Dominique Jeulin

Mines Paris, PSL University | ParisTech · Département Mathématiques et Systèmes (MINES ParisTech)

Complex large models of multi-scale microstructures of porous media do not exist in a manner adequately efficient to render their comprehensive analysis of textural and structural properties possible. The simulation of experimental processes, such as gas adsorption, raises two issues. First, the modeling of these complex materials must be sufficien...

Complex large models of multi-scale microstructures of porous media do not exist in a manner adequately efficient to render their comprehensive analysis of textural and structural properties possible. The simulation of experimental processes, such as gas adsorption, raises two issues. First, the modeling of these complex materials must be sufficien...

Random sets models derived from truncated RF, with an application to Gaussian random functions, are introduced. Covariance and order m central correlation functions are given. The model is illustrated by examples of application.

This chapter introduces the mosaic model, where subdomains of space have a constant value (univariate or multivariate). It is built on a random tessellation of space. Its Choquet capacity is given and illustrated by order two and order three probability distributions. Special cases are the Poisson and the STIT mosaic models.

Sequential random function models, intermediary between the Boolean RF and the Dead Leaves RF, are built from primary RF by alternating the operations ˅ and ˄. These types of models might simulate rough surfaces evolving by a sequence of depositions and abrasions. After the construction of this model, the univariate and bivariate distributions are...

The Dilution RF (DRF) combines primary RF located on Poisson points by addition. The Dilution RF is infinite divisible according to the addition operation. The scalar RF built on a Poisson point process and on Poisson varieties, as well as the multivariate case to simulate multispectral data are presented.

Simple probabilistic models of fracture of 3D polycrystals involving transgranular and intergranular cracks are based on undamaged paths and appropriate percolation thresholds. In a second part, theoretical extensions of phase field models for crack initiation and propagation to the case of locally heterogeneous and anisotropic fracture energy are...

This chapter recalls the construction and the main properties of random closed sets: i) The Choquet topology, for the closed sets of a space E, enables us to build a probability space of closed random sets, characterized by their Choquet capacity. ii) From the same approach extended to upper or lower semi continuous numerical functions, it is possi...

As a consequence of microstructural heterogeneities, fluctuations in the mechanical properties of materials are observed in experiments. This requires a probabilistic approach to relate the microstructure to the overall materials properties, and to predict scale effects in the fluctuations of properties. In this chapter, the problem of the strength...

A prediction of apparent properties of random structures is obtained from the numerical solution of the PDE concerning the physical fields on real images or on simulations of random media in bounded domains. For this purpose, numerical calculations are made by Finite Elements or by FFT. This numerical approach involves a statistical definition of a...

Models of stochastic point processes are basic models of random sets with a rather simple geometry. The archetype model is the Poisson point process, which simulates a population of particles without any spatial interaction. It can be used as seeds for other models developed in other chapters, called grain models. Variants of the Poisson point proc...

The measurements used to analyze the morphology of random media, experimentally available from image analysis, are introduced: measurements are obtained in a two-steps approach: transformation and basic measurement; their prototypes are the basic operations of mathematical morphology (erosion and dilation) by appropriate structuring elements, coupl...

New versions of the Boolean RACS and RF, as well as the Dead Leaves random tessellations and Color Dead Leaves are obtained by imposing conditions on the choice of primary grains and primary functions, depending on the location of sequential Poisson points. These models are iteratively generated by a time sequence of Cox Processes. Their probabilis...

Generalizations of usual random tessellation models in \({\mathbb{R}}^{n}\) generated by Poisson point processes are introduced, and their functional probability \(P(K)\) is given. They are obtained from Boolean random function, providing a generic way of simulation of a wide range of random tessellations.

The probabilistic characterization of random tessellations is introduced. The construction and the main properties of some random tessellations (Voronoi, Johnson-Mehl, Laguerre, Poisson, Cauwe, and iterated tessellation models) and of their extensions are given.

A general methodology is introduced for probabilistic texture segmentation in binary, scalar, or multispectral images. Textural information is obtained from morphological operations on images. Starting from a fine partition of the image in regions, hierarchical segmentations are set up in a probabilistic framework by means of probabilistic distance...

Spatial and temporal multivariate RF models, where interactions between components act through chemical reactions, are introduced.These models give rise to morphogenesis. A first part gives a general description of Reaction-Diffusion models at two different scales:on a macroscopic scale, chemical concentration variables are solution of a system of...

