Search

Morphological models are commonly used to describe microstructures observed in heterogeneous materials. Usually, these models depend upon a set of parameters that must be chosen carefully to match experimental observations conducted on the microstructure. A common approach to perform the parameters determination is to try to minimize an objective function, usually taken to be the discrepancy between measurements computed on the simulations and on the experimental observations, respectively. In this article, we present a Bayesian approach for determining the parameters of morphological models, based upon the definition of a posterior distribution for the parameters. A Monte Carlo Markov Chains (MCMC) algorithm is then used to generate samples from the posterior distribution and to identify a set of optimal parameters. We show on several examples that the Bayesian approach allows us to properly identify the optimal parameters of distinct morphological models and to identify potential correlations between the parameters of the models.

Abstract 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).

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.

In this article, we study the microstructure of cold sprayed films of copper particles deposited onto a carbon fiber reinforced polymer. The microstructure of the coating is made of a packing of seemingly round-shaped particles of varying sizes embedded in a polymer matrix. The copper particles are separated by thin interstices. The coating is designed to cover the body of recent commercial aircrafts. Its role is to protect the aircraft from lightning impact by ensuring that the surface is conductive enough to evacuate electrical charges. A high resistivity contrast is observed between the copper particles and the polymer matrix. Therefore, the global resistivity of the material is highly dependent on the microstructure geometry. Following an approach commonly used in materials science, to investigate its influence on the electrical properties of the global material at the macroscopic scale, we design a 3D multiscale stochastic model that enables us to simulate the microstructure. The model is based upon a generalization of the classical JohnsonMehl tessellation, which accounts for the interstices that appear between copper particles. The method is very general and could potentially be applied to model any microstructure exhibiting similar interstices between aggregates of particles.

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.

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 eyes, in a paint layer. Making use of optical and scanning electron microscopy (SEM) images, we estimate the dispersion of particles in terms of correlation functions. Particles tend to aggregate into clusters, as shown by the presence of oscillations in the correlation functions. Furthermore, the volume fraction of particles is non-uniform in space. It is highest in the middle of the layer and lowest near the surfaces of the layer. To model this microstructure, we explore two models. The first one is a deposit model where particles fall onto a surface. It is unable to reproduce the observed measurements. We then introduce a "stack" model where clusters are first modeled by a 2D Poisson point process, and a bi-directional deposit model is used to implant particles in each cluster. Good agreement is found with respect to SEM images in terms of correlation functions and density of particles along the layer height.

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