本文的目的主要在不同的變形方式下於利用Eshelby 的

公式和平均值定理來作等效模數的推導。首先簡述界面

效應的起源和運用的範圍，接著利用變分的方法來推導

複合材料在界面效應下的位移平衡方程式、連結界面之

間的力學行為以及自然的邊界條件，其次利用Eshelby

的公式和平均值定理來推導球形與圓柱形複合材料之間

的表面力與表面能等界面效應對於等效體積模數、等效

剪力模數和等效熱膨脹係數的影響。並且當忽略界面效

應時，證明推導的等效模數會與完美界面的答案吻合。

最後進行數值的模擬實際計算界面效應對於等效模數的

影響，發現材料的性質會受到不同的界面以及內含物半

徑大小而改變。

The main purpose of this thesis is to explore

the effective modulus of composite materials

incorporating the effects of surface/interface

stress. We first outline the physical

interpretation of the interface effect and the

potential aspects of the application. Secondly,

we use the method of calculus of variations to

obtain the equilibrium equation of the

admissible displacements, the mechanics behavior

at the interface and natural transition

conditions. Thirdly, Eshelby formula together

with the average theorem are employed to

investigate how the surface stress and surface

energy of the spherical and cylindrical

composite materials influence effective bulk

modulus, effective shear modulus and thermal

conductivity. In the absence of the interface

effect, we show that the effective modulus

reduce exactly to the corresponding solution

with perfect bounding interfaces. Finally,

numerical simulation are illustrated to

demonstrate the relation between the interface

effect and effective modulus. We find that the

interface effect and the radii of the inclusion

dramatically influence the over behavior as well

as the local fields.

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