复合材料与界面纳米结构热传导问题分子动力学与连续介质跨尺度耦合模型与算法

曹礼群+黄记祖

摘 要：构一体化的热、力耦合多尺度模型与算法研究是力学、数学、物理学与材料科学多学科交叉的前沿领域，也是重大装备研发中需要着重解决的基础科学问题。材料与结构在裂纹、空洞、夹杂、纤维取向、基体分布形态等方面具有内在的不确定性，其损伤和破坏还表现为复杂的热力耦合非线性多尺度力学行为。尺度间隙和跨尺度连接，涉及微—细—宏观不同尺度间数学物理模型的联系与差别等基本问题，建立微/纳米尺度的热、力模型，揭示热、力耦合的物理机制，发展材料与结构一体化的宏—细—微观耦合的多尺度模型与算法，具有重要的理论与实际意义。结果表明：复合材料界面结构对于材料的力、热、电、磁等物理、力学性能有十分重要的影响。我们针对复合材料与界面纳米结构热传导问题，发展了一类分子动力学与连续模型跨尺度耦合模式、MD/FEM耦合算法，并编写了相关计算程序。主要进展有：（1）实现了纳米结构导热系数等热学参数的分子动力学计算和量子校正；（2）发展了复合材料和多孔材料周期及随机结构热传导问题连续模型的多尺度算法；（3）提出了一类分子动力学与连续模型的跨尺度关联模式和MD/FEM耦合算法；（4）实现了三维复合材料和界面纳米结构的MD/FEM计算。

关键词：分子动力学-连续介质耦合模型 热传导 多尺度渐近展开 分子动力学 有限元方法

A Molecular Dynamics-Continuum Coupled Model for Heat Transfer in Composite Materials

Cao Liqun1 Huang Jizu2

（1.Academy of Mathematics and Systems Science； 2.Institute of Software Chinese Academy of Sciences）

Abstract：The heat transfer problem in composite materials has been investigated which contain the nano-scale interface. A molecular dynamics-continuum coupled model is developed to study the heat transport from the macro- to the micro-scales. The model includes four major steps：（1）A reverse non-equilibrium molecular dynamics （RNEMD） is used to calculate some physical parameters such as the thermal conductivities on the interface.（2）The homogenization method is applied to compute the homogenized thermal conductivities of composite materials.（3）the temperature field in the global structure of composite materials is computed with the multiscale asymptotic method for the macroscopic heat transfer equation.（4）A molecular dynamics-continuum coupled model has been developed to reevaluate the temperature field of composite materials， in particular， the local temperature field near the interface. The numerical results in one-， two- and three-dimensional structures of composite materials including the nano-scale interface are given. Good agreement has been achieved between the numerical results of the proposed coupled algorithm and those of the full MD simulation， demonstrating the accuracy of the present method and its potential applications in the thermal engineering of composite materials.

Key Words：A molecular dynamics-continuum coupled model； Heat transfer； Multiscale asymptotic expansion； Molecular dynamics； Finite element method

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