Thin elastic inclusions in a transversally isotropic material

We propose a model of thin elastic inclusions that reduces the problem to the treatment of plane surfaces of discontinuity of displacements in a transtropic space. By representing the solution of the equilibrium equations in terms of harmonic functions and applying the technique of integral Fourier transformation, the problem is reduced to the solution of a system of two-dimensional singular integral equations relative to displacement jumps of the discontinuity surfaces. For illustration we consider an ellipsoidal inclusion in a homogeneous uniaxial tension field for which exact solutions of the integral equations are found and expressions for the stresses within the inclusion and in its neighborhood are obtained in explicit form.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 27, No. 2, pp. 80–85, March–April, 1991.