Sequential models with support in \( {\mathbb{R}}^{n} \) are developed. For each point x in \( {\mathbb{R}}^{n} \), the models combine families of independent random sets or random functions, indexed by a parameter t. By a masking process, the Dead Leaves models (and its generalized version, the Markovian jumps sequential RF) simulate random images...

Models of random structures with a bounded support, that can be used as primary grains in the previous chapters, are proposed:several families of random sets are studied (populations of spheres and of ellipsoids in \( {\mathbb{R}}^{3} \)), Poisson polyhedra, random aggregates; similarly,models of random functions are built according to different pr...

Problems of change of scale in physics of random media handled in this chapter concern the prediction of the macroscopic behavior of a physical system from its microscopic behavior. Most physical properties of random media are concerned by this approach, like for instance the dielectric permittivity ϵ in electrostatics, the permeability K or flows...

The Boolean RF are a generalization of the Boolean RACS. Their construction based on the combination of a sequence of primary RF by the operation ∨ (supremum) or ∧ (infimum), and their main properties (among which the supremum or infimum infinite divisibility) are given in the following cases: scalar RF built on a Poisson point process and on Poiss...

The models of random sets introduced in this chapter are based on the Poisson point process, used as seeds for the Boolean RACS, which gives good simulations of two phase connected media, for which a percolation threshold can be estimated. Properties of this model and examples of application with proper identification of its parameters are given. G...

This book covers methods of Mathematical Morphology to model and simulate random sets and functions (scalar and multivariate). The introduced models concern many physical situations in heterogeneous media, where a probabilistic approach is required, like fracture statistics of materials, scaling up of permeability in porous media, electron microsco...

Computing an array of all pairs of geodesic distances between the pixels of an image is time consuming. In the sequel, we introduce new methods exploiting the redundancy of geodesic propagations and compare them to an existing one. We show that our method in which the source point of geodesic propagations is chosen according to its minimum number o...

Morphological characterization of porous media is of paramount interest, mainly due to the connections between their physicochemical properties and their porous microstructure geometry. Heterogeneity can be seen as a geometric characteristic of porous microstructures. In this paper, two novel topological descriptors are proposed, based on the M-tor...

The methods used to extract chord-length distributions from small-angle scattering data assume a structure consisting of spatially uncorrelated and disconnected convex regions. These restrictive conditions are seldom met for a wide variety of materials such as porous materials and semicrystalline or phase-separated copolymers, the structures of whi...

We propose a new computer aided detection framework for tumours acquired on DCE-MRI (Dynamic Contrast Enhanced Magnetic Resonance Imaging) series on small animals. In this approach we consider DCE-MRI series as multivariate images. A full multivariate segmentation method based on dimensionality reduction, noise filtering, supervised classification...

Simple probabilistic models of fracture of 3D polycrystals involving transgranular and intergranular cracks are proposed, based on undamaged paths and appropriate percolation thresholds. In a second part, we propose theoretical extensions of phase field models for crack initiation and propagation to the case of locally heterogeneous and anisotropic...

The intact grains of the dead leaves model enables us to generate random media with non overlapping grains. Using the time non homogeneous sequential model with convex grains, theoretically very dense packings can be generated, up to a full covering of space. For these models, the theoretical volume fraction, the size distribution of grains, and th...

Architectured materials involve geometrically engineered distributions of microstructural phases at a scale comparable to the scale of the component, thus calling for new models in order to determine the effective properties of materials. The present chapter aims at providing such models, in the case of mechanical properties. As a matter of fact, o...

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 cra...

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 s...

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 pol...

A procedure is proposed to simulate numerically experimental capillary condensation and evaporation isotherms in porous media, and to simulate random microstructures based on such isotherms. The present methodology is applied to a mesoporous material made of nanometric alumina “platelets”. First, a numerical method is developed to compute the adsor...

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 p...

By employing multi-scale random models of γ-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 F...

This article is dealing with the effects of surface preparation of the substrate on aluminum cold-sprayed coating bond strength. Different sets of AA2024-T3 specimens have been coated with pure Al 1050 feedstock powder, using a conventional cold spray coating technique. The sets were grit-blasted (GB) before coating. The study focuses on substrate...

A general methodology is introduced for texture segmentation in binary, scalar, or multispectral images. Textural information is obtained from morphological operations on images. Starting from a fine partition of the image in regions, hierarchical segmentations are designed in a probabilistic framework by means of probabilistic distances conveying...

