Application of piezoelectric materials requires an improvement in their performance characteristics which can be obtained by designing new topologies of microstructures (or unit cells) for these materials. The topology of the unit cell (and the properties of its constituents) determines the effective properties of the piezocomposite. By changing the unit cell topology, better performance characteristics can be obtained in the piezocomposite. Based on this idea, we have proposed in this work an optimal design method of piezocomposite microstructures using topology optimization techniques and homogenization theory. The topology optimization method consists of ®nding the distribution of material phase and void phase in a periodic unit cell, that optimizes the performance characteristics, subject to constraints such as property symmetry and stiffness. The optimization procedure is implemented using sequential linear programming. In order to calculate the effective properties of a unit cell with complex topology, a general homogenization method applied to piezoelectricity was implemented using the ®nite element method. This method has no limitations regarding volume fraction or shape of the composite constituents. Although only two-dimensional plane strain topologies of microstructures have been considered to show the implementation of the method, this can be extended to threedimensional topologies. Microstructures obtained show a large improvement in performance characteristics compared to pure piezoelectric material or simple designs of piezocomposite unit cells. IntroductionPiezoelectric materials have the property of converting electrical energy (electric ®eld and applied electrical charge) into mechanical energy (strain and stress) and vice versa. They are widely used in electromechanical sensors and actuators such as robotics sensors, ultrasonic transducers for medical imaging and non destructive evaluation (NDE), underwater acoustics (some hydrophones and naval sonars), and other applications. The main goal in the transducer design in all these applications is to increase the response of the transducer which can be achieved, for example, by increasing the electromechanical energy conversion. The energy conversion depends on many factors, one of the most important being the properties of the piezoelectric material. In this work, we consider ultrasonic imaging and naval sonar applications. In these applications, it is well known that materials such as``1±3 piezocomposite'' (piezoceramic rods embedded in a soft polymer matrix) allow greater sensitivity, in both low and high frequency applications, than pure piezoceramic (see Auld 1991, andSmith 1993). This improvement occurs because the composite material provides effective properties (elastic, piezoelectric, and dielectric) that produce a better performance than pure piezoelectric materials. These effective (homogenized) properties can be determined by considering the topology of the composite microstructure (or unit cell, the smallest structure that is periodic ...

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