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中文核心期刊

磁电颗粒增强复合材料的多场耦合Voronoi有限单元法

MULTIPHYSICS-COUPLED VORONOI CELL FINITE ELEMENT METHOD FOR MAGNETOELECTRIC PARTICLE-REINFORCED COMPOSITES

  • 摘要: 针对随机颗粒磁电复合材料中夹杂边界复杂、多场耦合响应求解困难及传统有限元计算成本较高的问题, 本文建立一种力-电-磁多场耦合Voronoi有限单元方法(multiphysics-coupled Voronoi cell finite element method, MC-VCFEM), 用于磁电颗粒复合材料细观场分析与宏观等效性能预测. 该方法采用Voronoi图对夹杂及其邻近基体进行区域划分, 在广义修正余能泛函框架下统一描述力学平衡方程以及电学和磁学高斯定律. 单元内部独立构造满足控制方程的自平衡应力场、电位移场和磁感应强度场, 边界采用位移、电势和磁势插值, 实现相邻单元间的连续协调. 以BaTiO3-CoFe2O4颗粒复合材料为研究对象, 分别建立圆形、椭圆形、不同倾角椭圆及随机多夹杂细观模型, 分析其局部力-电-磁耦合响应, 并与网格细化有限元结果进行对比验证. 在此基础上, 进一步研究夹杂体积分数、形状和取向对等效弹性、电学、磁学及磁电耦合参数的影响. 结果表明, 所提方法在显著减少单元数量和系统自由度的同时, 仍可获得与有限元结果较为一致的计算精度; 夹杂几何特征对界面附近局部场集中及宏观等效性能具有明显影响, 其中椭圆夹杂的取向变化会进一步引起材料等效参数的方向性差异.

     

    Abstract: To address the challenges posed by complex inclusion geometries, difficult solution of coupled multi-field responses, and the high computational cost of conventional finite element methods for particulate magnetoelectric composites with randomly distributed inclusions, a multiphysics-coupled Voronoi cell finite element method (MC-VCFEM) is developed for microscale field analysis and macroscopic effective-property prediction. In the proposed method, Voronoi tessellation is used to partition the inclusions and their neighboring matrix regions, while the mechanical equilibrium equation and the Gauss’s laws for electricity and magnetism are formulated within a unified framework based on a generalized modified complementary energy functional. Within each element, self-equilibrated stress, electric displacement, and magnetic flux density fields satisfying the corresponding governing equations are independently constructed, while displacement, electric potential, and magnetic potential are interpolated along the element boundaries to enforce interelement compatibility. Taking BaTiO3-CoFe2O4 particulate magnetoelectric composites as a representative material system, microstructural models with circular inclusions, elliptical inclusions, elliptical inclusions with different inclination angles, and multiple randomly distributed inclusions are established. Their local coupled mechanical-electrical-magnetic responses are investigated and validated against reference finite element solutions obtained using refined meshes. On this basis, the effects of inclusion volume fraction, shape, and orientation on the effective elastic coefficients, dielectric permittivities, magnetic permeabilities, and magnetoelectric coupling coefficients are examined. The results show that the proposed method significantly reduces the number of elements and total degrees of freedom while maintaining close agreement with conventional finite element solutions. Inclusion geometry has a pronounced influence on local field concentrations and macroscopic effective properties. In particular, changes in the orientation of elliptical inclusions further cause directional differences in the effective material parameters.

     

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