复合材料热传导系数均匀化计算的实现方法

Realization methods of computational homogenization for thermal conductivity coefficient of composites

均匀化理论可以有效预测周期性结构复合材料的等效热传导系数,然而其控制方程的载荷项形式特殊,通用有限元软件中没有对应的载荷形式,难以直接求解。提出一种本构关系及场变量的类比方法,证明了在此类比下等效热传导系数均匀化方程与等效弹性模量均匀化方程是等价的。根据求解等效弹性模量均匀化方程的热应变法,提出一种新的等效热传导系数均匀化方程数值求解方法。以ABAQUS为平台,预测单向纤维复合材料以及金属蜂窝夹芯板的等效热传导系数,计算结果与参考值吻合良好。该方法为基于通用有限元软件的复合材料等效热传导系数的均匀化计算提供了简便途径。

The computational homogenization method has been proved to be a valid method which can be used to predict the equivalent thermal conductivity coefficient of periodical-structure composites.Due to the unconventional load item form of the control equations,there is no corresponding load forms in general finite element software,and it is difficult to solve directly.An analogy method of constitutive relationships and field variables was presented,and it proves that the homogenization equations of equivalent thermal conductivity coefficient and equivalent elastic modulus are equivalent in this analogy.By utilizing the thermal strain method for homogenization equations of solving equivalent elastic modulus,a novel computational solving approach for equivalent thermal conductivity coefficient of homogenization equations was proposed.The equivalent thermal conductivity coefficient of unidirectional fiber reinforced composites and metallic honeycomb panel were calculated by using ABAQUS as platform,the calculation results agree well with reference results.This method provides a simple way for the computational homogenization of equivalent thermal conductivity coefficient of composites in common finite element software.