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The work deals with a macroscopically isotropic energetic material based on triamino-trinitrobenzene (TATB) crystals bonded with a small volume fraction of a thermoplastic polymer. This material is shown experimentally to display an irreversible thermal expansion behavior characterized by dilatancy and variations of its thermal expansion coefficient when heated or cooled outside a narrow reversibility temperature range. The analysis of cooling results suggests the existence of residual stresses in the initial state, attributed to the manufacturing process. Microstructure-level FFT computations including the very strong anisotropic thermoelastic TATB crystal response and temperature-dependent binder plasticity, show that strong internal stresses develop in the disoriented crystals under thermal load, either heating or cooling. Upon cooling, binder plastic yielding in hindered, thus promoting essentially brittle microcracking, while it is favored upon heating. Despite its low volume fraction, the role of the binder is essential, its plastic yielding causing stress redistribution and residual stresses upon cooling back to ambient.

International audience; The electronic conductivity, at the multiscale, of lithium-ion positive composite electrodes based on LiNi_{1/3}Mn_{1/3}Co_{1/3}O_2 and/or carbon-coated LiFePO_4, carbon black and poly(vinylidene fluoride) mixture is modeled. The electrode microstructures are acquired numerically in 3D by X-ray tomography and FIB/SEM nanotomography and numerically segmented to perform electrostatic simulations using Fast Fourier Transform (FFT) method. Such simulations are easy and quick to perform because they are directly computed on the grid represented by the voxels in the 3D volumes. Numerical results are compared with experimental measurements of the multiscale electronic conductivity by broadband dielectric spectroscopy (BDS). A good prediction is realized for the bulk conductivities of the C/LiFePO_4 phase and the CB/PVdF mixture. The combination of X-ray and FIB/SEM tomography, FFT simulation method, and BDS is thus well adapted to understand the influence of the electrode composition and microstructure on its electronic conductivity.

International audience; In this article an “hyper-reduced” scheme for the Crisfield’s algorithm (Crisfield, 1981) applied to buckling simulations and plastic instabilities is presented. The two linear systems and the ellipse equation entering the algorithm are projected on a reduced space and solved in a reduced integration domain, resulting in a system of “hyper-reduced” equations. Use is made of the Gappy proper orthogonal decomposition to recover stresses outside the reduced integration domain. Various methods are proposed to construct a reduced bases, making use of simulation data obtained with standard finite element method and a stress-based error criterion for the hyper reduced calculations is proposed. A “greedy” algorithm coupled with this error criterion is used to generate intelligently full standard finite element simulations and enrich the reduced base, demonstrating the adequacy of the error criterion. Finally, numerical results pertaining to elastoplastic structures undergoing finite strains, with emphasis on buckling and limit load predictions are presented. A parametric study on the geometry of the structure is carried out in order to determine the domain of validity of the proposed hyper-reduced modeling approach.

We develop a methodology for classifying defects based on their morphology and induced mechanical response. The proposed approach is fairly general and relies on morphological operators (Angulo and Meyer in 9th international symposium on mathematical morphology and its applications to signal and image processing, pp. 226-237, 2009) and spherical harmonic decomposition as a way to characterize the geometry of the pores, and on the Grassman distance evaluated on FFT-based computations (Willot in C. R., Méc. 343(3):232–245, 2015), for the predicted elastic response. We implement and detail our approach on a set of trapped gas pores observed in X-ray tomography of welded joints, that significantly alter the mechanical reliability of these materials (Lacourt et al. in Int. J. Numer. Methods Eng. 121(11):2581–2599, 2020). The space of morphological and mechanical responses is first partitioned into clusters using the “k-medoids” criterion and associated distance functions. Second, we use multiple-layer perceptron neural networks to associate a defect and corresponding morphological representation to its mechanical response. It is found that the method provides accurate mechanical predictions if the training data contains a sufficient number of defects representing each mechanical class. To do so, we supplement the original set of defects by data augmentation techniques. Artificially-generated pore shapes are obtained using the spherical harmonic decomposition and a singular value decomposition performed on the pores signed distance transform. We discuss possible applications of the present method, and how medoids and their associated mechanical response may be used to provide a natural basis for reduced-order models and hyper-reduction techniques, in which the mechanical effects of defects and structures are decorrelated (Ryckelynck et al. in C. R., Méc. 348(10–11):911–935, 2020).

