A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects: part I – reconsideration of curvature-based flexoelectricity theory

A new non-classical theory of elastic dielectrics is developed using the couple stress and electric field gradient theories that incorporates the couple stress, quadrupole and curvature-based flexoelectric effects. The couple stress theory and an extended Gauss’s law for elastic dielectrics with quadrupole polarization are applied to derive the constitutive relations of this new theory through energy conservation. The governing equations and the complete boundary conditions are simultaneously obtained through a variational formulation based on the Gibbs-type variational principle. The constitutive relations of general anisotropic and isotropic materials with the corresponding independent material constants are also provided, respectively. To illustrate the newly proposed theory and to show the flexoelectric effect in isotropic materials, one pure bending problem of a simply supported beam is analytically solved by directly applying the formulas derived. The analytical results reveal that the flexoelectric effect is present in isotropic materials. In addition, the incorporation of both the couple stress and flexoelectric effects always leads to increased values of the beam bending stiffness.

Stability in constrained temperature-rate-dependent thermoelasticity

In an anisotropic temperature-rate-dependent thermoelastic material four plane harmonic waves may propagate in any direction, all dispersive and attenuated, and all stable in the sense that their amplitudes remain bounded in the direction of travel. In this paper, the material is additionally assumed to suffer an internal constraint of the deformation-temperature type, i.e. the temperature is a prescribed function of the deformation gradient. In this constrained thermoelastic material four waves continue to propagate but instabilities are now found. Constrained temperature-rate-dependent thermoelasticity is then combined with generalized thermoelasticity in which the rate of change of heat flux also appears in the heat conduction equation. Four waves again propagate but instabilities are found as before. Anisotropic and isotropic materials are both considered.