压电、压磁及电磁耦合弹性介质材料的弹性常数与工程材料常数之间的关系

Relationship Between Elastic Constants and Engineering Constants of the Piezoelectric-piezomagnetic and Elastic Media

从横观各向同性的压电、压磁和电磁耦合弹性介质材料的平衡方程、梯度方程和本构方程出发,导出了三维压电、压磁和电磁耦合弹性介质材料的弹性常数在二维情况下的表达式。同时,讨论了平面应力、平面应变和轴对称情况下材料常数的对应关系,进而分析了z轴极化的压电、压磁和电磁耦合弹性介质材料的弹性常数与工程常数之间的关系。分析结果表明压电、压磁和电磁耦合弹性介质材料的弹性常数和泊松比与弹性、压电、介电、压磁、电磁和磁通率等常数有关,这是由于该材料的机电耦合性导致其弹性常数和泊松比较单一材料的要复杂的多。

Start from balance equation,gradient equation and constitutive equation of transversely isotropic piezoelectricpiezomagnetic and elastic media, the expressions of elastic constants of three dimensional piezoelectricpiezomagnetic and elastic media under twodimensional condition are derived.Meanwhile, the correspondence relationship of material constants under plane stress plane stain and the axisymmetrical situations are discussed.The relationship between elastic constants and engineering contants of the piezoelectricpiezomagnetic and elastic media are also analyzed.The result indicate that the elastic constants and Poisson's ratio of the piezoelectricpiezomagnetic and elastic media materials are related to the elastic constants,the piezoelectric constants,the dielectric constants,the piezomagneticnts constants,the electromagnetic constants and the magnetic permeability constants of it.Due to the mechanical and electrical coupling of this material,the elastic constants and Poiaaon's ratio are more complex than that of other single materials.