Microconfigured piezoelectric artificial materials for hydrophones Aaron T. Crumm Æ John W. Halloran Æ Emilio C. N. Silva Æ Francisco Montero de Espinosa Received: 16 November 2005 / Accepted: 21 December 2006 / Published online: 11 May 2007 Ó Springer Science+Business Media, LLC 2007 Abstract Piezoelectric PZT–air composites with a com- plex design optimized for hydrophones were fabricated as arrays of hundreds of 60 l units using a microfabrication technique involving coextrusion of mixtures of thermo- plastic with PZT powder or carbon powder. The measured piezoelectric coefficient was 300 pC/N with a figure of merit of 18 pm 2 /N, in excellent agreement with the pre- dicted properties. Introduction The general concept of creating designed structures with specific properties is familiar for large objects, such as vehicles or buildings. Usually designers heuristically optimize for such goals as maximum strength for minimum material. More recently, optimal design techniques have used computational optimal design methods and have ad- dressed other properties. An example is the topology optimization and homogenization algorithm pioneered by Bendsøe and Kikuchi in 1988 [1]. The technique is used to design the fine-scale structure for composite materials with pre-determined (prescribed) or improved properties not available in common materials. Such a fine-scale com- posite structure can be considered an ‘‘Artificial Material’’ (AM). This paper addresses piezoelectric artificial materi- als optimized for sensitivity as hydrophones, from a mi- croconfigured composite design of lead zirconate titanate (PZT) and air. The topology optimization and homogenization method used to design piezoelectric composites with elastic and piezoelectric coefficients optimized for transducer are presented in detail elsewhere [2–5]. Very briefly, the de- sign algorithm considers a small unit that, in this case, consists of voxels of solid piezoelectric material and voids. The properties are computed from the staring arrangement of voxels, and compared to the target properties. The algorithm progresses through a series of iterations that re- fines an arrangement of voxels (three dimensional pixels) towards a user defined property target. The ultimate goal of the process is to develop a repeat unit of solid and void voxels, which achieves agreement with the initial property target. Finite Element Analysis (FEA) is done on the unit cell to calculate a set of homogenized properties that de- scribe the interaction of its boundaries with an infinite number of identical neighbors. Proper homogenization re- duces the computing power required to reach a solution so that is becomes practical to perform many design itera- tions. The computer assembles an array of many unit cells and the calculated macro-properties are compared against the user defined property goal and any other constraints imposed on the problem (stiffness, volume fraction, Pois- son ratio [6], piezoelectric response, coefficient of thermal expansion [7], etc.). If the solution is not converged, the algorithm enters a topology optimization subroutine where A. T. Crumm  J. W. Halloran (&) Department of Materials Science and Engineering, University of Michigan, 3062 Dow Building, Ann Arbor, MI 48109-2136, USA e-mail: john_halloran@engin.umich.edu E. C. N. Silva Department of Mechatronics and Mechanical Systems Engineering, Escola Polite ´cnica, University of Sa ˜o Paulo, Sao Paulo, Brazil F. Montero de Espinosa Instituto de Acu ´stica, Consejo Superior de Investigationes Cientificas, Madrid, Spain 123 J Mater Sci (2007) 42:3944–3950 DOI 10.1007/s10853-006-1478-5