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Morphological Models

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  • Abdallah B, Willot F, Jeulin D (2015) Stokes flow through a Boolean model of spheres: representative volume element. Transp Porous Media 109(3):711–726

    Google Scholar 

  • Altendorf H, Jeulin D, Willot F (2014a) Influence of the fiber geometry on the macroscopic elastic and thermal properties. Int J Solids Struct 51(23):3807–3822

    Google Scholar 

  • Altendorf H, Latourte F, Jeulin D, Faessel M, Saintoyant L (2014b) 3D reconstruction of a multiscale microstructure by anisotropic tessellation models. Image Anal Stereology 33(2):121–130

    Google Scholar 

  • Balberg I, Anderson CH, Alexander S, Wagner N (1984) Excluded volume and its relation to the onset of percolation. Phys Rev B 30(7):3933–3943

    Google Scholar 

  • Bretheau T, Jeulin D (1989) Caractéristiques morphologiques des constituants et comportement élastique d’un matériau biphasé Fe/Ag. Revue Phys Appl 24:861–869

    Google Scholar 

  • Cailletaud G, Jeulin D, Rolland P (1994) Size effect on elastic properties of random composites. Eng Comput 11(2):99–110

    Google Scholar 

  • Chiu SN, Stoyan D, Kendall WS, Mecke J (2013) Stochastic geometry and its applications. Wiley, Chichester

    Google Scholar 

  • Dirrenberger J, Forest S, Jeulin D (2014) Towards gigantic RVE sizes for 3D stochastic fibrous networks. Int J Solids Struct 51(2):359–376

    Google Scholar 

  • Escoda J, Jeulin D, Willot F, Toulemonde C (2015) Three-dimensional morphological modelling of concrete using multiscale Poisson polyhedra. J Microsc 258(1):31–48

    Google Scholar 

  • Escoda J, Willot F, Jeulin D, Sanahuja J, Toulemonde C (2016) Influence of the multiscale distribution of particles on elastic properties of concrete. Int J Eng Sci 98:60–71

    Google Scholar 

  • Eyre DJ, Milton GW (1999) A fast numerical scheme for computing the response of composites using grid refinement. Eur Phys J Appl Phys 6:41–47

    Google Scholar 

  • Figliuzzi B, Jeulin D, Faessel M, Willot F, Koishi M, Kowatari N (2016) Modelling the microstructure and the viscoelastic behaviour of carbon black filled rubber materials from 3D simulations. Technische Mechanik 32(1–2):22–46

    Google Scholar 

  • Gasnier JB, Willot F, Trumel H, Figliuzzi B, Jeulin D, Biessy M (2015) A Fourier-based numerical homogenization tool for an explosive material. Matériaux & Techniques 103(3):308

    Google Scholar 

  • Jean A, Jeulin D, Forest S, Cantournet S, N’Guyen F (2011) A multiscale microstructure model of carbon black distribution in rubber. J Microsc 241(3):243–260

    Google Scholar 

  • Jeulin D (1991a) Modèles Morphologiques de Structures Aléatoires et de Changement d’Echelle, Thèse de Doctorat d’Etat ès Sciences Physiques, Université of Caen

    Google Scholar 

  • Jeulin D (1991b) Modèles de Fonctions Aléatoires multivariables. Sci Terre 30:225–256

    Google Scholar 

  • Jeulin D (1994). Fracture statistics models and crack propagation in random media. Appl Mech Rev 47(1):141–150

    Google Scholar 

  • Jeulin D (2000) Random texture models for materials structures. Stat Comput 10:121

    Google Scholar 

  • Jeulin D (2001) Random structure models for homogenization and fracture statistics. In: Jeulin D, Ostoja-Starzewski M (eds) Mechanics of random and multiscale microstructures. Springer, Berlin, p 33

    Google Scholar 

  • Jeulin D (2005) Random structures in physics. In: Bilodeau M, Meyer F, Schmitt M (eds) Space, structure and randomness. Lecture notes in statistics, vol 183. Springer, Berlin, p 183

    Google Scholar 

  • Jeulin D (2009) Multi scale random models of complex microstructures. In: Chandra T, Wanderka N, Reimers W, Ionescu M (eds) Thermec 2009. Materials science forum, vol 638–642, pp 81–86

    Google Scholar 

  • Jeulin D (2010) Analysis and modeling of 3D microstructures, chapter 19. In: Talbot H, Najman L (eds) Mathematical morphology: from theory to applications. ISTE/Wiley, New York

    Google Scholar 

  • Jeulin D (2012) Morphology and effective properties of multi-scale random sets: a review. Comptes rendus de l’Académie des Sciences, Paris 240(4–5):219–229. https://doi.org/10.1016/j.crme.2012.02.004

    Google Scholar 

  • Jeulin D (2014) Random tessellations generated by Boolean random functions. Pattern Recogn Lett 47:139–146

    Article  Google Scholar 

  • Jeulin D (2015a) Boolean random functions. In: Schmidt V (ed) Stochastic geometry, spatial statistics and random fields. Springer International Publishing, Cham, pp 143–169

    Google Scholar 

  • Jeulin D (2015b) Power laws variance scaling of Boolean random varieties. Methodol Comput Appl Probab Rn 7:3

    Google Scholar 

  • Jeulin D (2016) Iterated Boolean random varieties and application to fracture statistics models. Appl Math 61(4):363–386

    Article  MathSciNet  MATH  Google Scholar 

  • Jeulin D, Jeulin P (1981) Synthesis of rough surfaces by random morphological models. Proc 3rd Eur Symp Stereology Stereol Iugosl 3(suppl 1):239–246

