THE EFFECTIVE PROPERTIES OF PIEZOCOMPOSITES, PART Ⅰ: SINGLE INCLUSION PROBLEM

The problem of a piezoelectric ellipsoidal inclusion in an infinite non-piezoelectric matris is very important in engineering. In this paper, it is solved viaGreen’s function technique. The closed-form solutions of the electroelastic Eshelby’stensors for this kind of problem are obtained. The electroelastic Eshelby’s tensors canbe expressed by the Eshelby’s tensors of the perfectly elastic inclusion problem and theperfectly dielectric inclusion problem. Since the closed-form solutions of the Eshelby’stensors of the perfectly elastic inclusion problem and the perfectly dielectric inclusionproblem can be given by theory of elasticity and electrodynamics, respectively, theelectroelastic Eshelby’s tensors can be obtained conveniently. Using these results,the closed-form solutions of the constraint elastic fields and the constraint electricfields inside the piezoelectric ellipsoidal inclusion are also obtained. These expressionscan be readily utilized in solutions of numerous problems in the micromechanics ofpiezoelectric solids, such as the deformation and energy analysis, damage evolutionand fracture of the piezoelectric materials.