Finite element calculation of elastodynamic stress field around a notch tip via contour integrals

Direct computation of the mixed-mode dynamic asymptotic stress field around a notch tip is difficult because the mode I and mode II stresses are in general governed by different orders of singularity. In this paper, we propose a pair of elastodynamic contour integrals J_kR(t). The integrals are shown to be path-independent in a modified sense and so they can be accurately evaluated with finite element solutions. Also, by defining a pair of generalized stress intensity factors (SIFs) K_I,β(t) and K_II,β(t), the relationship between J_kR(t) and the SIF's is derived and expressed as functions of the notch angle β. Once the J_kR(t)-integrals are accurately computed, the generalized SIF's and, consequently, the asymptotic mixed-mode stress field can then be properly determined. No particular singular elements are required in the calculation. The proposed numerical scheme can be used to investigate the dynamic amplifying effect in the near-tip stress field.