Tuesday, 12 October 2004 - 3:30 PM

This presentation is part of : Active Materials

Exact Results for the Piezoelectric Properties of Composite Ellipsoid Assemblages (keynote lecture)

Graeme W. Milton, University of Utah, Department of Mathematics, 155 S. 1400 E. Rm. 233, Salt Lake City, UT 84112 and Yakov Benveniste, Department of Solid Mechanics, Materials and Systems, Tel Aviv University, Ramat-Aviv, Tel Aviv, 69978, Israel.

Piezoelectric materials are an important class of active materials whose elastic response can be controlled through the application of suitable electrical currents. Sometimes composite piezoelectric materials have advantages over pure piezoelectric materials such as in the design of hydrophones. Here we show that for a model class of composites, namely assemblages of coated spheres, or coated ellipsoids, there exist certain exact relations between the various effective moduli characterizing the overall response of the piezoelectric composite. These exact relations can be used as benchmarks for numerical calculations and approximation schemes. The key to these exact relations is to look for solutions where the electrical potentials and displacement field components are each a superposition of the potentials which solve the conductivity equations in the same microgeometry.

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