Asymptotic solution of the elasticity equations in the vicinity of an elliptical crack front. (January 2020) - Schapira, Yaron; Yosibash, Zohar
Highlights: Asymptotic solution to the elasticity system for an elliptical singular edge in a 3-D domain is derived. For traction free elliptical crack front, the explicit displacements and stress tensor are provided. The presented solution coincides with the one by Leblond and Torlai [15] given to the order of ρ 0 . Abstract: The asymptotic solution of the elasticity equations in the vicinity of an elliptical singular edge is derived and presented explicitly for an elliptical crack with traction free BCs. It is composed of edge stress intensity functions (ESIFs), which are functions along the singular edge, eigenfunctions and their shadows. The recursive equations to derive the eigenfunctions and their shadows are provided. The explicit presentation of the series is required to identify the different quantities of interest as the ESIFs and the T-stresses and allows the extension of the quasi dual function method for the extraction of the ESIFs along elliptical singular edge. We also present the dual eigenfunctions needed to extract K I in the case of an elliptical crack with traction free BCs.