Modal decomposition from partial measurements

International audienceA data set over space and time is assumed to have a low rank representation in separated spatial and temporal modes. The problem of evaluating these modes from a temporal series of partial measurements is considered. Each elementary instantaneous measurement captures only a window (in space) of the observed data set, but the window position varies in time so as to cover the entire region of interest and would allow for a complete measurement would the scene be static. A novel procedure, alternative to the Gappy Proper Orthogonal Decomposition (GPOD) methodology, is introduced. It is a xed point iterative procedure where modes are evaluated sequentially. Tested upon very sparse acquisition (1% of measurements being available) and very noisy synthetic data sets (10% noise), the proposed algorithm is shown to outperform two variants of the GPOD algorithm, with much faster convergence, and better reconstruction of the entire data set

Sub-minute in situ Fracture Test in a Lab CT-scanner

International audienceThe present study aims at demonstrating the feasibility of performing a fracture test in less than one minute in a lab CT scanner despite the severe time constraints of tomography acquisition. After introducing the basic concepts of Projection-based Digital Volume Correlation (P-DVC), the specific implementation of this methodology to a wedge splitting test on a refractory material is presented. The kinematics of the test is described over a mesh tailored to the sample geometry, and the elastic behavior of the sample is exploited through finite element computations to provide sensitivity fields of experimental boundary conditions to allow for their "measurements." Enhancing the simulation to account for crack advance with extended finite element analyses allows the sensitivity of the procedure to the crack position to be assessed. A confidence interval for the refractory toughness is finally obtained

Fast 4D tensile test monitored via X-CT: Single projection based Digital Volume Correlation dedicated to slender samples

International audienceThe measurement of 4D (i.e., 3D space and time) displacement fields of in situ tests within X-ray Computed Tomography scanners (i.e., lab-scale X-CT) is considered herein using projection-based Digital Volume Correlation. With one single projection per loading (i.e. time) step, the developed method allows for loading not to be interrupted and to vary continuously during the scan rotation. As a result, huge gains in acquisition time (i.e., more than two orders of magnitudes) to be reached. The kinematic analysis is carried out using predefined space and time bases combined with model reduction techniques (i.e., Proper Generalized Decomposition with space-time decomposition). The accuracy of the measured kinematic basis is assessed via gray level residual fields. An application to an in situ tensile test composed of 127 time steps is performed. Because of the slender geometry of the sample, a specific beam space regularization is used, which is composed of a stack of rigid sections. Large improvements on the residual, whose SNR evolves from 9.9 dB to 26.7 dB, validate the procedure

Etude expérimentale d'un matériau architecturé à comportement de second gradient du déplacement

Le récent développement des procédés d'obtention par méthode additive a relancé l'intérêt pour certains matériaux architecturés, type « treillis », qui n'étaient jusque-là que difficilement réalisables. Ces méta-matériaux présentent parfois des comportements homogénéisés complexes sortant du cadre de la modalisation élastique du premier gradient. La très grande majorité de leurs études sont alors théoriques ou numériques ([1] est une exception), et posent donc la question de leur validité : quelle est l'importance de ces effets « exotiques » sur un matériau architecturé réel, et à quel point ces matériaux sont-ils influencés par les défauts de fabrication ? La difficulté d'une approche expérimentale vient du fait que les méthodes de caractérisation standard ont été pensées dès le XIXe siècle dans le cadre de la théorie du premier gradient. Les conditions aux limites habituellement appliquées à chaque extrémité d'une éprouvette par une machine d'essai sont de type « translation principale uniforme ». Celles-ci imposent donc une cinématique globale propice à l'étude d'un comportement sensible au premier gradient de déplacement (une déformation de traction ou cisaillement uniforme dans la zone utile), mais contraignent la cinématique à des gradients de déformation a priori nuls (sauf à avoir une zone utile non homogène), et des déplacements aux limites complémentaires nuls, et limitent les gradients de déformation (sauf à avoir une zone utile non homogène). A titre d'illustration, le cas d'un essai de traction simple montre des conditions aux limites de déplacement homogène non nul selon l'axe de l'éprouvette, et nul perpendiculairement. L'effet de Poisson est existant mais l'amplitude des déplacements qu'il provoque est diminué par ces conditions limites. Aucun gradient de déformation selon l'axe principal ou selon l'axe perpendiculaire n'étant imposé, l'étude de comportement type second gradient est alors caduque (la région à proximité des conditions aux limites présente un gradient de déformation, mais est très limitée en terme de taille de zone observable). L'essor des techniques d'identification par mesure de champs cinématiques [2] permet de reconcevoir fondamentalement les méthodes d'essai : nul besoin d'une zone utile homogène. Au contraire, l'hétérogénéité est source de richesse. De la même manière, les moyens de sollicitation doivent évoluer et tendre vers des moyens de contrôle d'un champ, permettant d'imposer des gradients d'effort(s) ou de déformation. C'est dans cette approche que se situe l'étude proposée ici : développer un moyen d'essai utilisant une sollicitation de champ d'effort dans le plan de l'éprouvette et une mesure de champ de déplacement afin d'étudier des matériaux architecturés sensibles aux seconds gradients de déplacement. Le matériau architecturé choisi est similaire à un nid d'abeille produit industriellement (Flex-Core de Hexcel®). Il a une cellule présentant un seul plan de symétrie, ce qui implique des couplages entre premier et second gradients [3].   [1] J. Marty, J. Re?thore?, A. Combescure, Experimental investigation of higher-order homogenization schemes under large strain International Journal of Solids and Structures 88?89 (2016) 263-273 [2] M.A. Sutton, Computer Vision-Based, Noncontacting Deformation Measurements in Mechanics: A Generational Transformation, Applied Mechanics Reviews 65 (2013) [3] N. Auffray, J. Dirrenberger and G. Rosi, A complete description of bi-dimensional anisotropic strain-gradient elasticity, International Journal of Solids and Structures 69-70 (2015) 195-21

