Variational Upper and Lower Bounds of Piezoelectric Composites with Randomly Distributed Non-Ellipsoidal Inclusions
Piezoelectric composite materials are widely used in underwater acoustic engineering,medicine and ultrasonic testing because of their high electromechanical coupling coefficient and piezoelectric constant,low density and high acoustic impedance.The Hashin-Shtrikman variational principle can predict the bounds of the effective modulus of composite materials,which is beneficial for the optimization of the piezoelectric composites.At present,the Hashin-Shtrikman bounds method for piezoelectric composites is suitable for ellipsoidal inclusions without considering the distribution of inclusions,but is not suitable for non-ellipsoidal inclusions.In this paper,based on the Hashin-Shtrikman variational method,the bounds of the effective modulus of transversely isotropic piezoelectric composites are solved by using the microstructure parameters reflecting the distribution characteristics and the shape of inclusions.This method is suitable for inclusions of any shape.When the ellipsoidal domain shape is the same as the ellipsoidal inclusion shape,this method is consistent with the traditional method for the bounds of Hashi-Shtrikman of piezoelectric composite materials.When the shape of the ellipsoidal domain is different from that of the ellipsoidal inclusion and the inclusion content is low,the bounds of the partial effective modulus obtained by this method are more compact.In addition,the bounds of the effective modulus of the transversely isotropic piezoelectric matrix containing square inclusions are calculated.The results show that the material is transversely isotropic and has little difference with the bounds of the effective modulus of the ellipsoidal inclusion.In this paper,the calculation method of the bounds of piezoelectric composites considering inclusion distribution and inclusion shape is established,which provides reference for the study of piezoelectric composites.
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