Line Inclusions in Anisotropic Elastic Solids

A line inclusion located at x₂ = 0, |x₁| < 1 in the anisotropic elastic medium of infinite extent under uniform loading at infinity is considered. Stroh’s formalism is used to find the displacement and stress fields. The inclusion can be rigid or elastic. Conditions on the loading under which the line inclusion does not disturb the homogeneous field are derived. For the rigid inclusion, a real form solution is obtained for the stress and displacement along x₂ = 0. When the inclusion is elastic (and anisotropic), a pair of singular Fredholm integral equations of the second kind is derived for the difference in the stress on both surfaces of the inclusion. The pair can be decoupled and asymptotic solutions of the integral equation are obtained when λ, which represents the relative rigidity of the matrix to the inclusion, is small. For the general cases, the integral equation is solved by a numerical discretization. Excellent agreements between the asymptotic and numerical solutions are observed for small λ.