Second-order estimates of the self-consistent type for viscoplastic polycrystals

The ‘second–order’ homogenization procedure of Ponte Castañeda is used to propose new estimates of the self–consistent type for the effective behaviour of viscoplastic polycrystals. This is accomplished by means of appropriately generated estimates of the self–consistent type for the relevant ‘linear thermoelastic comparison composite’, in the homogenization procedure. The resulting nonlinear self–consistent estimates are the only estimates of their type to be exact to second order in the heterogeneity contrast, which, for polycrystals, is determined by the grain anisotropy. In addition, they satisfy the recent bounds of Kohn and Little for two–dimensional power–law polycrystals, which are known to be significantly sharper than the Taylor bound at large grain anisotropy. These two features combined, suggest that the new self–consistent estimates, obtained from the second–order procedure, may be the most accurate to date. Direct comparison with other self–consistent estimates, including the classical incremental and secant estimates, for the special case of power–law creep, appear to corroborate this observation

Second-order estimates of the self-consistent type for viscoplastic polycrystals

The ‘second–order’ homogenization procedure of Ponte Castañeda is used to propose new estimates of the self–consistent type for the effective behaviour of viscoplastic polycrystals. This is accomplished by means of appropriately generated estimates of the self–consistent type for the relevant ‘linear thermoelastic comparison composite’, in the homogenization procedure. The resulting nonlinear self–consistent estimates are the only estimates of their type to be exact to second order in the heterogeneity contrast, which, for polycrystals, is determined by the grain anisotropy. In addition, they satisfy the recent bounds of Kohn and Little for two–dimensional power–law polycrystals, which are known to be significantly sharper than the Taylor bound at large grain anisotropy. These two features combined, suggest that the new self–consistent estimates, obtained from the second–order procedure, may be the most accurate to date. Direct comparison with other self–consistent estimates, including the classical incremental and secant estimates, for the special case of power–law creep, appear to corroborate this observation

Demodulation of Spatial Carrier Images: Performance Analysis of Several Algorithms Using a Single Image

http://link.springer.com/article/10.1007%2Fs11340-013-9741-6#Optical full-field techniques have a great importance in modern experimental mechanics. Even if they are reasonably spread among the university laboratories, their diffusion in industrial companies remains very narrow for several reasons, especially a lack of metrological performance assessment. A full-field measurement can be characterized by its resolution, bias, measuring range, and by a specific quantity, the spatial resolution. The present paper proposes an original procedure to estimate in one single step the resolution, bias and spatial resolution for a given operator (decoding algorithms such as image correlation, low-pass filters, derivation tools ...). This procedure is based on the construction of a particular multi-frequential field, and a Bode diagram representation of the results. This analysis is applied to various phase demodulating algorithms suited to estimate in-plane displacements.GDR CNRS 2519 “Mesures de Champs et Identification en Mécanique des Solide

Effect of a nonuniform distribution of voids on the plastic response of voided materials: a computational and statistical analysis

This study investigates the overall and local response of porous media composed of a perfectly plastic matrix weakened by stress-free voids. Attention is focused on the specific role played by porosity fluctuations inside a representative volume element. To this end, numerical simulations using the Fast Fourier Transform (FFT) are performed on different classes of microstructure corresponding to different spatial distributions of voids. Three types of microstructures are investigated: random microstructures with no void clustering, microstructures with a connected cluster of voids and microstructures with disconnected void clusters. These numerical simulations show that the porosity fluctuations can have a strong effect on the overall yield surface of porous materials. Random microstructures without clusters and microstructures with a connected cluster are the hardest and the softest configurations, respectively, whereas microstructures with disconnected clusters lead to intermediate responses. At a more local scale, the salient feature of the fields is the tendency for the strain fields to concentrate in specific bands. Finally, an image analysis tool is proposed for the statistical characterization of the porosity distribution. It relies on the distribution of the ‘distance function’, the width of which increases when clusters are present. An additional connectedness analysis allows us to discriminate between clustered microstructures

Segmented simultaneous multi-slice diffusion-weighted imaging with navigated 3D rigid motion correction

