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The causal differential scattering approach to calculating the effective properties of random composite materials with a particle size distribution

Young, A. and Mulholland, A.J. and O'Leary, R.L. (2009) The causal differential scattering approach to calculating the effective properties of random composite materials with a particle size distribution. Springer Proceedings in Physics, 128. pp. 49-59. ISSN 0930-8989

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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.