    Google Scholar 

  • Jeulin D, Moreaud M (2005) Multi-scale simulation of random spheres aggregates-Application to nanocomposites. In: Chraponski J, Cwajna J, Wojnar L (eds) Proceedings of the 9th European congress on stereology and image analysis, Zakopane, vol 1, pp 341–348

    Google Scholar 

  • Jeulin D, Moreaud M (2006a) Percolation d’agrégats multi-é chelles de sphères et de fibres: application aux nanocomposites. In: Proceeding of Matériaux, Dijon

    Google Scholar 

  • Jeulin D, Moreaud M (2006b) Percolation of multi-scale fiber aggregates. In: Lechnerova R, Saxl I, Benes V (eds) Proceedings of the S4G, 6th international conference stereology, spatial statistics and stochastic geometry, Prague, 26–29 June 2006. Union Czech Mathematicians and Physicists, pp 269–274

    Google Scholar 

  • Kanit T, Forest S, Galliet I, Mounoury V, Jeulin D (2003) Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int J Sol Str 40:3647–3679

    Article  MATH  Google Scholar 

  • Matheron G (1967) Eléments pour une théorie des milieux poreux. Masson, Paris

    Google Scholar 

  • Matheron G (1969) Théorie des ensembles aléatoires, Cahiers du Centre de Morphologie Mathématique, fasc. 4, edited by Paris School of Mines

    Google Scholar 

  • Matheron G (1971) The theory of regionalized variables and its applications. Paris School of Mines publications, Paris

    Google Scholar 

  • Matheron G (1975) Random sets and integral geometry. Wiley, New York

    MATH  Google Scholar 

  • Mecke K, Stoyan D (2005) The Boolean model: from Matheron till today. In: Bilodeau M, Meyer F, Schmitt M (eds) Space, structure and randomness. Lecture notes in statistics, vol 183. Springer, Berlin, pp 151–182

    Chapter  Google Scholar 

  • Milton GW (1982) Bounds on the elastic and transport properties of two-component composites. J Mech Phys Solids 30:177–191

    Article  MathSciNet  MATH  Google Scholar 

  • Milton GW (1986) Modeling the properties of composites by laminates. In: Ericksen JL, Kinderlehrer D, Kohn R, Lions JL (eds) Homogenization and effective moduli of materials and media. Springer, Berlin, pp 150–174

    Chapter  Google Scholar 

  • Moulinec H, Suquet P (1998) A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput Methods Appl Mech Eng 157:69–94

    Article  MathSciNet  MATH  Google Scholar 

  • Paciornik S, Gomes OFM, Delarue A, Schamm S, Jeulin D, Thorel A (2003) Multi-scale analysis of the dielectric properties and structure of resin/carbon-black nanocomposites. E P J Appl Phys 21:17–26

    Article  Google Scholar 

  • Rintoul M, Torquato S (1997) Precise determination of the critical threshold and exponents in a three-dimensional continuum percolation model. J Phys A Math Gen 30:L585–L592

    Article  MATH  Google Scholar 

  • Savary L, Jeulin D, Thorel A (1999) Morphological analysis of carbon-polymer composite materials from thick sections. Acta Stereol 18(3):297–303

    Google Scholar 

  • Serra J (1982) Image analysis and mathematical morphology. Academic Press, London

    MATH  Google Scholar 

  • Serra J (ed) (1988) Image analysis and mathematical morphology, vol 2. Academic Press, London

    Google Scholar 

  • Serra J (1989) Boolean random functions. J Microsc 156(1):41–63

    Article  MathSciNet  Google Scholar 

  • Wang H, Pietrasanta A, Jeulin D, Willot F, Faessel M, Sorbier L, Moreaud M (2015) Modelling mesoporous alumina microstructure with 3D random models of platelets. J Microsc 260(3):287–301

    Article  Google Scholar 

  • Wang H, Willot F, Moreaud M, Rivallan M, Sorbier L, Jeulin D (2017) Numerical simulation of Hindered diffusion in γ-alumina catalyst supports. Oil Gas Sci Technol–Revue d’IFP Energies nouvelles 72(2):8

    Article  Google Scholar 

  • Willot F, Jeulin D (2009) Elastic behavior of composites containing Boolean random sets of inhomogeneities. Int J Eng Sci 47:313–324

    Article  MathSciNet  MATH  Google Scholar 

  • Willot F, Jeulin D (2011) Elastic and electrical behavior of some random multiscale highly contrasted composites. Int J Multiscale Comput Eng 9(3):305–326

    Article  Google Scholar 

  • Willot F, Abdallah B, Jeulin D (2016) The permeability of Boolean sets of cylinders. Oil & Gas Science and Technology–Revue d’IFP Energies nouvelles 71(4):52

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Center for Mathematical Morphology, MINES Paristech, PSL Research University, F 77300, 35 rue Saint Honoré, Fontainebleau, France

    Dominique Jeulin

Authors
  1. Dominique Jeulin
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Corresponding author

Correspondence to Dominique Jeulin .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, Queensland, Australia

    Andreas Öchsner

Section Editor information

  1. Department of Mechanical Science & Engineering, Institute for Condensed Matter Theory and Beckman Institute, University of Illinois at Urbana–Champaign, 1206 West Green Street, 61801, Urbana, IL, USA

    Martin Ostoja-Starzewski

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Jeulin, D. (2018). Morphological Models. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_70-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_70-1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

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