The effective piezoelectric and flexoelectric properties of heterogeneous solid bodies with constituents obeying a piezoelectric behavior are evaluated in full generality, based on the asymptotic expansion method. The successive situations of materials obeying a piezoelectric and flexoelectric behavior at the macroscale is envisaged in the present work. Closed-form expressions for the effective flexoelectric properties are obtained for stratified materials. A general theory for laminated piezoelectric plates is formulated on the basis of the formulated asymptotic models, and the response of the homogeneous substitution plate is evaluated for a loading consisting of a pure bending moment, triggering electric fields and strain and electric fields gradients within the plate thickness. The local mechanical and electric fields at the microscopic level within the initial heterogeneous stratified domain are evaluated by solving unit cell boundary value problems for the localization operators. An effective flexoelectric plate model for a stratified composite is constructed, showing the generation of the gradient of an electric field under application of a pure bending moment.

基于渐近展开法，对成分服从压电行为的异质固体的有效压电和挠曲电性能进行了全面评估。目前的工作设想了材料在宏观尺度上服从压电和挠曲电行为的连续情况。对于分层材料，获得了有效挠曲电性能的闭式表达式。在渐近模型的基础上制定了叠层压电板的一般理论，并评估了均匀置换板对由纯弯矩、触发电场和板内应变和电场梯度组成的载荷的响应厚度。通过求解定位算子的晶胞边界值问题来评估初始异质分层域内微观层面的局部机械和电场。构建了分层复合材料的有效柔性电板模型，显示了在施加纯弯矩的情况下电场梯度的产生。