Also published as WO2013045594 (A1), US9196034 (B2), FR2980896 (A1), FR2980896 (B1), EP2761588 (A1), CN103858147 (A), CN103858147 (B)

Long …bers or strati…ed media show very long range correlations. This media can be simulated by models of Boolean random varieties. We study for these models the non standard scaling laws of the variance of the local volume fraction with the volume of domains K: on a large scale, a the variance of the local volume fraction decreases with power laws...

Models of random sets and of point processes are introduced to simulate some specific clustering of points, namely on random lines in R2 and R3 and on random planes in R3. The corresponding point processes are special cases of Cox processes. The generating distribution function of the probability distribution of the number of points in a convex set...

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 F...

In this paper, a new methodology to build automatically 3D adapted meshes, ready for numerical simulations and directly from images, is proposed. It is based on the Immersed Image Method, which interpolates the image information on an initial mesh and combines it with parallel automatic anisotropic mesh adaptation with a control of the number of me...

A general framework of spatio-spectral segmentation for multi-spectral images is introduced in this paper. The method is based on classification-driven stochastic watershed (WS) by Monte Carlo simulations, and it gives more regular and reliable contours than standard WS. The present approach is decomposed into several sequential steps. First, a dim...

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 segme...

Volume fraction and spatial repartition of fillers impact the physical properties of rubber. Extended percolating networks of nano-sized fillers significantly modify the macroscopic mechanical properties of rubbers. Random models that describe the multiscale microstructure of rubber and efficient Fourier-based numerical algorithms are combined to p...

Corrigendum of A MIXED BOOLEAN AND DEPOSIT MODEL FOR THE MODELING OF METAL PIGMENTS IN PAINT LAYERS (2015 IMAGE ANAL STEREOL 34:125–34).

The optical properties of a hematite-epoxy coating are predicted numerically and compared with el-lipsometry measurements. The highly-heterogeneous dispersion of nanocubic hematite particles in the epoxy resin is simulated using a previously developed two-scales random model. The local anisotropic permittivity tensor of hematite particles, and that...

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....

This work focuses on a mesoporous material made up of nanometric alumina 'platelets' of unknown shape. We develope 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...

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 siz...

The notion of Boolean random functions is considered which is a generalization of Boolean random closed sets. Their construction is based on the combination of a sequence of primary random functions by the operation ∨ (supremum) or ∧ (infimum), and their main properties (among which the supremum or infimum infinite divisibility) are given in the ca...

The EVOLVE cell, named after a running FP7 project, is an innovative SOFC concept that integrates advanced materials, providing multiple functionalities (electrochemical activity, ion or/and electron conduction, gas diffusion…), and an inventive anode current collector made of a NiCrAl preoxidized foam impregnated with a conductive perovskite. Ther...

A general methodology is introduced for texture segmentation in binary, scalar, or multispectral images. Textural information is obtained from morphological operations of images. Starting from a fine partition of the image in regions, hierarchical segmentations are designed in a probabilistic framework by means of probabilistic distances conveying...

Pigments made of metal particles of around 10 µm or 20 µm produce sparkling effects in paints, due to the specular reflection that occurs at this scale. Overall, the optical aspect of paints depend on the density and distribution in space of the particles. In this work, we model the dispersion of metal particles of size up to 50 µm, visible to the...

This paper describes the development of a numerical homogenization tool adapted to TATB-based pressed explosives. This is done by combining virtual microstructure modeling and Fourier-based computations. The polycrystalline microstructure is represented by a Johnson-Mehl tessellation model with Poisson random nucleation and anisotropic growth of gr...

Les matériaux présentant un coefficient de Poisson négatif (auxétiques) font l'objet d'une recherche soutenue depuis au moins deux décennies, spécifiquement dans le domaine des structures composites légères et des milieux cellulaires. Les résultats publiés dans la littérature font état d'une amélioration du module de cisaillement, de la résistance...

The thermoelastic response of a TATB-based pressed explosive is studied using morphological modeling and a numerical Fourier scheme. First, we characterize the polycrystalline-like microstructure in terms of the (2D) granulometry and covariance functions, measured on SEM micrograph images. The granulometry is found to be close to a Rayleigh distrib...

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 usin...

The present paper refers to an innovative SOFC concept named EVOLVE after a running FP7 project which integrates advanced materials and an inventive anode current collector made from a NiCrAl preoxidized foam impregnated with a conductive perovskite. Even if the concept is the beneficial combination of Metal supported cell (MSC) and Anode supported...

