两相复合介质内部电场及宏观介电常数的三维模拟

建立三维模型,用蒙特卡洛有限元法对两相复合介质的内部电场分布进行模拟,并由此计算出介质的宏观介电常数εm.发现由三维模型计算出的低介相中的电场能量占总能量的比例高于二维模型.三维模型符合实际复合介质中微粒间并联程度大于串联程度的事实,因此由三维模型得出的电场分布和ε_m值比二维模型更加精确.得出了新的两相复合介质宏观介电常数预测公式:ε^α_m=V₁ε^α₁+V₂ε^α₂,其中α=(V₁²+20V₁V₂+5V₂²)/11,V₁+V₂=1,ε₁<ε₂.该公式与若干文献中的实验结果相吻合.

3-Dimensional Simulation of the Interior Electric Field and Macro Dielectric Constant of a Two-Phased Composite Material

The interior electric field of a two-phased composite material was simulated by using Monte Carlo and finite element methods with 3-dimensional model, from which the macro dielectric constant, ε_m, of the material was calculated. The results show that the percentage of electric field energy stored in the low-permittivity phase to total energy calculated with 3-dimensional model is larger than that calculated with 2-dimensional model. Since the 3-dimensional model accords with the fact that the particles in real composite material are more parallel than serial connected, the simulated distribution of the electric field and ε_m with 3-dimensional model are more accurate than with 2-dimensional model. A new equation for predicting the macro dielectric constant of a two-phased compound derivedis: ε^α_m=V₁ε^α₁+V₂ε^α₂, where α=(V²₁+20V₁V₂+20V₁V₂+5V²₂)/11, V₁+V₂=1 and ε₁<ε₂. This equation agrees well with the data from some literatures.