The direct flexoelectricity in solid dielectrics, as an electromechanical mechanism coupling polarization and strain gradient, exhibits strong size dependence and structures associated (geometry or microstructure). In this work, a novel asymmetric micro-cylinder composed of functionally graded (FG) materials is designed to evaluate computationally the role of flexoelectricity in the electromechanical response. However, analytical solutions involving strain gradient elasticity and flexoelectricity make the universal coupling phenomenon in multiple fields difficult for such asymmetric graded structure. Based on the mixed finite element method (FEM), we introduce Lagrange multipliers to enforce the kinematic relationship between the displacement field and its gradient, so as to help understand the flexoelectric performance of the proposed FG micro-cylinder. Code verification as well as validation of the mixed FEM for the present FG structure is obtained by comparing numerical results with analytical solutions for a traditional composite micro-cylinder. The simulated results show that the designed FG configuration highlights the critical role of material composition and material distribution on the effective electromechanical response. At the same time, a reasonable gradient function can greatly improve the mechanical and electrical properties of materials. Our results suggest that computer simulations can help to understand and quantify the physical properties of flexoelectric devices.

作为耦合极化和应变梯度的机电机制，固体电介质中的直接柔电具有很强的尺寸依赖性和相关的结构（几何或微观结构）。在这项工作中，设计了一种由功能梯度（FG）材料组成的新型不对称微圆柱体，以通过计算来评估柔电在机电响应中的作用。但是，涉及应变梯度弹性和挠性电的解析解使得这种不对称渐变结构在多个领域都难以实现普遍耦合现象。基于混合有限元方法（FEM），我们引入了拉格朗日乘子来增强位移场与其坡度之间的运动关系，从而有助于了解所提出的FG微圆柱体的柔电性能。通过将数值结果与传统复合微圆柱体的解析解进行比较，可以获得代码验证以及针对当前FG结构的混合FEM的验证。仿真结果表明，所设计的FG配置突出了材料成分和材料分布对有效机电响应的关键作用。同时，合理的梯度函数可以大大改善材料的机械和电气性能。我们的结果表明，计算机仿真可以帮助理解和量化柔性电子设备的物理特性。通过将数值结果与传统复合微圆柱体的解析解进行比较，可以获得代码验证以及针对当前FG结构的混合FEM的验证。仿真结果表明，所设计的FG配置突出了材料成分和材料分布对有效机电响应的关键作用。同时，合理的梯度函数可以大大改善材料的机械和电气性能。我们的结果表明，计算机仿真可以帮助理解和量化柔性电子设备的物理特性。通过将数值结果与传统复合微圆柱体的解析解进行比较，可以获得代码验证以及针对当前FG结构的混合FEM的验证。仿真结果表明，所设计的FG配置突出了材料成分和材料分布对有效机电响应的关键作用。同时，合理的梯度函数可以大大改善材料的机械和电气性能。我们的结果表明，计算机仿真可以帮助理解和量化柔性电子设备的物理特性。仿真结果表明，所设计的FG配置突出了材料成分和材料分布对有效机电响应的关键作用。同时，合理的梯度函数可以大大改善材料的机械和电气性能。我们的结果表明，计算机仿真可以帮助理解和量化柔性电子设备的物理特性。仿真结果表明，所设计的FG配置突出了材料成分和材料分布对有效机电响应的关键作用。同时，合理的梯度函数可以大大改善材料的机械和电气性能。我们的结果表明，计算机仿真可以帮助理解和量化柔性电子设备的物理特性。