International audience; Experimental conductivity measurements, obtained on NMC 532 -based electrodes with markedly different porosities and made with percolating and non-percolating CB/PVdF phase, are compared with full-field numerical predictions. These ones are based on segmented nanotomography images and phase bulk properties and contain no tunable parameter. A good agreement between the calculated and measured transport properties is observed. 3D current density fields give insights on the microstructure impacts on the current density distribution. Ionic transport is dominated by low tortuosity micrometric channels. Results also highlight the presence of “dead areas” in porosity that are crossed by a very low ionic current showing that, at high rate, the effective porosity may reduce to the micrometric pore network. For electronic conductivity, the CB/PVdF mixture percolation threshold is evaluated at 6%–7% in volume. Even below this key value threshold, CB/PVdF aggregates significantly improve electronic conductivity by forming gateways between NMC clusters thus minimising the constriction resistances between them. The size of the representative volume element relative to electronic and ionic conductivities is also investigated.

Better understanding of how the microstructure of composite electrodes affect their electrochemical performance is still required to achieve Lithium ion batteries of higher energy and power densities [1]. Novel opportunity for progressing in this direction and explore relationships between composite electrode microstructure and electrochemical performance is implementation of X-ray computed tomography (XRCT) and focused ion beam in combination with scanning electron microscopy (FIB-SEM) techniques [2]. Sophisticated characterization techniques such as broadband dielectric spectroscopy (BDS) [3] and/or Pulsed Field Gradient Spin - Echo NMR (PFG-SE NMR) [4] can also be used to measure transport properties and relate them to the composite electrode microstructure. Finally, numerical simulations performed on 3D volumes acquired by XRCT or FIB/SEM is a powerful tool to calculate effective transport properties and finely analyze the impact of the composite electrode microstructure [5]. In this work, the microstructure of LiNi0.5Mn0.3Co0.2O2 (hereafter called NMC532)-based positive composite electrodes designed for EV applications were deeply investigated in relationship with their electrical properties. The composite electrode microstructures were acquired numerically in 3D at different scales by X-ray tomography and FIB-SEM tomography. Image analysis tools were developed to extract specific textural parameters (e.g. distribution and percolation of the carbon/binder mixture, type and tortuosity of the porosity, contact area of the active material with these other phases) to assess the electronic and ionic conductivities at different locations and spatial scales. In complement, 3D-resolved simulations with the Fast Fourier Transform (FFT) method were carried out to calculate the effective electronic and ionic conductivities of the composite electrodes and characterize the local current density paths for both type of charges (electrons and ions). From our results, it becomes apparent that it is possible to find a good compromise between the electronic and ionic conductivities that results in improved electrochemical performance by optimizing the microstructure. Acknowledgments Financial funding from the ANR program no. ANR-15-CE05-0001-01 is acknowledged. We also acknowledge the CLYM (Consortium Lyon Saint-Etienne de Microscopie) for the access to the FIB/SEM device used in this study. References [1] D. Mohanty, E. Hockaday, J. Li, D.K. Hensley, C. Daniel, D.L. Wood III, Effect of electrode manufacturing defects on electrochemical performance of lithium-ion batteries: Cognizance of the battery failure sources, J. Power Sources 2016, 312, 70-79. [2] N. Besnard, A. Etiemble, T. Douillard, O. Dubrunfaut, P. Tran-Van, L. Gautier, S. Franger, J.-C. Badot, E. Maire, B. Lestriez, Multiscale morphological and electrical characterization of charge transport limitations to the power performance of positive electrode blends for lithium-ion batteries, Adv. Energy Mater, 2017, 7, 1602239. [3] J.-C. Badot, B. Lestriez, O. Dubrunfaut, Interest in broadband dielectric spectroscopy to study the electronic transport in materials for lithium batteries, Mater. Sci. Eng. B - Adv. Funct. Solid-State Mater., 2016, 213, 190-198. [4] S. J. Tambio, M. Deschamps, V. Sarou-Kanian, A. Etiemble, T. Douillard, E. Maire, B. Lestriez, Self-Diffusion of Electrolyte Species in Model Battery Electrodes Using Magic Angle Spinning and Pulsed Field Gradient Nuclear Magnetic Resonance, J. Power Sources, 2017, 362, 315-322. [5] F. Cadiou, F. Willot, B. Lestriez, T. Douillard, A. Etiemble, J-C. Badot, O. Valentin, E. Maire, Numerical simulation of effective electrical conductivity of Lithium-ion battery positive electrodes, J. Electrochem. Soc., 2019, 166, A1692-A1703. Figure 1

