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.
|Title of host publication||Ultrasonic Wave Propagation in Non Homogeneous Media|
|Publisher||Springer Berlin Heidelberg|
|Number of pages||12|
|Publication status||Published - 30 Jan 2009|
|Name||Springer Proceedings in Physics|
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