36 research outputs found

    Probability that a band-gap extremum is located on the irreducible Brillouin-zone contour for the 17 different plane crystallographic lattices

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    After recalling the first Brillouin zone (BZ) and the first irreducible Brillouin zone (IBZ) of a lattice in terms of its plane crystallographic group, we investigate the danger of restricting a band-gap detection to the contour of the IBZ, instead of its full IBZ. Based on hundreds of porous phononic crystal simulations, we provide for the 17 plane crystallographic groups (i) statistics of the band-gap localizations, (ii) probabilities to get non-full band-gaps, and (iii) averages of the bandwidth error made when only the IBZ contour is considered. It is found that for phononic crystals, the IBZ contour provides accurate results only for highly symmetric lattices.status: Published onlin

    Bloch theorem with revised boundary conditions applied to glide, screw and rotational symmetric structures

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    Wave propagation in complex periodic systems is often addressed with the Bloch theorem, and consists in applying periodic boundary conditions to a discretized unit cell. While this method has been developed for structures periodic by translation, in a recent work, for quasi-one-dimensional wave propagation, it has been shown that screw (translation plus rotation) and glide (translation plus reflection) periodicities can be accounted for as well, keeping the Cartesian coordinate system but revisiting the periodic boundary conditions. The goal of the present paper is to generalize this concept to quasi-two-dimensional wave propagation (two dimensional waves propagating in three dimensional structures). Dispersion relations for a set of reduced problems are then compared to results from the classical method, when available. By considering a smaller periodicity, the computational cost is decreased and the number of folding curves and non-interacting intersecting curves is reduced, improving their interpretability. While the size of a unit cell is divided by a factor two when glide symmetries are considered, this ratio is significantly increased for screw or rotational symmetries. Moreover, the proposed revisited Bloch method is applicable to screw symmetric structures that do not possess purely translational symmetries, and for which the classical method cannot be used (e.g. chiral nanotubes, longitudinally wrinkled helicoids).publisher: Elsevier articletitle: Bloch theorem with revised boundary conditions applied to glide, screw and rotational symmetric structures journaltitle: Computer Methods in Applied Mechanics and Engineering articlelink: http://dx.doi.org/10.1016/j.cma.2017.01.034 content_type: article copyright: 漏 2017 Elsevier B.V. All rights reserved.status: publishe

    Bloch Theorem Applied To Structures With Additional Symmetries: Reduced Unit Cell And Irreducible Brillouin Zone

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    Bloch theorem provides a useful tool to analyze wave propagation in periodic systems. While this method has been developed for structures periodic by translation, we show that when glide (translation plus reflection) or screw (translation plus rotation) symmetries are present, they can be accounted by revisiting the boundary conditions of the Bloch theorem. By considering a smaller periodicity, the computational cost decreases and the interpretability of the dispersion diagram improves (i.e. the number of folding and non-interacting intersecting curves is reduced). Concerning computational cost reduction, we recall the choice of the irreducible Brillouin zone in terms of the unit cell symmetries, and we show that band-gap characteristics can be obtained from the irreducible Brillouin zone contour, only when bisectors or diagonals of the unit cell are mirror axes. Otherwise, the full irreducible Brillouin zone has to be considered.status: publishe

    Bloch theorem for isogeometric analysis of periodic problems governed by high-order partial differential equations

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    With the emergence of isogeometric analysis (IGA), numerical rotation-free solutions to high-order partial differential equations (PDEs) are facilitated. Indeed, IGA allows the use of high-order-continuous basis functions through the domain. For periodic systems, the Bloch theorem is useful for analyzing wave propagation, restricting the analysis to a single unit cell and applying periodic boundary conditions. However, in the literature, boundary conditions are only accounting for C0-continuity, and we propose in the present paper to enforce the G1-continuity as well or to maintain the angle in case of unit cells meeting at kinks. While G1-continuity is enforced by maintaining the collinearity between adjacent control points, in the presence of kinks, variations of the field derived with respect to opposite in-plane edge normals are linked by the Rodrigues rotation matrix. This method applied at collocation points belonging to the unit cell edges can be viewed as a novel approach of coupling multi-patch geometries with kinks, avoiding the use of nonlinear multipliers or additional bending strip elements. Both transfer-matrix and indirect methods of the Bloch theorem are investigated, for respectively quasi-one and quasi-two-dimensional wave propagation in periodic structures discretized by NURBS-based IGA. Dispersion curves of a set of numerical problems treating isogeometric rotation-free extensible elastica (beams) and Kirchhoff-Love shells are then analyzed.publisher: Elsevier articletitle: Bloch theorem for isogeometric analysis of periodic problems governed by high-order partial differential equations journaltitle: Computer Methods in Applied Mechanics and Engineering articlelink: http://dx.doi.org/10.1016/j.cma.2016.09.015 content_type: article copyright: 漏 2016 Elsevier B.V. All rights reserved.status: publishe

    The effect of Nb on the hydrogen embrittlement susceptibility of Q&P steel under static and dynamic loading

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    In the present study, the effect of Niobium (Nb) on the hydrogen embrittlement resistance of Quenched and Partitioning (Q&P) steel is investigated. For this purpose, the hydrogen uptake level and its impact on the mechanical properties of a Nb-free and a 0.024 wt% Nb Q&P steel are thoroughly analysed. The hydrogen trapping capacity is evaluated via thermal desorption spectroscopy (TDS). In-depth analysis of the desorption kinetics at different heating rates allows identification and quantification of the available trapping sites. The hydrogen embrittlement sensitivity of both steels is characterized using static and dynamic tensile tests. The addition of Nb results in an increase of the hydrogen concentration by more than 25%. The larger hydrogen content in the Nb steel, as a result of the higher fraction of grain boundaries/interphases, gives rise to a more severe embrittlement of the Nb steel compared to the Nb-free one. In addition to the larger hydrogen fraction in the Nb Q&P steel, the larger retained austenite fraction of low stability is detrimental due to the larger fraction of high carbon martensite formed when straining. This results in higher susceptibility to hydrogen embrittlement of the Nb microalloyed steel due to the brittle character of the high carbon martensite that forms easily during straining. Under dynamic loading conditions, the hydrogen embrittlement of both steels is minimal, which is attributed to a reduced hydrogen diffusion and the suppression of the transformation induced plasticity (TRIP) effect due to adiabatic heating.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Team Jilt Sietsm
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