International audience; Cold spray is a promising process to coat polymers and carbon fiber-reinforced polymer (CFRP). Thechoice of the metal-polymer couple of materials, however, has a strong influence on coating build-upand properties. In the present work, we show that spraying mixtures of copper and polymer particleslead to composite coating. We observe that the polymer promotes coating build-up onto CFRP to theexpense of the electrical conductivity of the coating as a result of its insulating properties. The presentwork investigates the influence of the coating microstructure on electrical conductivity. Various copperpowders, with different morphologies, particle sizes and oxygen contents were mixed with a PEEK(Polyaryl-Ether-Ether-Ketone) powder. Cold spray of these powders resulted into composite coatingsand we study the microstructures and electrical properties of such coatings as a function of powdercharacteristics and spraying parameters. A morphological model of the coating microstructure wasdeveloped to reproduce numerically microstructures in 3D. The conductivity of the coatings wasmeasured experimentally for various copper powders. Careful selection of blends of copper and PEEKpowders coupled with optimized spraying parameters led to metal-polymer coatings onto CFRP with afairly high electrical conductivity.

International audience; Effective conductivity and permeability of a versatile, graph-based model of random structures are investigated numerically. This model, originally introduced in Gaiselmann et al. (2014) allows one to simulate a wide class of realistic materials. In the present work, an extensive dataset of two-phase microstructures with wide-ranging morphological features is used to assess the relationship between microstructure and effective transport properties, which are computed using Fourier-based methods on digital images. Our main morphological descriptors are phase volume fractions, mean geodesic tortuosity, two “hydraulic radii” for characterizing the length scales of heterogeneities, and a “constrictivity” parameter that describes bottleneck effects. This additional parameter, usually not considered in homogenization theories, is an essential ingredient for predicting transport properties, as observed in Gaiselmann et al. (2014). We modify the formula originally developed in Stenzel et al. (2016) for predicting the effective conductivity and propose a formula for permeability. For the latter one, different geometrical definitions of the hydraulic radius are compared. Our predictions are validated using tomographic image data of fuel cells.

International audience; This work addresses the problem of the reconstruction of the local fields distribution occurring in heterogeneous linear elastic solids. The constitutive heterogeneities are crystals and cracks. Through comparisons with FFT computations, it is shown that self-consistent estimates together with an assumption of normal distribution at the phase scale provide an accurate description of the elastostatic field histograms in polycrystals without cracks. In the case of inter and transgranular cracks, full-field FFT simulations indicate that the field histograms present van Hove singularities. Their natures are determined analytically in the low-density regime, in the case of an homogeneous medium containing cracks.

International audience; The thermoelastic responses of a cracked TATB polycrystal is modeled using Fourier-based numerical computations and linear homogenization estimates. The numerical method is based on a Fourier scheme previously investigated (Gasnier et al., 2018) and the homogenization schemes include a new self-consistent estimate recently developed for cracked polycrystals. The effect of various populations of intergranular and transgranular microcracks are compared, with special attention to thermal behavior in the percolating regime. A model of micro-cracks is proposed for the TATB material in its initial state and the variations of the volumetric expansion coefficient of the TATB polycrystal under thermal cycles, during cooling and heating, are interpreted.

International audience; The influence of a population of randomly-oriented cracks on the macroscopic thermal and linear-elastic response of a hexagonal polycrystal is addressed using a self-consistent method. Coupling between micro-cracks and crystal anisotropy is taken into account through the effective medium where all inhomogeneities are embedded. In the absence of cracks, the proposed approach reduces to the self-consistent estimate of Berryman (2005). The accuracy of the present method is first assessed using numerical, Fourier-based computations. In the absence of crystal anisotropy, the estimates for the effective elastic properties are close to that obtained numerically for a homogeneous body containing disk-shaped cracks, with Boolean spatial dispersion. Various other analytical estimates and bounds, that are available for homogeneous cracked bodies, are also considered and compared to the present approach. Second, the combined role of crystal anisotropy and micro-cracks is investigated analytically, specifically when the in-plane shear modulus of the crystal becomes zero. The cracks-density perco-lation threshold is found to diminish abruptly in this limit. This "advanced" percolation threshold is concomitant to the onset of large, weakly-loaded regions surrounding cracks in strongly-anisotropic crystals.

