Application of the method of multiple scales to unravel energy exchange in nonlinear locally resonant metamaterials

In this paper, the effect of weak nonlinearities in 1D locally resonant metamaterials is investigated via the method of multiple scales. Commonly employed to the investigate the effect of weakly nonlinear interactions on the free wave propagation through a phononic structure or on the dynamic response of a Duffing oscillator, the method of multiple scales is here used to investigate the forced wave propagation through locally resonant metamaterials. The perturbation approach reveals that energy exchange may occur between propagative and evanescent waves induced by quadratic nonlinear local interaction

Fracture initiation in multi-phase materials: a systematic three-dimensional approach using a FFT-based solver

This paper studies a two-phase material with a microstructure composed of a hard brittle reinforcement phase embedded in a soft ductile matrix. It addresses the full three-dimensional nature of the microstructure and macroscopic deformation. A large ensemble of periodic microstructures is used, whereby the individual grains of the two phases are modeled using equi-sized cubes. A particular solution strategy relying on the Fast Fourier Transform is adopted, which has a high computational efficiency both in terms of speed and memory footprint, thus enabling a statistically meaningful analysis. This solution method naturally accompanies the regular microstructural model, as the Fast Fourier Transform relies on a regular grid. Using the many considered microstructures as an ensemble, the average arrangement of phases around fracture initiation sites is objectively identified by the correlation between microstructure and fracture initiation -- in three dimensions. The results show that fracture initiates where regions of the hard phase are interrupted by bands of the soft phase that are aligned with the direction of maximum shear. In such regions, the hard phase is arranged such that the area of the phase boundary perpendicular to the principal strain direction is maximum, leading to high hydrostatic tensile stresses, while not interrupting the shear bands that form in the soft phase. The local incompatibility that is present around the shear bands is responsible for a high plastic strain. By comparing the response to a two-dimensional microstructure it is observed that the response is qualitatively similar (both macroscopically and microscopically). One important difference is that the local strain partitioning between the two phases is over-predicted by the two-dimensional microstructure, leading to an overestimation of damage

Une nouvelle procédure d’identification des paramètres de lois cohésives

L’objectif est ici d’introduire un nouvel outil de caractérisation de lois cohésives, modèle le plus couramment utilisé pour décrire et simuler le phénomène de délaminage. Cet outil est basé sur une méthode de corrélation d’image globale, où la définition de l’espace de recherche cinématique est adéquatement choisie. Après avoir présenté le principe de cette méthode, on s’intéresse à sa validation, ainsi qu’à son comportement au bruit. Cette validation est réalisée numériquement, (i) en construisant un ensemble d’images à l’aide d’un outil de simulation évolué du délaminage et (ii) en identifiant à partir de ces images les caractéristiques du comportement de l’interface

Experimental characterization and model identification of directional hardening effects in metals for complex strain path changes

AbstractThe purpose of the current work is the development and application of a new experimental technique and testing device for investigating the complex behavior of sheet metals during non-proportional loading. The method is based on plain strain pure bending, enabling the investigation of large deformation cyclic reversed loading, orthogonal pure bending, as well as springback. The key feature of the pure bending experiment is the absence of contact forces, material slip and friction. Furthermore, during the pure bending test, the strain gradient through the thickness is kinematically prescribed because the specimen is subjected to a plane strain condition in de direction parallel to the rotational axis (Tan et al., 1995), which allows for a straightforward comparison of the pure bending experiments and parallel simulations. The latter is used here via the identification of a recent model for directional hardening effects and arbitrary strain path changes, (Wang et al., 2006, 2008). The current method facilitates experimental investigation of hardening stagnation after reverse loading and cross hardening going well beyond that which is possible with existing methods based on the cyclic shear or tension-shear of sheet metal strips (Bouvier et al., 2005, 2006a,b; Flores et al., 2007.), or pure and three-point bending (Omerspahic et al., 2006; Antonelli et al., 2007; Carbonnière et al., 2009; Yoshida et al., 1998; Weinmann et al., 1988)

Probing protoplanetary disks with silicate emission: Where is the silicate emission zone?

