has a smaller molar volume than the folded state. However, the origin of the volume change upon unfolding, ΔV(u), has yet to be determined. We have examined systematically the effects of protein size and sequence on the value of ΔV(u) using as a model system a series of deletion variants of the ankyrin repeat domain of the Notch receptor. The results provide strong evidence in support of the notion that the major contributing factor to pressure effects on proteins is their imperfect internal packing in the folded state. These packing defects appear to be specifically localized in the 3D structure, in contrast to the uniformly distributed effects of temperature and denaturants that depend upon hydration of exposed surface area upon unfolding. Given its local nature, the extent to which pressure globally affects protein structure can inform on the degree of cooperativity and long-range coupling intrinsic to the folded state. We also show that the energetics of the protein's conformations can significantly modulate their volumetric properties, providing further insight into protein stability.     

Connected functional working spaces: a framework for the teaching and learning of functions at upper secondary level

ZDM – Mathematics Education - This paper aims at contributing to remedy the narrow treatment of functions at upper secondary level. Assuming that students make sense of functions by working...