Purpose To improve the robustness of diffusion-weighted imaging (DWI) data acquired with segmented simultaneous multi-slice (SMS) echo-planar imaging (EPI) against in-plane and through-plane rigid motion.Theory and Methods The proposed algorithm incorporates a 3D rigid motion correction and wavelet denoising into the image reconstruction of segmented SMS-EPI diffusion data. Low-resolution navigators are used to estimate shot-specific diffusion phase corruptions and 3D rigid motion parameters through SMS-to-volume registration. The shot-wise rigid motion and phase parameters are integrated into a SENSE-based full-volume reconstruction for each diffusion direction. The algorithm is compared to a navigated SMS reconstruction without gross motion correction in simulations and in vivo studies with four-fold interleaved 3-SMS diffusion tensor acquisitions.Results Simulations demonstrate high fidelity was achieved in the SMS-to-volume registration, with submillimeter registration errors and improved image reconstruction quality. In vivo experiments validate successful artifact reduction in 3D motion-compromised in vivo scans with a temporal motion resolution of approximately 0.3 s.Conclusion This work demonstrates the feasibility of retrospective 3D rigid motion correction from shot navigators for segmented SMS DWI.Radiolog

Image distortion correction for MRI in low field permanent magnet systems with strong B-0 inhomogeneity and gradient field nonlinearities

Objective To correct for image distortions produced by standard Fourier reconstruction techniques on low field permanent magnet MRI systems with strong B-0 inhomogeneity and gradient field nonlinearities. Materials and methods Conventional image distortion correction algorithms require accurate Delta B-0 maps which are not possible to acquire directly when the B-0 inhomogeneities also produce significant image distortions. Here we use a readout gradient time-shift in a TSE sequence to encode the B-0 field inhomogeneities in the k-space signals. Using a non-shifted and a shifted acquisition as input, Delta B-0 maps and images were reconstructed in an iterative manner. In each iteration, Delta B-0 maps were reconstructed from the phase difference using Tikhonov regularization, while images were reconstructed using either conjugate phase reconstruction (CPR) or model-based (MB) image reconstruction, taking the reconstructed field map into account. MB reconstructions were, furthermore, combined with compressed sensing (CS) to show the flexibility of this approach towards undersampling. These methods were compared to the standard fast Fourier transform (FFT) image reconstruction approach in simulations and measurements. Distortions due to gradient nonlinearities were corrected in CPR and MB using simulated gradient maps. Results Simulation results show that for moderate field inhomogeneities and gradient nonlinearities, Delta B-0 maps and images reconstructed using iterative CPR result in comparable quality to that for iterative MB reconstructions. However, for stronger inhomogeneities, iterative MB reconstruction outperforms iterative CPR in terms of signal intensity correction. Combining MB with CS, similar image and Delta B-0 map quality can be obtained without a scan time penalty. These findings were confirmed by experimental results. Discussion In case of B-0 inhomogeneities in the order of kHz, iterative MB reconstructions can help to improve both image quality and Delta B-0 map estimation.Radiolog

Stochastic neighbor embedding as a tool for visualizing the encoding capability of magnetic resonance fingerprinting dictionaries

Objective To visualize the encoding capability of magnetic resonance fingerprinting (MRF) dictionaries. Materials and methods High-dimensional MRF dictionaries were simulated and embedded into a lower-dimensional space using t-distributed stochastic neighbor embedding (t-SNE). The embeddings were visualized via colors as a surrogate for location in low-dimensional space. First, we illustrate this technique on three different MRF sequences. We then compare the resulting embeddings and the color-coded dictionary maps to these obtained with a singular value decomposition (SVD) dimensionality reduction technique. We validate the t-SNE approach with measures based on existing quantitative measures of encoding capability using the Euclidean distance. Finally, we use t-SNE to visualize MRF sequences resulting from an MRF sequence optimization algorithm. Results t-SNE was able to show clear differences between the color-coded dictionary maps of three MRF sequences. SVD showed smaller differences between different sequences. These findings were confirmed by quantitative measures of encoding. t-SNE was also able to visualize differences in encoding capability between subsequent iterations of an MRF sequence optimization algorithm. Discussion This visualization approach enables comparison of the encoding capability of different MRF sequences. This technique can be used as a confirmation tool in MRF sequence optimization.Radiolog

