本文主旨在推導含兩個圓形異質體與裂紋交互作用之反平面彈性力學之通解，裂紋位於基材或是異質體，研究中使用Muskhelishvili二維反平面等向彈性力學理論為基礎。藉由複變理論、保角映射法、解析連續的技巧、裂紋位於基材或是異質體之應力函數以級數形式表示，其應力函數可簡化成規則收斂級數。已知差排函數之均質解，再藉由積分可求出裂縫之解，最後可求得出模態三應力強度因子數值解。文中考慮含兩個圓形異質體與裂紋之無窮平面交互作用，考慮兩種情況分別裂縫在基材上或是在異質內等實例。

A general solution to the elastic problem of two circular inclusions and a crack embedded either in an infinite matrix or inclusion under a remote uniform shear is provided in this work. Based upon the method of analytical continuation in conjunction with alternating technique, a convergent series solution either in the inclusion or in the matrix is derived in an elegant form. By applying the existing solutions for dislocation, the integral equations for a line crack are formulated and the mode-III stress intensity factors are obtained numerically. Numerical examples of the interaction between two circular inclusions and a crack are discussed in detail and displayed in graphic form.

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