Numerical homogenization techniques for active control

The piezoelectric fiber based composite materials are of interest to aeronautics because of their light mass and high actuation capacity. Considering the expensive manufacturing cost of complex active structural systems, one cannot get away from using numerical tools to study their performances and design. Then, in view of using F.E. tools, and because their characteristic length is smaller than the physical wavelengths which are considered, homogenization techniques are currently used to model their behavior. The paper presents a new numerical homogenization technique that has been developed to deal with some drawbacks of the previous analytical methods. Based on the use of the F.E. code ATILA, two different methods are combined : the Representative Elementary Volume (RVE) and the Wave Propagation (WP). As a first validation case, the results are compared with those obtained with the other existing homogenization techniques. Then, the method is applied to model the acoustic behavior of a 1-3 PZT5A (epoxy) piezocomposite immersed in water.