高阶电机材料的内置广义周期性条件的计算均匀化
Computational homogenization of higher-order electro-mechanical materials with built-in generalized periodicity conditions
AI总结：
本文提出一种内置广义周期性条件的高阶机电均匀化方法，用于研究含挠曲电等效应的周期超材料，可表征各向异性并验证表观压电性。
摘要：
我们提出了一种在高阶机电理论背景下实现高阶广义周期性条件的公式，该理论包括挠曲电效应、应变梯度弹性和梯度介电性，旨在研究周期性架构超材料。该理论导致四阶控制偏微分方程，周期性条件涉及原始场（位移和电势）及其法向导数在周期边界上的连续性，以及相应的对偶广义力（牵引力、双牵引力、表面电荷密度和双表面电荷密度）的连续性。我们不是将这些条件作为显式约束数值施加，而是开发了一个近似空间，该空间通过构造满足广义周期性。我们的方法自然地允许我们沿任意方向施加一般的宏观场（应变/应力和电场/电位移），从而能够表征材料的各向异性。我们将所提出的方法应用于研究具有表观压电性的周期性架构超材料。我们首先通过将结果与大型周期结构直接比较来验证该方法，然后将其应用于评估几何极化二维晶格中各向异性的表观压电性，最后展示了该方法在三维架构超材料中的应用。
英文摘要：
We present a formulation for high-order generalized periodicity conditions in the context of a high-order electromechanical theory including flexoelectricity, strain gradient elasticity and gradient dielectricity, with the goal of studying periodic architected metamaterials. Such theory results in fourth-order governing partial differential equations, and the periodicity conditions involve continuity across the periodic boundary of primal fields (displacement and electric potential) and their normal derivatives, continuity of the corresponding dual generalized forces (tractions, double tractions, surface charge density and double surface charge density). Rather than imposing these conditions numerically as explicit constraints, we develop an approximation space which fulfils generalized periodicity by construction. Our method naturally allows us to impose general macroscopic fields (strains/stresses and electric fields/electric displacements) along arbitrary directions, enabling the characterization of the material anisotropy. We apply the proposed method to study periodic architected metamaterials with apparent piezoelectricity. We first verify the method by directly comparing the results with a large periodic structure, then apply it to evaluate the anisotropic apparently piezoelectricity of a geometrically polarized 2D lattice, and finally demonstrate the application of the method in a 3D architected metamaterial.
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