Abstract The magnitude and distribution of strain imposed on the peripheral airspaces by mechanical ventilation at the microscopic level and the consequent deformations are unknown despite their importance for understanding the mechanisms occurring at the onset of ventilator-induced lung injury. Here a 4-Dimensional (3D + time) image acquisition and processing technique is developed to assess pulmonary acinar biomechanics at microscopic resolution. Synchrotron radiation phase contrast CT with an isotropic voxel size of 6 µm3 is applied in live anesthetized rats under controlled mechanical ventilation. Video animations of regional acinar and vascular strain are acquired in vivo. Maps of strain distribution due to positive-pressure breaths and cardiovascular activity in lung acini and blood vessels are derived based on CT images. Regional strain within the lung peripheral airspaces takes average values of 0.09 ± 0.02. Fitting the expression S = kV n , to the changes in peripheral airspace area (S) and volume (V) during a positive pressure breath yields an exponent n = 0.82 ± 0.03, suggesting predominant alveolar expansion rather than ductal expansion or alveolar recruitment. We conclude that this methodology can be used to assess acinar conformational changes during positive pressure breaths in intact peripheral lung airspaces.

We study a model of crowd motion following a gradient vector field, with possibly additional interaction terms such as attraction/repulsion, and we present a numerical scheme for its solution through a Lagrangian discretization. The density constraint of the resulting particles is enforced by means of a partial optimal transport problem at each time step. We prove the convergence of the discrete measures to a solution of the continuous PDE describing the crowd motion in dimension one. In a second part, we show how a similar approach can be used to construct a Lagrangian discretization of a linear advection-diffusion equation, interpreted as a gradient flow in Wasserstein space. We provide also a numerical implementation in 2D to demonstrate the feasibility of the computations.

Background: Morphometric changes in the lung alveolar and acinar structures induced by breathing remain largely unknown. This is due to a lack of non-destructive techniques allowing quantitative morphometry of the peripheral lung. Here, we propose a new method to quantify the morphometry of the distal lung in small animals. Methods: Using synchrotron radiation phase-contrast X-ray tomography, we acquired 3D images of intact adult rat lungs with a spatial resolution of 3 µm, immediately post-mortem at 0 and 6 cmH2O airway pressure (Paw). We used an « r- tubular neighborhood » of the solid phase, that is the part of the empty phase which is located at distance less than r from the solid phase, to assess the underlying geometrical structure. Results: Figure 1 represents a segmented view of the image obtained after preprocessing. We found a mean alveolar diameter of 55 and 78 µm at 0 and 6 cmH2O Paw, respectively, in a representative rat. Conclusions: Our data show that this novel approach is feasible and allows measuring the local size of alveoli in a robust way, and to investigate its dependence on Paw.

The following data can be used for benchmarking numerical simulations of crack propagation test on quasi-brittle materials. Two crack propagation tests are proposed here, close to the well-known Nooru-Mohamed tests, but with modern instrumentation so that they provide trustworthy data. They present initiation and propagation. The goal is to compare your simulation results with the measured crack paths and force-displacement curves. The input data consists in specimen geometry, experimentally determined material properties (Young modulus, tensile strength, compressive strength and fracture energy) and the measured boundary conditions.

This 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.

A new type of mixed mode crack propagation test is proposed. A single crack is initiated and propagates in a stable way up to complete failure. A combination of tensile, shear and in-plane rotation performed by a 6-axis testing machine is prescribed. The rotation creates a tension/compression gradient in the sample ensuring the stability, while the shear direction is closely related to the orientation of the crack and the tensile load is responsible for the actual propagation. The experiment is performed in an interactive manner, namely, depending on the crack tip position estimated by Digital Image Correlation (DIC) during the test, the loading is changed to bifurcate the crack. The displacements of the sample surfaces are assessed using multiple DIC measurements and displacement sensors. The displacement fields on each face of the sample give access to the crack pattern, and also to the actual boundary conditions that are crucial for a faithful numerical analysis of the test. Last, the 6 load components are recorded enabling for a complete description of the 3D mechanical behavior of the specimen.