Damage Detection in a Polymer Matrix Composite from 4D Displacement Field Measurements

Standard Digital Volume Correlation (DVC) approaches enable quantitative analyses of specimen deformation to be performed by measuring displacement fields between discrete states. Such frameworks are thus limited by the number of scans (due to acquisition duration). Considering only one projection per loading step, Projection-based Digital Volume Correlation (P-DVC) allows 4D (i.e., space and time) full-field measurements to be carried out over entire loading histories. The sought displacement field is decomposed over a basis of separated variables, namely, temporal and spatial modes. In the present work, the spatial modes are constructed via scan-wise DVC, and only the temporal amplitudes are sought via P-DVC. The proposed method is applied to a glass fiber mat reinforced polymer specimen containing a machined notch, subjected to in situ cyclic tension and imaged via X-ray Computed Tomography. The P-DVC enhanced DVC method employed herein enables for the quantification of damage growth over the entire loading history up to failure

Experimental database of mixed-mode crack propagation tests performed on mortar specimens with a hexapod and full-field measurements. Part II: interactive loading

International audienceThis second paper presents a series of 4 crack propagation tests with the same experimental protocol as in a companion paper, but with some significant loading modifications. The first difference is that the loading is composed of in-plane rotation in addition to tension and shear translations. The second difference is that the loading is manually changed during the tests, depending on the crack tip location. This leads to tests with several bifurcations, and/or different loading ratios during the same test. One of them leads to mode I+II, and then mode I+III crack propagation. Some tests end with instabilities while others are controlled to be stable up to the complete failure of the specimen. In some cases, crack closure and friction between the crack faces occur

Development of a 3D model of clinically relevant microcalcifications

A realistic 3D anthropomorphic software model of microcalcifications may serve as a useful tool to assess the performance of breast imaging applications through simulations. We present a method allowing to simulate visually realistic microcalcifications with large morphological variability. Principal component analysis (PCA) was used to analyze the shape of 281 biopsied microcalcifications imaged with a micro-CT. The PCA analysis requires the same number of shape components for each input microcalcification. Therefore, the voxel-based microcalcifications were converted to a surface mesh with same number of vertices using a marching cube algorithm. The vertices were registered using an iterative closest point algorithm and a simulated annealing algorithm. To evaluate the approach, input microcalcifications were reconstructed by progressively adding principal components. Input and reconstructed microcalcifications were visually and quantitatively compared. New microcalcifications were simulated using randomly sampled principal components determined from the PCA applied to the input microcalcifications, and their realism was appreciated through visual assessment. Preliminary results have shown that input microcalcifications can be reconstructed with high visual fidelity when using 62 principal components, representing 99.5% variance. For that condition, the average L2 norm and dice coefficient were respectively 10.5 $\mu$m and 0.93. Newly generated microcalcifications with 62 principal components were found to be visually similar, while not identical, to input microcalcifications. The proposed PCA model of microcalcification shapes allows to successfully reconstruct input microcalcifications and to generate new visually realistic microcalcifications with various morphologies