Spatial Statistics and Micromechanics of Materials

  • Dominique Jeulin
Part of the Lecture Notes in Physics book series (LNP, volume 600)


The prediction of elastic properties and of fracture strength of materials from their microstructure is an old but still active problem, implying many theoretical questions and important practical consequences. In both cases, statistical correlation functions deduced from the geometry by image analysis measurements, or obtained for specific models of random media, enter into the estimation of overall properties of materials. Concerning elastic properties of random media, useful bounds can be worked out from their three-points statistics. This is illustrated for various models of random media, including multiscale textures producing so-called “optimal microstructures”. This method also provides estimators (upper bounds) of the elastic moduli of porous media. Fracture statistics models based on random functions allow us to predict the probability of fracture of materials, depending on the scale, the applied stress field, and the microstructure. Recent developments are reviewed in brittle fracture (using the weakest link model, or Griffith crack propagation in random media) and in the case of materials submitted to an increasing damage during the fracture process.


Duplex Stainless Steel Fracture Statistic Boolean Model Hard Sphere Model Order Bound 
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© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Dominique Jeulin
    • 1
  1. 1.Centre de Morphologie Mathématique Ecole des Mines de ParisFontainebleauFrance

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