隨著科技的進步，許多技術關注在微小產品的製成，考慮微小尺度下材料的特性，當物體尺寸逐漸縮小時，表面積對體積的比率逐漸增大，此時界面/表面應力對物體之力學行為有相當大的影響，因此不可忽略考慮。本文將以基本纖維複合材料問題為架構，考慮表面應力，引入界面條件，重新探討複合材料之反平面等效剪力模數。利用複變函數定義場量分析，選用幾何形狀較為廣義的橢圓形，透過廣義自洽法建立雙層共焦橢圓形模型，並藉由保角映射技巧和平均值定理求解代表整體材料之元素彈力特性，分析複合材料在奈米尺度下，尺寸、形狀、面積比和嵌入纖維強度對表面力的影響，透過等效剪力模數來觀察表面力在小尺度下的應力行為。

This study investigates the problem of nano composites with surface stress under antiplane shear deformation. The ratio of surface area to volume increases when the size of medium shrinks, thus the mechanical behavior of the medium will be greatly affected by the interface imperfection. Therefore, the interface/surface stress is not negligible for nano scale solids. The model we discuss is the basic fibrous composite. The cross section is a confocal elliptic subjected to an antiplane shear loading on the matrix in far field. The effective antiplane shear modulus is obtained through generalized self-consistent method. The boundary condition particularly leads into the interface condition that is traction force of discontinuous. The elastic field is defined by potential function, by applying the conformal mapping technique and average theorem to solve the effective antiplane shear modulus. Finally, we demonstrate numerical results to discuss the influences of size, shape, concentration factor and shear modulus of fiber inclusion on effective behavior. The results confirm that the surface effect is significant when the size scale approach to the order of nanometer.

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