Size effects and idealized dislocation microstructure at small scales: Predictions of a Phenomenological model of Mesoscopic Field Dislocation Mechanics: Part II

In Part I of this set of two papers, a model of mesoscopic plasticity is developed for studying initial-boundary value problems of small scale plasticity. Here we make qualitative, finite element method-based computational predictions of the theory. We demonstrate size effects and the development of strong inhomogeneity in simple shearing of plastically constrained grains. Non-locality in elastic straining leading to a strong Bauschinger effect is analyzed. Low shear strain boundary layers in constrained simple shearing of infinite layers of polycrystalline materials are not predicted by the model, and we justify the result based on an examination of the no-dislocation-flow boundary condition. The time-dependent, spatially homogeneous, simple shearing solution of PMFDM is studied numerically. The computational results and an analysis of continuous dependence with respect to initial data of solutions for a model linear problem point to the need for a nonlinear study of a stability transition of the homogeneous solution with decreasing grain size and increasing applied deformation. The continuous-dependence analysis also points to a possible mechanism for the development of spatial inhomogeneity in the initial stages of deformation in lower-order gradient plasticity theory. Results from thermal cycling of small scale beams/films with different degrees of constraint to plastic flow are presented showing size effects and reciprocal-film-thickness scaling of dislocation density boundary layer width. Qualitative similarities with results from discrete dislocation analyses are noted where possible.We discuss the convergence of approximate solutions with mesh refinement and its implications for the prediction of dislocation microstructure development, motivated by the notion of measure-valued solutions to conservation laws.     

Dispersive bending waves in uniform bars

The traveling bending waves in a long beam of rectangular cross section were measured and calculated. The bending waves were induced by impacting with a steel sphere and measured with strain gages at several distances from the point of impact. The impact force was calculated as a function of time by integrating the dynamic equations of the sphere and the beam. The force spectrum was then found using a fast-Fourier-transform (FFT) calculation and multiplied by the moment-frequency response of the beam to determine the moment spectrum. The moment-time function was calculated by an inverse FFT. The traveling wave is dispersive; its spectrum was found from that at the point of impact by phase shifting each component by an angle proportional to the distance and to the square root of the frequency. Again the time curve was determined by an inverse FFT. The indentation stiffness of the beam was found to be very much less than that of the elastic half space because of transverse bending. After the impact force was recalculated with this correction, the calculated moment-time traces agreed very well with the measured ones.     

Seismic Evaluation of Multi-Storey RC Frame Using Modal Pushover Analysis

The recently developed pushover analysis procedure has led a new dimension to performance-based design in structural engineering practices. With the increase in the magnitude of monotonic loading, weak links and failure modes in the multi-storey RC frames are usually formed. The force distribution and storey displacements are evaluated using static pushover analysis based on the assumption that the response is controlled by fundamental mode and no mode shift takes place. Himalayan-Nagalushai region, Indo-Gangetic plain, Western India, Kutch and Kathiawar regions are geologically unstable parts of India and some devastating earthquakes of remarkable intensity have occurred here. In view of the intensive construction activity in India, where even a medium intensity tremor can cause a calamity, the authors feel that a completely up-to-date, versatile method of aseismic analysis and design of structures are essential. A detailed dynamic analysis of a 10-storey RC frame building is therefore performed using response spectrum method based on Indian Standard Codal Provisions and base shear, storey shear and storey drifts are computed. A modal pushover analysis (MPA) is also carried out to determine the structural response of the same model for the same acceleration spectra used in the earlier case. The major focus of study is to bring out the superiority of pushover analysis method over the conventional dynamic analysis method recommended by the code. The results obtained from the numerical studies show that the response spectrum method underestimates the response of the model in comparison with modal pushover analysis. It is also seen that modal participation of higher modes contributes to better results of the response distribution along the height of the building. Also pushover curves are plotted to illustrate the displacement as a function of base shear.     

Fluides viscoélastiques non linéaires satisfaisant à un principe de superposition étude théorique et experimentale

Summary This study is devoted to incompressible viscoelastic fluids in which a superposition principle for stress is assumed. In order to respect the material objectivity, this summation of incremental stress, with corresponding memory factor, is operated in a rheological (corotational) frame. Theoretical study for these fluids in viscometric flows was conducted up to explicit solutions. This study shows some impossibility ranges for such flows. The determination of the memory functions from this type of flow involvesFourier transform and so, would need the knowledge of all the kinematic range, and this is impossible.The study in relaxation tests permits the determination of the memory functions. So, we performed these experiments, to get memory functions which were independent of the kinematics.Using the function so obtained, we can compute and predict some experimental results in steady flows; and the comparison between these two results was quite good.

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Zusammenfassung Wir untersuchen inkompressible viskoelastische Fluide, die einem Superpositionsprinzip für die Spannungen genügen. Um dem Prinzip der Bezugsindifferenz zu entsprechen, wird die Summation der Spannungs-inkremente in einem korotationalen Bezugssystem vorgenommen. Die theoretische Untersuchung wird für viskosimetrische Strömungen mit kreisförmigen oder geradlinigen Stromlinien für einfache Randwertprobleme bis zu expliziten Lösungen durchgeführt. Dabei findet man, daß es Bereiche gibt, für die solche Strömungen nicht existieren. Die Bestimmung der Gedächtnisfunktion aus diesen Strömungsformen würde eineFourier-Transformation erfordern und darum die Kenntnis des gesamten kinematischen Bereichs voraussetzen, was nach vorstehendem Ergebnis unmöglich ist.Mit Hilfe von Relaxationsversuchen kann man die Gedächtnisfunktion unmittelbar erschließen. Durch solche Experimente erhalten wir Gedächtnisfunktionen, die von der Kinematik unabhängig sind. Unter Verwendung dieser Funktionen lassen sich einige theoretische Aussagen über stationäre Strömungen erhalten, die mit dem Experiment verglichen werden können. Es ergibt sich eine recht gute Übereinstimmung.

