Electric potential distribution due to shear in cuboids

For unidirectional electric field strength confined to the component E3, the transverse electric flux density components D, D2 as well as shear stress 

The internal energy of an electrostatic system is represented by the product of the correlated field strength and flux density components, as exemplarily derived for the virtual work of internal charges, Eq. (3.53). The shear strain induced flux density components Di and D2, as given in Eq. (4.22), do not contribute by virtue of the above assumption. Thus, the assumption of unidirectional electric field strength is equivalent to the neglect of shear associated electrostatic energy contributions. 

For the remaining case of unidirectional electric flux density confined to the component D3, the transverse electric field strength components E, E2 may be expressed in terms of the shear strains 731, 723. Therewith Ei and E2 can be eliminated from the constitutive equations by static condensation. Thus, this modification of Eqs. (4.20) represents a purely mechanical interaction with strengthened shear stiffnesses as the result of the piezoelectric effect  

Thereby, from the energetic point of view again, the shear associated electrostatic energy contributions, so to speak, are transferred to the elastic energy. 

The implications of both discussed simplifications of the constitutive relations may be illustrated by sununarizing all the shear cases. With the assumption of unidirectional electric field strength for the stresses of Eqs. (4.22), respectively, unidirectional electric flux density for the stresses of Eqs. (4.23), whereby the additional terms of the latter are furnished with the variables t 23 and U31, and Eq. (4.21), this reads as follows  

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