Preface to a special issue of the International Journal of Solids and Structures. This is not a research article.; International audience; This volume gathers contributions presented at the International Workshop on Physics and Mechanics of Random Structures: From Morphology to Material Properties held on the Ile d’Oléron (Atlantic coast, France), June 17–22, 2018 (Willot and Forest, 2018; Oleron, 2019). This exceptional workshop was organized on the occasion of the (official) retirement of Prof. Dominique Jeulin from his position at Mines ParisTech, where he has been working for more than 30 years to the development of mathematical morphology and physics and mechanics of random media.

International audience; Impact experiments were performed at the french-german research Institute of Saint-Louis on three energetic materials composed of 70 % in weight of RDX particles embedded in a wax matrix. These materials differ by the microstructural properties of the explosive particles. The experimental results reveal that the detonation thresholds, and so the sensitivity to shock, are different for each sample. To better understand these results, we characterize the microstructural properties of these compositions. The microstructures of the three materials are imaged with micro-computed tomography (µCT) at CEA Gramat. First, the 3D µCT images are filtered and segmented. Then, an analysis of the segmented volume is performed (granulometry, covariance and weight fraction). Each labeled grain is extracted and characterized by several descriptors such as volume, surface, angularity, sphericity or intra-granular porosity. Virtual microstructures are generated with the extracted grains. Each grain is precisely selected depending on its properties to generate a controlled microstructure. This allows to modify only one microstructural parameter at a time. The virtual microstructures are built to be consistent with the global analysis of the µCT segmented volumes. They respect both morphological granulometry and spatial covariance of the µCT segmented volumes. These numerical materials are intended to be used in mesoscale finite element simulations to study the effects of the microstructure on the shockwave propagation.

International audience; In view of a better understanding of the thermomechanical behavior of pressed explosives, a Fourier-based computational tool is used to perform numerical homogenization and compare predictions to experimental macroscopic properties. This is first done in a purely thermoelastic context on simplified polycrystalline virtual microstructures, then extended to cracked polycrystalline ones. A further extension is proposed, aiming at predicting the nucleation and propagation of (micro)-cracks. Besides, a mean-field (self-consistent) approach is also followed, providing accurate thermoelastic predictions. It is currently being extended to account for linear (non-ageing) viscoelasticity of the binder. The study of irreversible deformation mechanisms of the TATB crystal, in view of their incorporation in the full-field tool, is the subject of the companion paper.

International audience; In previous work, impact experiments were performed at ISL on three energetic materials composed of 70% in weight of RDX particles embedded in a wax matrix. These materials differ by the microstructural properties of the explosive particles. The experimental results reveal that the detonation thresholds, and so the sensitivity to shock, are different for each sample. To better understand these results, we characterize the microstructural properties of these compositions and generate virtual microstructures representative of the real microstructures. First, the microstructures of the three materials are imaged with micro-computed tomography (µCT). The 3D µCT volumes are filtered and segmented. Image processing results are crosschecked with experimental analyses conducted at ISL (weight fraction, particles diameter distribution and particles bulk density distribution) to ensure the reliability of the segmentations. Virtual microstructures of each material are generated with real grains of RDX extracted from the segmented volumes. The virtual microstructures are built to be consistent with the µCT segmented volumes. The morphological granulometry and the spatial covariance of both real and virtual microstructures are compared to verify that the numerical materials are representative of the real materials.

