利用 格林函数法的*Eshelby夹 外场的一般显 解 解

At present, there is still no literature giving a generic explicit analytical solution for the exterior field of elliptical inhomogeneous inclusions. In this paper, the generic explicit analytical solutions for both interior and exterior fields of Eshelby's elliptical inhomogeneous inclusion, with uniform eigenstrain distribution and subjected to far-field loading, are obtained. Additionally, the generic solution applying to the well-known Inglis's elliptical hole problem is investigated, and the analytical solution in rectangular coordinate system is obtained in a new form. By virtue of the equivalent eigenstrain principle, Eshelby's elliptical inhomogeneous inclusion model is formulated with complex variable Green's function method in the framework of plane elasticity. The generic explicit analytical solution for Eshelby's elliptical inhomogeneous inclusion with uniform eigenstrain distribution and subjected to far-field loading is obtained. Its application to liquid inclusion problems is particularly explored, and some existing issues in this topic are clarified. The results show that(i)both interior pressure and far-field loading would lead drastically stress concentration in the vicinity of the endpoints of the major axis;(ii)the presence of liquid inclusion may soften the shear modulus of the composite systems. The generic explicit analytical solution for Eshelby's elliptical inhomogeneous inclusion problems obtained in this study provides a concise and convenient form for application, and its research results in the liquid inclusion problem can explain the microscopic mechanism of soil liquefaction and the influence of liquid inclusions on soil landslides. In addition, compared with the Inglis's solution within curvilinear coordinate system, the solution in rectangular coordinates is generic and compact.