### Abstract

An implementation of the Causal Differential Method (CDM) for modelling the effective properties of a random two-phase composite material is presented.
Such materials are commonly used as ultrasonic transducer matching layersor backing layers. The method is extended to incorporate a particle size distribution in the inclusion phase. Numerical issues regarding the implementation and convergence of the method are discussed. It is found that, for a given frequency of excitation, the calculated velocity for the composite has a distribution whose variance
increases as the volume fraction of inclusions increases. The model predictions would suggest that to reliably and repeatedly manufacture these composites, with a desired mechanical impedance, a low volume fraction of inclusions should be used.

Original language | English |
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Title of host publication | Ultrasonic Wave Propagation in Non Homogeneous Media |

Publisher | Springer Berlin Heidelberg |

Pages | 49-59 |

Number of pages | 12 |

ISBN (Electronic) | 9783540891055 |

ISBN (Print) | 9783540891048 |

DOIs | |

Publication status | Published - 30 Jan 2009 |

### Publication series

Name | Springer Proceedings in Physics |
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Volume | 128 |

ISSN (Print) | 0930-8989 |

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## Cite this

Young, A., Mulholland, A., & O'Leary, R. (2009). The causal differential scattering approach to calculating the effective properties of random composite materials with a particle size distribution. In

*Ultrasonic Wave Propagation in Non Homogeneous Media*(pp. 49-59). (Springer Proceedings in Physics; Vol. 128). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-89105-5_5