复合材料热传导性能的变分渐近均匀化细观力学模型
Variational asymptotic homogenization micromechanics model for thermal conductivity of composites

为准确预测非均质复合材料的有效热导率和局部温度场分布, 采用单胞变分渐近均匀化方法构建了一种新的细观力学模型。首先从非均质连续体热传导变分问题入手, 使用变分渐近法将其细观力学模型转换为约束条件下泛函的最小化——取驻值问题;使用有限元法(FEM)推导了离散形式能量泛函的最小化求解过程;根据宏观性能(如全局温度及相应的梯度和波动函数)重构单胞的局部温度场和热通量。采用多个二元复合材料算例验证了所构建理论和程序的有效性和准确性。 A new micromechanics model was developed to accurately predict the effective thermal conductivity and local distribution of temperature field of heterogeneous composites using the variational asymptotic method for unit cell homogenization. Starting from a variational statement of the thermal conductivity problem of the heterogeneous continuum, the micromechanics model was formulated as a constrained minimization problem using the variational asymptotic method. The finite element method (FEM) was then used to solve the minimize solving process of energy functional with discrete form. To handle realistic microstructures in engineering applications, this new model was implemented using the FEM. The local fields within unit cell were recovered in terms of the macroscopic behavior including the global temperature and the corresponding gradient, and the fluctuation function. For validation, several binary composites examples were used to demonstrate the effectiveness and accuracy of the proposed theory. 国家自然科学基金(11272363,51279218);中央高校基本科研业务费专项资金(106112014CDJZR200017,106112013CDJZR200003)