Laguerre tessellations are suitable models for many polycrystalline materials. In this work, we present a reconstruction-based approach to fit a spatial Laguerre tessellation model to a plane section of a cellular material under the condition that one section of the model resembles the observed section of the material. To account for this special r...

A general methodology is introduced for texture segmentation in binary, scalar, or multispectral images. Textural information is obtained from morphological operations on images. Starting from a …fine partition of the image in regions, hierarchical segmentations are designed in a probabilistic framework by means of probabilistic distances conveying...

In the context of automated analyses of electron-backscattered-diffraction images, we present in this paper a novel method to automatically extract morphological properties of prior austenitic grains in martensitic steels based on raw crystallographic orientation maps. This quantification includes the estimation of the mean chord length in specific...

This introductory paper aims at summarizing some problems and state-of-the-art techniques encountered in image processing for material analysis and design. Developing generic methods for this purpose is a complex task given the variability of the different image acquisition modalities (optical, scanning or transmission electron microscopy; surface...

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...

This work focuses on the linear elastic and thermal properties of real and virtual, computer-generated fibrous composites. A stochastic microstructure model is used to generate densely-assembled 3D systems of curved, non overlapping fibers with specific orientation distributions. This model is first optimized to approach the characteristics of a re...

Generalizations of various random tessellation models generated by Poisson point processes are introduced, and their functional probability P(K)P(K) is given. They are obtained from Boolean random function models, and alternatively from a geodesic distance, providing a generic way of simulation of a wide range of random tessellations, as illustrate...

Focused ion beam tomography has proven to be capable of imaging porous structures on a nano-scale. However, due to shine-through artefacts, common segmentation algorithms often lead to severe dislocation of individual structures in z-direction. Recently, a number of approaches have been developed, which take into account the specific nature of focu...

We propose a new computer aided detection framework for tumours acquired on DCE-MRI (Dynamic Contrast Enhanced Magnetic Resonance Imaging) series on small animals. In this approach we consider DCE-MRI series as multivariate images. A full multivariate segmentation method based on dimensionality reduction, noise filtering, supervised classification...

In the area of tessellation models, there is an intense activity to fully understand the classical models of Voronoi, Laguerre and Johnson-Mehl. Still, these models are all simulations of isotropic growth and are therefore limited to very simple and partly convex cell shapes. The here considered microstructure of martensitic steel has a much more c...

A coating buildup model was developed, the aim of which was simulating the microstructure of a tantalum coating cold sprayed onto a copper substrate. To do so, first was operated a fine characterization of the irregular tantalum powder in 3D, using x-ray microtomography and developing specific image analysis algorithms. Particles were grouped by sh...

In this work, a numerical model of the cold spray process was developed to reproduce microstructures obtained in coatings by simulating the deformation of impinging particles and resulting coating build-up. The model employs a library of particle images generated by x-ray microtomography. To each image, a velocity is assigned and the deformation th...

In the present study, X-ray microtomography is used to examine cold-sprayed tantalum splats on copper substrates. To resolve tantalum splats intermeshed with other splats of the same chemical composition, a contrasting medium of some sort is required. For this purpose, the feedstock powder is coated with an iron layer by means of fluidized-bed chem...

For the simulation of fiber systems, there exist several stochastic models: systems of straight non overlapping fibers, systems of overlapping bending fibers, or fiber systems created by sedimentation. However, there is a lack of models providing dense, non overlapping fiber systems with a given random orientation distribution and a controllable le...

The structure of the ureteric tree in developing mouse and rat kidneys has previously been quantified in two dimensions. While this type of analysis may provide evidence of changes in ureteric growth, these measurements are effectively inaccurate, as the ureteric tree is a three-dimensional (3D) object. Here we describe a method for measuring the u...

X-ray microtomography from solid propellant allows studying the microstructure of fragmented grains in damaged samples. A new reconstruction algorithm of fragmented grains for 3D images is introduced. Based on a watershed transform of a morphological closing of the input image, the algorithm can be used with different sets of markers. Two of them a...

The size of representative volume element (RVE) for 3D stochastic fibrous media is investigated. A statis-tical RVE size determination method is applied to a specific model of random microstructure: Poisson fibers. The definition of RVE size is related to the concept of integral range. What happens in microstruc-tures exhibiting an infinite integra...

Generalizations of various random tessellation models generated by Poisson point processes are proposed and their functional probability P(K) is given. They are interpreted as characteristics of Boolean random functions models, which provide a generic way of simulation of general random tessellations.

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...