Regularized joint water-fat separation with B-0 map estimation in image space for 2D-navigated interleaved EPI based diffusion MRI

Purpose To develop a new water-fat separation and B-0 estimation algorithm to effectively suppress the multiple resonances of fat signal in EPI. This is especially relevant for DWI where fat is often a confounding factor. Methods Water-fat separation based on chemical-shift encoding enables robust fat suppression in routine MRI. However, for EPI the different chemical-shift displacements of the multiple fat resonances along the phase-encoding direction can be problematic for conventional separation algorithms. This work proposes a suitable model approximation for EPI under B-0 and fat off-resonance effects, providing a feasible multi-peak water-fat separation algorithm. Simulations were performed to validate the algorithm. In vivo validation was performed in 6 volunteers, acquiring spin-echo EPI images in the leg (B-0 homogeneous) and head-neck (B-0 inhomogeneous) regions, using a TE-shifted interleaved EPI sequence with/without diffusion sensitization. The results are numerically and statistically compared with voxel-independent water-fat separation and fat saturation techniques to demonstrate the performance of the proposed algorithm. Results The reference separation algorithm without the proposed spatial shift correction caused water-fat ambiguities in simulations and in vivo experiments. Some spectrally selective fat saturation approaches also failed to suppress fat in regions with severe B-0 inhomogeneities. The proposed algorithm was able to achieve improved fat suppression for DWI data and ADC maps in the head-neck and leg regions. Conclusion The proposed algorithm shows improved suppression of the multi-peak fat components in multi-shot interleaved EPI applications compared to the conventional fat saturation approaches and separation algorithms.Neuro Imaging ResearchRadiolog

Numéro thématique des Comptes Rendus Mécanique en lʼhonneur dʼAndré Zaoui

La Mécanique des Matériaux a connu, en France et dans le monde, un développement spectaculaire au cours des dernières décennies, rendu à la fois nécessaire par les besoins d’innovation et de sûreté de secteurs industriels comme l’énergie et les transports, et possible par les avancées contemporaines en Physique et en Mécanique des Milieux Continus. Tout matériau est, par nature, hétérogène à une et souvent plusieurs échelles. La prise en compte, à une échelle pertinente, de cette hétérogénéité gouvernant les interactions entre mécanismes élémentaires est bien souvent la clef de la compréhension et de la prédiction du comportement mécanique des matériaux à leur échelle macroscopique d’usage. La Micromécanique des Matériaux, à laquelle ce numéro thématique des Comptes Rendus Mécanique est consacré, a précisément pour objet d’aborder ces problèmes de transition d’échelles. Ce numéro thématique est tout naturellement l’occasion d’honorer l’un des acteurs emblématiques du domaine, André Zaoui, qui a contribué de façon essentielle à l’établissement de la démarche micro–macro sur des bases théoriques rigoureuses validées par une approche expérimentale ambitieuse. Par ses travaux personnels, par la création, en avance sur son temps, d’une équipe de recherche dédiée aux expériences micromécaniques, par ses enseignements et ses actions de structuration de la recherche, André Zaoui a initié, puis constamment encouragé,ce domaine en France, l’ancrant solidement dans un dialogue fructueux entre expériences à petite échelle et modélisation

In-situ Analysis of Laminated Composite Materials by X-ray Micro-Computed Tomography and Digital Volume Correlation

The complex mechanical behaviour of composite materials, due to internal heterogeneity and multi-layered composition impose deeper studies. This paper presents an experimental investigation technique to perform volume kinematic measurements in composite materials. The association of X-ray micro-computed tomography acquisitions and Digital Volume Correlation (DVC) technique allows the measurement of displacements and deformations in the whole volume of composite specimen. To elaborate the latter, composite fibres and epoxy resin are associated with metallic particles to create contrast during X-ray acquisition. A specific in situ loading device is presented for three-point bending tests, which enables the visualization of transverse shear effects in composite structures