The present study aims at proposing a new generation of experimental protocol for analysing crack propagation in quasi brittle materials. The boundary conditions are controlled in real-time to conform to a predefined crack path. Servo-control is achieved through a full-field measurement technique to determine the pre-set fracture path and a simple predictor model based on linear elastic fracture mechanics to prescribe the boundary conditions on the fly so that the actual crack path follows at best the predefined trajectory. The final goal is to identify, for instance, non-local damage models involving internal lengths. The validation of this novel procedure is performed via a virtual test-case based on an enriched damage model with an internal length scale, a prior chosen sinusoidal crack path and a concrete sample. Notwithstanding the fact that the predictor model selected for monitoring the test is a highly simplified picture of the targeted constitutive law, the proposed protocol exhibits a much improved sensitivity to the sought parameters such as internal lengths as assessed from the comparison with other available experimental tests.

In order to experimentally validate concrete damage models and better characterize the concrete behavior during mixed-mode crack propagation, multiaxial tests are developed. The goal is to perform rich and discriminating tests by using state of the art techniques. The loadings are applied using a hexapod controlled by a 3D displacement system and the cracking state is analyzed via digital image correlation. To probe its consistency the experimental results are compared to numerical simulations with a nonlocal (i.e., gradient-based) damage model. The importance of using accurate boundary conditions while performing the numerical simulations is underlined. The numerical simulations are congruous to the experimental results only when full-field boundary conditions are prescribed, and only in that case it is possible to evaluate the validity or more generally the parameter sensitivity of the damage/fracture model under investigation.

The identification of the parameters of several constitutive laws is performed with the integrated digital image correlation (IDIC) technique in a biaxial experiment for a cruciform specimen made of stainless steel. The sought material parameters are assessed with the contribution of both reaction forces (from load sensors) and displacement fields (measured via digital image correlation). For each constitutive law a global residual quantifying the model error is assessed.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Public Domain Toward 4D Mechanical Correlation François Hild, Amine Bouterf, Ludovic Chamoin, Hugo Leclerc, Florent Mathieu, Jan Neggers, Florent Pled, Zvonimir Tomičević, Stéphane Roux

The goal of the present study is to illustrate the full integration of sensor and imaging data into numerical procedures for the purpose of identification of constitutive laws and their validation. The feasibility of such approaches is proven in the context of in situ tests monitored by tomography. The bridging tool consists of spatiotemporal (i.e., 4D) analyses with dedicated (integrated) correlation algorithms. A tensile test on nodular graphite cast iron sample is performed within a lab tomograph. The reconstructed volumes are registered by resorting to integrated digital volume correlation (DVC) that incorporates a finite element modeling of the test, thereby performing a mechanical integration in 4D registration of a series of 3D images. In the present case a non-intrusive procedure is developed in which the 4D sensitivity fields are obtained with a commercial finite element code, allowing for a large versatility in meshing and incorporation of complex constitutive laws. Convergence studies can thus be performed in which the quality of the discretization is controlled both for the simulation and the registration. Incremental DVC analyses are carried out with the scans acquired during the in situ mechanical test. For DVC, the mesh size results from a compromise between measurement uncertainties and its spatial resolution. Conversely, a numerically good mesh may reveal too fine for the considered material microstructure. With the integrated framework proposed herein, 4D registrations can be performed and missing boundary conditions of the reference state as well as mechanical parameters of an elastoplastic constitutive law are determined in fair condition both for DVC and simulation.

The measurement of three dimensional displacement fields from tomographic image registration, or Digital Volume Correlation, usually operates over two volumes that have been reconstructed from numerous radiographs at the elementary voxel scale. It is shown herein that a single "reference" (i.e., fully reconstructed) volume, and very few radiographs of the deformed configuration may be sufficient to evaluate 3D displacement fields. The proposed algorithm can reduce the needed number of projection data by several orders of magnitude as shown on an experimental data set.