International audience; We compare two conceptually different stochastic microstructure models , i.e., a graph-based model and a pluri-Gaussian model, that have been introduced to model the transport properties of three-phase microstructures occurring, e.g., in solid oxide fuel cell electrodes. Besides comparing both models, we present new results regarding the relationship between model parameters and certain mi-crostructure characteristics. In particular, an analytical expression is obtained for the expected length of triple phase boundary per unit volume in the pluri-Gaussian model. As a case study, we consider 3D image data which show a representative cutout of a solid oxide fuel cell anode obtained by FIB-SEM tomography. The two models are fitted to image data and compared in terms of morphological characteristics (like mean geodesic tortuosity and constrictivity) as well as in terms of effective transport properties. The Stokes flow in the pore phase and effective conductivities in the solid phases are computed numerically for realizations of the two models as well as for the 3D image data using Fourier methods. The local and effective physical responses of the model realizations are compared to those obtained from 3D image data. Finally, we assess the accuracy of the two methods to predict permeability as well as electronic and ionic conductivities of the anode.

International audience; The granular structures of energetic materials made of hexogene particles embedded in a matrix are characterized using a combination of flotation, light-scattering measurements and micro-computed tomography images. The complementary nature of the three characterization techniques, when employed with this type of material, allows one to derive accurate estimates for the grain size distribution and the particle bulk density distribution. Three types of granular formulations, with the same weight fraction of particles but markedly different grains morphology and shock-sensitivity properties, are addressed. The particles granulometry and intra-granular porosities differ from one material to another. The grains spatial dispersion in the three formulations, characterized by the scale-dependent local density, also varies from one formulation to another. Specifically, we show that samples containing elongated grains display “abnormal” variance scalings for the grains local density, as a result of long-range correlations in the granular packing structure. The use of virtual microstructures to predict the materials mechanical properties is addressed and discussed.

A general method is proposed to model 3D microstructures representative of three-phases anode layers used in fuel cells. The models are based on SEM images of cells with varying morphologies. The materials are first characterized using three morphological measurements: (cross-)covariances, granulometry and linear erosion. They are measured on segmented SEM images, for each of the three phases. Second, a generic model for three-phases materials is proposed. The model is based on two independent underlying random sets which are otherwise arbitrary. The validity of this model is verified using the cross-covariance functions of the various phases. In a third step, several types of Boolean random sets and plurigaussian models are considered for the unknown underlying random sets. Overall, good agreement is found between the SEM images and three-phases models based on plurigaussian random sets, for all morphological measurements considered in the present work: covariances, granulometry and linear erosion. The spatial distribution and shapes of the phases produced by the plurigaussian model are visually very close to the real material. Furthermore, the proposed models require no numerical optimization and are straightforward to generate using the covariance functions measured on the SEM images.

International audience; The mechanical role of the shape of the aggregates, and their spatial distribution in concrete materials is examined. The effect on the macroscopic mechanical response as well as on the local stress fields are investigated by numerical means, making use of a recently developed Poisson-polyhedra model in which the aggregates have polyhedral shapes. Comparison is made with previous microstructure models of spheres. Full-field computations are carried out on large volume size using Fourier methods. The field maps are used to determine zones of highest stress. Furthermore, the scale separation hypothesis for the computation of the elastic properties is investigated using numerical calculations on various multiscale microstructures. Finally, numerical predictions for the elastic properties are compared to experimental measurements, and the results discussed.

International audience; This study is part of a work dedicated to predicting the overall thermoelastic properties of microcracked polycrystals. In the present part, the suitability of Fourier-based methods to estimate the mechanical response of a homogeneous body containing cracks is explored. The effect of the Green operator's discretization on the local elastic fields surrounding the crack's tip is investigated and compared with exact and finite elements solutions. The biases inherent to the Fourier method, namely the effects of grid discretization and crack orientation relative to the grid, are scrutinized. A way to quantify and overcome these biases is given, therefore providing a low resource demanding method to deal with thousands of microcracks embedded in a polycrystal, object of the companion paper.

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This work focuses on a mesoporous material made of nanometric alumina "platelets" of unknown shape. We develop a 3D random microstructure to model the porous material , based on 2D Transmission Electron Microscopy (TEM) images, without prior knowledge on the spatial distribution of alumina inside the material. The TEM images , acquired on samples with thickness 300 nm, a scale much larger than the platelets's size, are too blurry and noisy to allow one to distinguish platelets or platelets aggregates individually. In a first step, the TEM images correlation function and integral range are estimated. The presence of long-range fluctuations, due to the TEM inhomogeneous detection , is detected and corrected by filtering. The corrected correlation function is used as a morphological descriptor for the model. After testing a Boolean model of platelets, a two-scales model of microstructure is introduced to replicate the statistical dispersion of platelets observed on TEM images. Accordingly a set of two-scales Boolean models with varying physically-admissible platelets shapes is proposed. Upon optimization, the model takes into account the dispersion of platelets in the microstructure as observed on TEM images. Comparing it to X-ray diffraction and nitrogen porosimetry data, the model is found to be in good agreement with the material in terms of specific surface area.

