A renormalisation approach to wave propagation in 0-3/3-3 connectivity composites

Particulate composite materials with variable connectivity are encountered extensively in ultrasonic applications. Examples include a wide range of propagation media, active piezocomposite transducers, matching layers and backing materials. The manner in which mechanical waves propagate in such materials depends strongly on particle distribution and dimensions, in addition to volume fraction. In this paper a commercial finite element package is used to study wave propagation through a realistic model of the complex microstructure of such composites. We also mathematically model a particular class of deterministically generated fractal composites using renormalisation and demonstrate this methodology by examining the propagation of a wave impulse through the Sierpinski Gasket.