DIC-based identification of the constitutive parameters of an elastoplastic law is addressed both from a general viewpoint, and applied to the particular case of dog-bone sample made of commercially pure titanium and subjected to tensile loading. A two-step procedure (Digital Image Correlation — DIC — followed by weighted Finite Element Method Updating — FEMU) is first presented. These two steps can be merged into a single-step procedure (i.e., Integrated-DIC or I-DIC). In both cases, the elastoplastic computations are performed with a commercial code (i.e., non-intrusive identification). When the suited weighting of FEMU is taken into account, which is based on DIC-processed image noise, both I-DIC and FEMU methods provide similar results. It is shown that the addressed experimental case requires the use of static (load) information to get precise estimates of the sought parameters.

Performing a single but complex mechanical test on small structures rather than on coupons to probe multiple strain states/histories for identification purposes is nowadays possible thanks to full-field measurements. The aim is to identify many parameters thanks to the heterogeneity of mechanical fields. Such an approach is followed herein, focusing on a blade root made of 3D woven composite. The performed test, which is analyzed using global Digital Image Correlation (DIC), provides heterogeneous kinematic fields due to the particular shape of the sample. This displacement field is further processed to identify the four in-plane material parameters of the macroscopic equivalent orthotropic behavior. The key point, which may limit the ability to draw reliable conclusions, is the presence of acquisition noise in the original images that has to be tracked along the DIC/identification processing to provide uncertainties on the identified parameters. A further regularization based on a priori knowledge is finally introduced to compensate for possible lack of experimental information needed for completing the identification.

A method based upon the sensitivity fields is proposed to optimize biaxial experimental procedures. The objective is to improve the identifiability of elastic parameters related to an a priori chosen constitutive law. This is achieved by minimizing the covariance matrix of the material parameters. This approach unifies full field measurements via image correlation, numerical simulations and identification procedure. The latter is performed on a biaxial experiment and aims at identifying elasto-plastic models.

The objective of the present study is to propose a protocol and a criterion to guide the design of specimen shape but also loading history to lower the sensitivity of the identified parameters to the measurement uncertainties. The identification quality of constitutive parameters is both related to the experimental procedures and the identification methods. In the measurement work, the identification quality is estimated by the covariance matrix of the identified material parameters [1, 2]. It accounts for different aspects of the problem, namely, the geometry of the studied structure, the chosen constitutive law, the set of parameters, the boundary conditions, the measurement uncertainties, the identification method and to a lesser extent the numerical simulation method. It is written relatively to the two identification techniques followed herein (i.e., Finite Element Updating Method (FEMU) and Integrated Digital Image Correlation (I-DIC) [3]). The first one consists of computing the set of constitutive parameters that minimize the displacement error χ

The minimization of the number of experimental tests to characterize the material behavior continues to be an important challenge. The main aim of this work is to set up a relevant and discriminating concrete fracture test, able to fully investigate its complex mechanical behavior within a single run. Therefore a hybrid cracking test on a concrete sample with controlled stress intensity factors (SIFs) is currently developed. Prior to the real test, a virtual one is conceived to validate the principle of the proposed hybrid test.

This work focuses on the influence of light reflection on Digital Images Correlation results at the macroscopic scale, and on a way to circumvent this problem. It shows that the local displacement uncertainty rises up to 5 times the usual one when a reflection occurs. An observation of the topography of the speckle reveals an important sub-pixel roughness that explains the grey level fluctuations at the pixel scale, spoiling the calculation of the gradient of the texture. To circumvent this problem, a new DIC algorithm is proposed, based on a single minimization with several pairs of images where the reflections are located in different regions. For each image, weighting functions are used to ‘exclude’ the reflection regions from the calculation, while the necessary information is obtained from the other images.