Published 6 issues per year
ISSN Print: 1543-1649
ISSN Online: 1940-4352
Indexed in
ELASTIC AND ELECTRICAL BEHAVIOR OF SOME RANDOMMULTISCALE HIGHLY-CONTRASTED COMPOSITES
ABSTRACT
The role of a non uniform distribution of heterogeneities on the elastic as well as electrical properties of composites is studied numerically and compared with available theoretical results. Specifically, a random model made of embedded Boolean sets of spherical inclusions (see, e.g., Proc. Eur. Conf. on Constitutive Models for Rubber, ECCMR 2007, Paris, Sept. 4-7) serves as the basis for building simple two-scale microstructures of \granular" type. Materials with infinitely contrasted properties are considered, i.e., inclusions elastically behave as rigid particles or pores, or as perfectly insulating or highly conducting heterogeneities. The inclusion spatial dispersion is controlled by the ratio between the two characteristic lengths of the microstructure. The macroscopic behavior as well as the local response of composites are computed using full-field computations, carried out with the fast fourier transfor method (C. R. Acad. Sci. Paris II, 318: 1417-1423, 1994). The entire range of inclusion concentrations and dispersion ratios up to the separation of length scales are investigated. As expected, the non uniform dispersion of inhomogeneities in multi scale microstructures leads to increased reinforcing or softening effects compared to the corresponding one-scale model (Willot and Jeulin, 2009); these effects are, however, still significantly far apart from Hashin-Shtrikman bounds. Similar conclusions are drawn regarding the electrical conductivity.
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Leclerc W., Karamian-Surville P., Effects of fibre dispersion on the effective elastic properties of 2D overlapping random fibre composites, Computational Materials Science, 79, 2013. Crossref
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Willot François, Gillibert Luc, Jeulin Dominique, Microstructure-induced hotspots in the thermal and elastic responses of granular media, International Journal of Solids and Structures, 50, 10, 2013. Crossref
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Willot François, Abdallah Bassam, Pellegrini Yves-Patrick, Fourier-based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields, International Journal for Numerical Methods in Engineering, 98, 7, 2014. Crossref
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Leclerc W., Karamian-Surville P., Vivet A., An efficient and automated 3D FE approach to evaluate effective elastic properties of overlapping random fibre composites, Computational Materials Science, 99, 2015. Crossref
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Willot François, Fourier-based schemes for computing the mechanical response of composites with accurate local fields, Comptes Rendus Mécanique, 343, 3, 2015. Crossref
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Escoda Julie, Willot François, Jeulin Dominique, Sanahuja Julien, Toulemonde Charles, Influence of the multiscale distribution of particles on elastic properties of concrete, International Journal of Engineering Science, 98, 2016. Crossref
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Matsutani Shigeki, Shimosako Yoshiyuki, On homogenized conductivity and fractal structure in a high contrast continuum percolation model, Applied Mathematical Modelling, 39, 23-24, 2015. Crossref
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Caspari Eva, Milani Marco, Rubino J. Germán, Müller Tobias M., Quintal Beatriz, Holliger Klaus, Numerical upscaling of frequency-dependent P- and S-wave moduli in fractured porous media, Geophysical Prospecting, 64, 4, 2016. Crossref
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Jeulin Dominique, Morphological Models, in Encyclopedia of Continuum Mechanics, 2018. Crossref
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Colabella Lucas, Ibarra Pino Ariel Alejandro, Ballarre Josefina, Kowalczyk Piotr, Cisilino Adrián Pablo, Calculation of cancellous bone elastic properties with the polarization-based FFT iterative scheme, International Journal for Numerical Methods in Biomedical Engineering, 33, 11, 2017. Crossref
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Demirel Serdar, Irving James, Roubinet Delphine, Comparison of REV size and tensor characteristics for the electrical and hydraulic conductivities in fractured rock, Geophysical Journal International, 216, 3, 2019. Crossref
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Alekseev M. V., Savenkov E. B., Berezin A. V., Markov M. B., Sadovnichii D. N., Numerical simulation of electromagnetic field propagation in heterogeneous material, PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON ADVANCED MATERIALS WITH HIERARCHICAL STRUCTURE FOR NEW TECHNOLOGIES AND RELIABLE STRUCTURES 2019, 2167, 2019. Crossref
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Jeulin Dominique, Multi Scale Random Sets: From Morphology to Effective Behaviour, in Progress in Industrial Mathematics at ECMI 2010, 17, 2012. Crossref
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Jeulin Dominique, Morphological Models, in Encyclopedia of Continuum Mechanics, 2020. Crossref
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Chen Zeyao, Xie Yi Min, Wang Zhe, Li Qing, Wu Xian, Zhou Shiwei, A comparison of fast Fourier transform-based homogenization method to asymptotic homogenization method, Composite Structures, 238, 2020. Crossref
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Sharma Sumit, Kumar Pramod, Modeling of Nanocomposites, in Mechanics of Particle‐ and Fiber‐Reinforced Polymer Nanocomposites, 2021. Crossref
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Willot François, Microstructure Modeling and Characterization, in Mechanical Engineering under Uncertainties, 2021. Crossref
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Schneider Matti, A review of nonlinear FFT-based computational homogenization methods, Acta Mechanica, 232, 6, 2021. Crossref
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Chen Zeyao, Wu Baisheng, Xie Yi Min, Wu Xian, Zhou Shiwei, FFT-based Inverse Homogenization for Cellular Material Design, International Journal of Mechanical Sciences, 231, 2022. Crossref