Two dimensional displacement and stress fields for tri-material V-notches and sharp inclusions in anisotropic plates

The singular behavior for multi-material V-notch notched plates is studied in this paper, considering both isotropic and anisotropic materials. Firstly, by introducing the asymptotic expansions of displacements near the apex of the sharp notch, the elastic governing equations are transformed into eigen ordinary differential equations. The stress singularity orders and eigen angular functions are then obtained solving the established equations by using the interpolating matrix method. Secondly, using in combination the results from proper finite element analyses and the asymptotic analytical solution derived, an over-deterministic method is employed to calculate the amplitudes of the coefficients in the asymptotic expansions of displacements and stresses near the V-notch tip. The efficiency of the proposed method is assessed analyzing several notched specimens made of different materials. The accuracy of the notch stress intensity factors and the displacement and stress fields are evaluated by comparison with results available in the literature, as well as the results obtained from a number of finite element analyses.