A nonlinear phenomenological model of flexoelectricity in thermoelastic solids is presented within the frame of continuum mechanics and extended thermodynamics, incorporating the quasi-electrostatic approximation where the time derivative of the electric displacement vector can be neglected in Maxwell–Ampère’s law. An expression for the energy flux is proposed, including many internal variables. An advantage of the proposed model is that it presents a unified approach to study several thermo-electromechanical couplings, including electrostriction, piezoelectricity, dependence of entropy and spontaneous polarization on flexoelectricity, among others. The model may be of interest in revealing the effects of such couplings on the properties of polarizable media, in particular ferroelectrics, when simple boundary conditions prevail. For a fully dynamic description of flexoelectricity, Hamilton’s principle and the variational principle for external forces should be used instead.

在连续介质力学和扩展热力学的框架内提出了热弹性固体中弯曲电的非线性唯象模型，结合了准静电近似，其中电位移矢量的时间导数可以在麦克斯韦-安培定律中忽略不计。提出了能量通量的表达式，包括许多内部变量。该模型的一个优点是它提供了一种统一的方法来研究几种热机电耦合，包括电致伸缩、压电、熵的依赖性和自发极化对挠曲电的依赖等。当简单边界条件占优势时，该模型可能有助于揭示这种耦合对可极化介质（特别是铁电体）特性的影响。为了完全动态地描述挠曲电性，应使用哈密顿原理和外力变分原理。