Random Structures in Physics

Jeulin, Dominique

doi:10.1007/0-387-29115-6_9

Cited by 19 publications

(20 citation statements)

References 42 publications

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“…By restricting our designs to certain numbers of non-overlapping objects and porosity, we aimed to establish an intuition towards understanding CTC. In general, the use of complicated structures as in references [25,26] indeed creates a more realistic set-up. With such an arrangement however, it is difficult to explain why and how the value of the CTC varies within and among groups which is the goal of our work.…”

Section: Discussionmentioning

confidence: 99%

Characterization of microstructures using contour tree connectivity for fluid flow analysis

Aydogan

Hyttinen

2014

J. R. Soc. Interface.

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Quantifying the connectivity of material microstructures is important for a wide range of applications from filters to biomaterials. Currently, the most used measure of connectivity is the Euler number, which is a topological invariant. Topology alone, however, is not sufficient for most practical purposes. In this study, we use our recently introduced connectivity measure, called the contour tree connectivity (CTC), to study microstructures for flow analysis. CTC is a new structural connectivity measure that is based on contour trees and algebraic graph theory. To test CTC, we generated a dataset composed of 120 samples and six different types of artificial microstructures. We compared CTC against the Euler parameter (EP), the parameter for connected pairs, the nominal opening dimension (d nom ) and the permeabilities estimated using direct pore scale modelling. The results show that d nom is highly correlated with permeability (R 2 ¼ 0.91), but cannot separate the structural differences. The groups are best classified with feature combinations that include CTC. CTC provides new information with a different connectivity interpretation that can be used to analyse and design materials with complex microstructures.

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Section: Discussionmentioning

confidence: 99%

Characterization of microstructures using contour tree connectivity for fluid flow analysis

Aydogan

Hyttinen

2014

J. R. Soc. Interface.

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“…Readers interested by a broad treatment of the mathematical morphology is referred to the pioneer work due to D. G. Kendall [18] and G. Matheron [19] or the most comprehensive and mathematically rigorous reference by J. Serra in [20]. Very useful presentations of the subject may be found in a series of publications by D. Jeulin and co-workers [1,2,21] and in [22][23][24]. In addition, a recent review of the problematical of RVE including non-linear behavior of materials is given by Ostoja-Strarzewski [25].…”

Section: Probabilistic Models Of Random Mediamentioning

confidence: 99%

“…For these reasons, one chooses to perform numerical simulations on simulated microstructures. Several schemes can be used to generate random microstructures [1,31].…”

Section: Definition 222mentioning

confidence: 99%

“…Knowledge of the statistical fluctuations of a given stochastic model is required to ensure, for example, the correctness of any numerical simulation. In this context, it is possible to define a range, namely the integral range, which gives information on the domain size of the structure for which the measured physical properties in this volume have a good statistical representativeness [1,19,23]. …”

Section: Definition 221mentioning

confidence: 99%

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Complexity science of multiscale materials via stochastic computations

Liu

Siad

Tian

et al. 2009

Numerical Meth Engineering

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SUMMARYNew technological advances today allow for a range of advanced composite materials, including multilayer materials and nanofiber-matrix composites. In this context, the key to developing advanced materials is the understanding of the interplay between the various physical scales present, from the atomic level interactions to the microstructural composition and the macroscale behavior. Using the developing 'multiresolution data sets mechanics', the 'predictive science-based governing laws of the materials microstructure evolutions' are derived and melted into a 'stochastic multiresolution design framework.' Under such a framework, the governing laws of the materials microstructure evolution will be essential to assess, across multiple scales, the impact of multiscale material design, geometry design of a structure, and the manufacturing process conditions, by following the cause-effect relationships from structure to property and then to performance.The future integrated multiscale analysis system will be constructed based on a probabilistic complexity science-based mathematical framework. Its verification, validation and uncertainty quantification are done through carefully designed experiments, and the life-cycled materials design for products design and manufacturing is performed through the use of petascale computing. The various techniques of microstructure reconstruction result in the generation of model microstructures that, at some level, has the same statistical properties as the real heterogeneous media. Having reconstructed the heterogeneous medium, one can then evaluate its effective properties via direct numerical simulation and compare these values with experimentally measured properties of the actual medium. The proposed analysis will be dynamic in nature to capture the multi-stage historical evolvement of material/structure performance over the life span of a product. In addition to providing more accurate assessment of structure performance with stochastic multiscale analysis, our development will provide the capability of predicting structure failures and system reliability to enable more reliable design and manufacturing decisions in product development.

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“…This expression was used to estimate the function involved in the calculation of the third-order upper and lower bounds σ u BSM and σ l BSM of the BSM (Torquato and Stell, 1985), which depends linearly on the volume fraction of spheres p. Many other models of random media show a similar behavior (Jeulin, 2005).…”

Section: Bounds Of Effective Propertiesmentioning

confidence: 99%

Prediction of Effective Properties of Porous Carbon Electrodes from a Parametric 3D Random Morphological Model

et al. 2017

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2Torben Prill et al.Abstract 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.

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Random Structures in Physics

Cited by 19 publications

References 42 publications

Characterization of microstructures using contour tree connectivity for fluid flow analysis

Characterization of microstructures using contour tree connectivity for fluid flow analysis

Complexity science of multiscale materials via stochastic computations

Prediction of Effective Properties of Porous Carbon Electrodes from a Parametric 3D Random Morphological Model

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