### Abstract

Statistical continuum theory based approaches are commonly used for the computation of the effective properties of heterogeneous materials. Statistical distribution and morphology of the microstructure are represented by n-point probability function. One-point probability function statistical representation of the microstructure leads to volume fraction dependent homogenization. However, second and higher order probability functions include the information of phase distribution and morphology. Most statistical based homogenization methods are limited to two-point probability function due to the lack of simple approximation of higher order probability functions that can be easily exploited. In this paper, a new approximation of the three-point probability function is proposed and discussed. The new approximation results are compared to existing approximations from the literature and to the real probability functions calculated from a computer generated two-phase micrographs.

Original language | English |
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Pages (from-to) | 3782-3787 |

Number of pages | 6 |

Journal | International Journal of Solids and Structures |

Volume | 46 |

Issue number | 21 |

DOIs | |

Publication status | Published - 15 Oct 2009 |

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### Keywords

- Heterogeneous media
- Probability functions
- Statistical continuum

### ASJC Scopus subject areas

- Modelling and Simulation
- Materials Science(all)
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics

### Cite this

*International Journal of Solids and Structures*,

*46*(21), 3782-3787. https://doi.org/10.1016/j.ijsolstr.2009.07.004