Recent results indicate that the grain size and crystallinity inferred from observations of silicate features may be correlated with the spectral type of the central star and/or disk geometry. In this paper, we show that grain size, as probed by the 10 μm silicate feature peak-to-continuum and 11.3 to 9.8 μm flux ratios, is inversely proportional to log Lsstarf. These trends can be understood using a simple two-layer disk model for passive irradiated flaring disks, CGPLUS. We find that the radius, R10, of the 10 μm silicate emission zone in the disk goes as (L*/L☉)^0.56, with slight variations depending on disk geometry (flaring angle and inner disk radius). The observed correlations, combined with simulated emission spectra of olivine and pyroxene mixtures, imply a dependence of grain size on luminosity. Combined with the fact that R10 is smaller for less luminous stars, this implies that the apparent grain size of the emitting dust is larger for low-luminosity sources. In contrast, our models suggest that the crystallinity is only marginally affected, because for increasing luminosity, the zone for thermal annealing (assumed to be at T > 800 K) is enlarged by roughly the same factor as the silicate emission zone. The observed crystallinity is affected by disk geometry, however, with increased crystallinity in flat disks. The apparent crystallinity may also increase with grain growth due to a corresponding increase in contrast between crystalline and amorphous silicate emission bands

Preservation of blood volume during edema removal in nephrotic subjects

Preservation of blood volume during edema removal in nephrotic subjects. During the gradual removal of edema with diuretics in 21 edematous patients with the nephrotic syndrome (NS) we monitored blood volume. For comparison, nine healthy subjects were studied after equilibration on diets containing 20, 200, and 1138mEq sodium. The initial extracellular fluid volume (ECFV) in the patients exceeded the final ECFV by 63.4 ± 8.4%. In 10 patients with a very low plasma oncotic pressure (8.2 ± 0.4mm Hg, Group 1), the blood volume changed little. In Group 2 (plasma oncotic pressure 13.4 ± 1.0mm Hg), it was 11.0 ± 2.5% higher at entry than after edema withdrawal. In the normal volunteers, the highest sodium intake raised the ECFV by 21.4 ± 4.1%. The accompanying rise in blood volume, 11.2 ± 3.0%, was larger than in the patients of Group 1 (2.4 ± 1.9%, P < 0.04), but not of Group 2 (8.1 ± 1.9%, NS) at similar degrees of expansion. There was no difference in blood volume between the edema-free patients and the normal subjects at low-sodium diet. The course of blood pressure and creatinine clearance during edema removal gave no evidence that functional hypovolemia was induced, but the plasma renin activity was higher than in the normal subjects at similar degrees of expansion. We conclude that the blood volume to ECFV relationship curve is flattened in the presence of hypoalbuminemia. Thus, the increase in blood volume that normally follows ECFV expansion is less in patients with the NS, but a drop below normal upon removal of edema is absent also

Functional relationships in the nephrotic syndrome

Functional relationships in the nephrotic syndrome. An analysis of 70 observations in patients with the nephrotic syndrome (NS) on a low sodium diet is presented. The following parameters were determined: plasma volume, plasma renin activity, plasma aldosterone concentration, serum albumin, urinary sodium and protein excretion, and creatinine clearance. In 41 instances glomerular filtration rate (GFR) and effective renal plasma flow (ERPF) were determined on the basis of 51Cr-EDTA and 125I-hippuran clearances, and the filtration fraction (FF) was calculated. The results in patients with minimal lesions (ML) and those with histological glomerular lesions (HL) were compared to determine whether these groups can be separated on the basis of signs of hypovolemia and primary renal sodium retention. Although a higher proportion of the ML patients showed extreme sodium retention and elevated plasma renin and aldosterone levels, these values tended to overlap and no differences were found for blood volume, blood pressure, and overall renal function between the groups. FF was markedly and equally depressed in both groups: 13.5 ± 1.6% in the ML and 14.2 ± 1.1% SEM in the HL group (NS). Analysis of the within-group relationships between the parameters under study revealed relatively few correlations, which supports the hypothesis that primary impairment of renal water and salt excretion is an important if not overruling factor in patients with the NS.Relations fonctionnelles au cours du syndrome néphrotique. Une analyse de 70 observations de malades atteintes de syndrome néphrotique (NS) en régime pauvre en sodium est présentée. Les paramètres suivants ont été déterminés: volume plasmatique, activité rénine plasmatique, aldostéronémie, albuminémie, natriurèse et protéinurie, et clearance de la créatinine. Dans 41 fois, le débit de filtration glomérulaire (GFR) et le débit plasmatique rénal efficace (ERPF) ont été déterminés par des clearances au 51Cr-EDTA et au 125I-hippuran, et on a calculé la fraction de filtration (FF). Les résultats des groupes de malades atteints de lésions minimes (ML) et de ceux atteints de lésions glomérulaires histologiques (HL) ont été comparés pour savoir s'il est possible de séparer ces groupes sur la base des signes d'hypovolémie et de rétention sodée d'origine rénale. Bien qu'une plus forte proportion de malades ML ait présenté une réntention sodée et une élévation des niveaux de rénine et d'aldostérone plasmatiques extrêmes, ces valeurs tendaient à se chevaucher et il n'a pas été trouvé de différence dans le volume sanguin, la pression artérielle et la fonction rénale globale entre les groupes. FF était diminuée de façon marquée et identique dans les deux groupes: 13,5 ± 1,6% dans le groupe ML et 14,2 ± 1,1% SEM dans le groupe HL (NS). Une analyse des interrelations à l'intérieur des groupes entre les paramètres étudiés a révélé relativement peu de corrélations, ce qui est en faveur de l'hypothèse que l'altération primitive de l'excrétion rénale d'eau et de sel est un facteur important, sinon capital chez les malades atteints de NS