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Avec 6 figures     

Turbulent flow structure at concordant and discordant open-channel confluences

Models of flow at river-channel confluences that consist of two concordant confluent channels with avalanche faces dipping into a scour zone are limited because this morphology may be the exception rather than the rule in nature. In this paper the mean and turbulent flow structure in the streamwise and vertical directions at both concordant and discordant laboratory confluences were examined in order to determine the effect of bed discordance on the flow field, and to assess its influence on sediment transport. Instantaneous velocities were measured with a laser Doppler anemometer using a dense spatial sampling grid. The spatial distribution of normal stress varies with bed geometry as bed discordance generates a distortion of the mixing layer between the confluent streams. Turbulent shear stress is larger in the discordant bed case and its peak is associated with the position of the mixing layer whereas for concordant beds the zone of mixing is characterised by a decrease in the Reynolds shear stress. Quadrant analysis also revealed differential dominating quadrants between the two bed geometries which will influence sediment transport routing and, consequently, the resulting bed morphology. These results highlight the need for significant modifications to current models of confluence flow dynamics in order to account for the bed configuration.We would like to thank Phil Fields of the Earth Sciences workshop at Leeds for his skillful construction of the confluence model and continued help during the course of this research. The LDA facility has been funded through grants from the UFC, NERC and University of Leeds. PB thanks NSERC for financial support and the Fonds FCAR for funding an eight month study-visit held at the Department of Earth Sciences, University of Leeds. AGR acknowledges the financial support of NSERC whilst JLB is grateful for the award of a Nuffield Science Foundation Fellowship which facilitated the preparation of this paper. We thank two anonymous reviewers for their constructive criticisms that helped clarifying the paper.     

Beyond microstructures: Using the Kerr Effect to characterize the macrostructures of synthetic polymers

The macrostructures of synthetic polymers are essentially the complete molecular chain architectures, including the types and amounts of constituent short‐range microstructures, such as the regio‐ and stereosequences of the inserted monomers, the amounts and sequences of monomers found in co‐, ter‐, and tetra‐polymers, branching, inadvertent, and otherwise, etc. Currently, the best method for characterizing polymer microstructures uses high field, high resolution ¹³C‐nuclear magnetic resonance (NMR) spectroscopy observed in solution. However, even ¹³C‐NMR is incapable of determining the locations or positions of resident polymer microstructures, which are required to elucidate their complete macrostructures. The sequences of amino acid residues in proteins, or their primary structures, cannot be characterized by NMR or other short‐range spectroscopic methods, but only by decoding the DNA used in their syntheses or, if available, X‐ray analysis of their single crystals. Similarly, there are currently no experimental means to determine the sequences or locations of constituent microstructures along the chains of synthetic macromolecules. Thus, we are presently unable to determine their macrostructures. As protein tertiary and quaternary structures and their resulting ultimate functions are determined by their primary sequence of amino acids, so too are the behaviors and properties of synthetic polymers critically dependent on their macrostructures. We seek to raise the consciousness of both synthetic and physical polymer scientists and engineers to the importance of characterizing polymer macrostructures when attempting to develop structure–property relations. To help achieve this task, we suggest using the electrical birefringence or Kerr effects observed in their dilute solutions. The molar Kerr constants of polymer solutes contributing to the birefringence of their solutions, under the application of a strong electric field, are highly sensitive to both the types and locations of their constituent microstructures. As a consequence, we may begin to characterize the macrostructures of synthetic polymers by means of the Kerr effect. To simplify implementation of the Kerr effect to characterize polymer macrostructures, we suggest that NMR first be used to determine the types and amounts of constituent microstructures present. Subsequent comparison of observed Kerr effects with those predicted for different microstructural locations along the polymer chains can then be used to identify the most likely macrostructures. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 155–166     

Random Latin squares and 2-dimensional expanders

Expander graphs have been playing an important role in combinatorics and computer science over the last four decades. In recent years a theory of high dimensional expanders is emerging, but as of now all known examples of expanders (random and explicit) have unbounded degrees. The question of existence of bounded degree high dimensional expanders was raised by Gromov and by Dotterrer and Kahle. In this paper we present a new model, based on Latin squares, of 2-dimensional complexes of bounded edge degrees that are expanders with probability tending to 1.     

Controlled release and long-term antibacterial activity of chlorhexidine digluconate through the nanoporous network of microfibrillated cellulose

The recent study focusing on paper coated with microfibrillated cellulose (MFC) revealed the ability of such a structure to achieve a controlled release of molecules introduced into its nanoporous network. The present study examines this concept using a chlorhexidine digluconate-based (CHX) antibacterial solution. Various analyses were performed, optical microscopy, FE-SEM and AFM to underline the structure of the nanoporous MFC network. Release studies were conducted in an aqueous medium following two different protocols and antibacterial tests were done to evaluate the efficiency of the final materials obtained. MFC coating provided a slower and more progressive release of CHX. Indeed, papers impregnated with CHX were active for 18 days, whereas papers coated with CHX/MFC retained their antibacterial activity for 45 days. In parallel, similar tests were carried out using a model coating slurry, and although the rate of release of CHX was also slowed down, the quantities released were insufficient to confer any antibacterial activity. In conclusion, this study suggests that the use of MFC as a coating could be very promising since it allows a controlled and progressive release of molecules preserving long-term antibacterial activity.