International audience; The Stokes flow is numerically computed in porous media based on 3D Boolean random sets of spheres. Two configurations are investigated in which the fluid flows inside the spheres or in the complementary set of the spheres. Full-field computations are carried out using the Fourier method of Wiegmann (2007). The latter is applied to large system sizes representative of the microstructure. The overall permeability of the two models as well as the representative volume element are estimated as a function of the pore volume fraction. We give numerical estimates for the asymptotic behavior of the permeability in the dilute limit for the solid phase, and close to the percolation threshold of the pores. FFT maps of the velocity field are presented, for increasing values of the pore volume fraction. The patterns of the local velocity field is analyzed using various morphological criteria. The tortuosity of the streamlines is found to be much higher than the geometrical tortuosity, for both models. The histograms of the velocity field are computed at increasing pore volume fraction. The covariance of orientation is used to characterize the spatial correlation of the velocity field.

This paper aims at developing a random morphological model for concrete microstructures. A 3D image of concrete is obtained by microtomography and is used in conjunction with the concrete formulation to build and validate the model through morphological measurements. The morphological model is made up of two phases, corresponding to the matrix, or cement paste and to the aggregates. The set of aggregates in the sample is modelled as a combination of Poisson polyhedra of different scales. An algorithm is introduced to generate polyhedra packings in the continuum space. The latter is validated with morphological measurements.

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v2: fixed an undefined reference to a Mathematica webpage (ref [26] in v2).; International audience; This work focuses on the variance properties of isotropic Boolean random sets containing randomly-oriented cylinders with circular cross-section. Emphasis is put on cylinders with large aspect ratios, of the oblate and prolate types. A link is established between the powerlaw decay of the covariance function and the variance of the estimates of the volume fraction of cylinders. The covariance and integral range of the Boolean mixtures are expressed in terms of the orientation-averaged covari-ogram of cylinders, for which exact analytical formulas and approximate expressions are provided.

International audience; By employing multi-scale random models of c-alumina, we have studied the influence of porosity, grain aspect ratio and aggregation state on the effective diffusion coefficient. Multi-scale Boolean models of platelets were used to produce digital volumes reproducing the alumina porous space. Iterative fast Fourier transform numerical simulation of Fick's diffusion were performed on the volume to obtain the effective diffusion coefficient. The tortuosity factors of the various simulated models show a simple dependence with pore volume fraction with an exponent guided by the platelet aspect ratio and the aggregation state. Comparisons with proton pulsed-field gradient nuclear magnetic resonance spectrometry show a satisfactory agreement.

Pore structures have a major impact on the transport and electrical properties of electrochemical devices, such as batteries and electric double-layer capacitors (EDLCs). In this work we are concerned with the prediction of the electrical conductivity, ion diffusivity and volumetric capacitance of EDLC electrodes, manufactured from hierarchically porous carbons. To investigate the dependence of the effective properties on the pore structures, we use a structurally resolved parametric model of a random medium. Our approach starts from 3D FIB-SEM imaging, combined with automatic segmentation. Then, a random set model is fitted to the segmented structures and the effective transport properties are predicted using full field simulations by iterations of FFT on 3D pore space images and calculations based on the geometric properties of the structure model. A parameter study of the model is used to investigate the sensitivity of the effective conductivity and diffusivity to changes in the model parameters. Finally, we investigate the volumetric capacitance of the EDLC electrodes with a geometric model, make a comparison with experimental measurements and do a parameter study to suggest improved microstructures. Fil: Prill, Torben. Fraunhofer ITWM; Alemania Fil: Jeulin, Dominique. Fraunhofer ITWM; Alemania Fil: Willot, François. Fraunhofer ITWM; Alemania Fil: Balach, Juan Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Química; Argentina Fil: Soldera, Flavio. Universitat Saarland; Alemania

A modified Green operator is proposed as an improvement of Fourier-based numerical schemes commonly used for computing the electrical or thermal response of heterogeneous media. Contrary to other methods, the number of iterations necessary to achieve convergence tends to a finite value when the contrast of properties between the phases becomes infinite. Furthermore, it is shown that the method produces much more accurate local fields inside highly-conducting and quasi-insulating phases, as well as in the vicinity of the phases interfaces. These good properties stem from the discretization of Green's function, which is consistent with the pixel grid while retaining the local nature of the operator that acts on the polarization field. Finally, a fast implementation of the "direct scheme" of Moulinec et al. (1994) that allows for parcimonious memory use is proposed.

