以彈性理論為基礎的複合材料理論，預測兩相複合材料的等效力學性質，以及應力應變在複合材料中的分布。本論文的目的，是以有限元素法計算不同均質複合材料的線彈性性質，如Voigt, Reuss 以及Hashin-Strikman 等模型，並將數值模擬結果與複合材料理論相互比對，在二維與三維的模擬結果中顯示，有限元的計算結果與古典複合材理論解很接近。此外，微結構對應的複合材料的上下限模型也被驗證。兩相複合材中的內含物裡面，假如內含物足夠小的話，內含物內的應力分佈是均勻的，與Eshelby的理論一致。另外，本論文也有探討介面上的應力與應變的連續與不連續性，以及均質線黏彈性的性質。

Theory of composite materials, based on the elasticity theory, predicts the effective mechanical properties of two-phase materials, as well as the stress and strain distributions inside the composites. The purpose of this thesis is to numerically study, by the finite element method, the homogenized, linear elastic properties of various composite models, such as Voigt, Reuss and Hashin-Strikman models, and to correlate the numerical results with the composite theory. In both two- and three-dimensional cases, the FEM calculated results are in good agreement with the classical composite theory. Furthermore, the microstructures which correspond the the upper and lower bounds of the composite models are verified. The stress distribution inside the inclusion of the two-phase composite is uniform, consistent with the Eshelby’s uniformity theorem. In addition, the discontinuity and continuity of the interfacial stresses and strains are discussed. Homogenization of linear viscoelastic properties is also studied.

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