The structure of the protoplanetary disk surrounding three young intermediate mass stars. II. Spatially resolved dust and gas distribution

[Abridged] We present the first direct comparison of the distribution of the gas, as traced by the [OI] 6300 AA emission, and the dust, as traced by the 10 micron emission, in the protoplanetary disk around three intermediate-mass stars: HD 101412, HD 135344 B and HD 179218. N-band visibilities were obtained with VLTI/MIDI. Simple geometrical models are used to compare the dust emission to high-resolution optical spectra in the 6300 AA [OI] line of the same targets. The disks around HD 101412 and HD 135344 B appear strongly flared in the gas, but self-shadowed in the dust beyond ~ 2 AU. In both systems, the 10 micron emission is rather compact (< 2 AU) while the [OI] brightness profile shows a double peaked structure. The inner peak is strongest and is consistent with the location of the dust, the outer peak is fainter and is located at 5-10 AU. Spatially extended PAH emission is found in both disks. The disk around HD 179218 is flared in the dust. The 10 micron emission emerges from a double ring-like structure with the first ring peaking at ~ 1 AU and the second at ~ 20 AU. No dust emission is detected between ~ 3 -- 15 AU. The oxygen emission seems also to come from a flared structure, however, the bulk of this emission is produced between ~ 1 -- 10 AU. This could indicate a lack of gas in the outer disk or could be due to chemical effects which reduce the abundance of OH -- the parent molecule of the observed [OI] emission -- further away from the star. The three systems, HD 179218, HD 135344 B and HD 101412, may form an evolutionary sequence: the disk initially flared becomes flat under the combined action of gas-dust decoupling, grain growth and dust settling.Comment: Accepted for publication in A&

C2D Spitzer-IRS spectra of disks around T Tauri stars: IV. Crystalline silicates

Aims. Dust grains in the planet-forming regions around young stars are expected to be heavily processed due to coagulation, fragmentation, and crystallization. This paper focuses on the crystalline silicate dust grains in protoplanetary disks for a statistically significant number of TTauri stars (96). Methods. As part of the cores to disks (c2d) legacy program, we obtained more than a hundred Spitzer/IRS spectra of TTauri stars, over a spectral range of 5-35 μm where many silicate amorphous and crystalline solid-state features are present. At these wavelengths, observations probe the upper layers of accretion disks up to distances of a dozen AU from the central object. Results. More than 3/4 of our objects show at least one crystalline silicate emission feature that can be essentially attributed to Mg-rich silicates. The Fe-rich crystalline silicates are largely absent in the c2d IRS spectra. The strength and detection frequency of the crystalline features seen at λ > 20 μm correlate with each other, while they are largely uncorrelated with the observational properties of the amorphous silicate 10 μm feature. This supports the idea that the IRS spectra essentially probe two independent disk regions: a warm zone (≤1 AU) emitting at ~ 10 μm and a much colder region emitting at λ > 20 μm (≤10 AU). We identify a crystallinity paradox, as the long-wavelength (λ > 20 m) crystalline silicate features are detected 3.5 times more frequently (~55% vs. ~15%) than the crystalline features arising from much warmer disk regions (λ ~ 10 μm). This suggests that the disk has an inhomogeneous dust composition within ~10 AU. The analysis of the shape and strength of both the amorphous 10 μm feature and the crystalline feature around 23 μm provides evidence for the prevalence of μm-sized (amorphous and crystalline) grains in upper layers of disks. Conclusions. The abundant crystalline silicates found far from their presumed formation regions suggest efficient outward radial transport mechanisms in the disks around TTauri stars. The presence of μm-sized grains in disk atmospheres, despite the short timescales for settling to the midplane, suggests efficient (turbulent) vertical diffusion, probably accompanied by grain-grain fragmentation to balance the expected efficient growth. In this scenario, the depletion of submicron-sized grains in the upper layers of the disks points toward removal mechanisms such as stellar winds or radiation pressure