This is a preface to a special issue of IA&S, not a research article; International audience; A few words on the present special topic, devoted to the multiscale modeling of granular media, and published in honor of Prof. Dominique Jeulin's enduring contribution to the wide field of image analysis, random structures and material science.

This work is a combined analytical and numerical study of the extreme values of the thermal and elastic fields occurring in a propellant composite material, a granular medium containing dense self-assembled spheroidal grains embedded in a matrix. First, a 3D microtomography image of a representative sample is segmented using morphological operators. Second, the local temperature and heat flux in the quasi-static thermal response is computed numerically, making use of the segmented microstructure and of experimental values of the heat conductivity in each phase. Such fields are readily derived by means of a Fast Fourier Transform method. Emphasis is put on the maximum values of the local fields: even at low contrast of properties between the grain and the matrix, the heat flux patterns is made of hot-spot zones located in-between grains that are close to each other with preferential directions. Third, the local extrema of the fields are investigated in the context of linear elasticity. Finally, analytical approximations are examined at low and high contrast of properties, on a simple hard-core model of cylinders, which is tantamount to a 2D granular microstructure.

International audience; Numerical and analytical results on the permeability of Boolean models of randomly-oriented cylinders with circular cross-section are reported. The present work investigates cylinders of prolate (highly-elongated) and oblate (nearly flat) types. The fluid flows either inside or outside of the cylinders. The Stokes flow is solved using full-fields Fourier-based computations on 3D binarized microstructures. The permeability is given for varying volume fractions of pores. A new upper-bound is derived for the permeability of the Boolean model of oblate cylinders. The behavior of the permeability in the dilute limit is discussed.

International audience; This study concerns the prediction of the elastic properties of a 3D mortar image, obtained by micro-tomography, using a combined image segmentation and numerical homogenization approach. The microstructure is obtained by segmentation of the 3D image into aggregates, voids and cement paste. Full-fields computations of the elastic response of mortar are undertaken using the Fast Fourier Transform method. Emphasis is made on highly-contrasted properties between aggregates and matrix, to anticipate needs for creep or damage computation. The Representative Volume Element, i.e. the volume size necessary to compute the effective properties with a prescribed accuracy, is given. Overall, the volumes used in this work were sufficient to estimate the effective response of mortar with a precision of 5%, 6% and 10% for contrasts ratio of 100, 1000 and 10000, respectively. Finally, a statistical and local characterization of the component of the stress field parallel to the applied loading is carried out.

International audience; The overall mechanical response as well as strain and stress field statistics of an heterogeneous material made of two randomly distributed, linear elastic phases, are investigated numerically. The Boolean model of spheres is used to generate microstructures consisting of either porous or rigid inclusions, at any volume fraction of the phases. Stress and strain field integral ranges, or equivalently the representative volume element, are computed and linked to features of the field statistics, and to the microstructure geometry.

International audience; Images of a hematite-based epoxy coating are obtained by scanning electron microscopy (SEM). At the scale of a few micrometers, they show aggregates of hematite nano-particles organized along thin curved channels. We first segment the images and analyze them using mathematical morphology. The heterogeneous dispersion of particles is quantified using the correlation function and the granulometry of the embedding (epoxy) phase. Second, a two-scales, 3D random microstructure model with exclusion zones is proposed to simulate the spatial distribution of particles. This simple model is parametrized by four geometrical parameters related to the exclusion zones solely. The microstructure is numerically optimized, in the space of morphological parameters, on the granulometry of the embedding epoxy phase and on the microstructure correlation function, by standard gradient-descent methods. Excellent agreement is found between the SEM images and our optimized model. Finally, the size of the representative volume element associated to the optimized microstructure model is compared with that of the SEM images.