Homogenization and Shape Sensitivity of Microstructures for Design of Piezoelectric Bio-Materials

Shape sensitivity of effective constitutive parameters is studied for homogenized piezoelectric composite which formerly was intended for bio-material application. It consists of the piezoelectric matrix in which elastic inclusions are distributed periodically. The microstructures are assumed to be parametrized in terms of the shape of the inclusions. Microstructures with elliptic inclusions are considered in numerical examples which indicate strong influence of the geometry on the homogenized piezoelectric properties. As the main theoretical result of the paper, the shape sensitivity formulae of the homogenized elastic, dielectric and piezoelectric coefficients are derived using the domain method of the material derivative.

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