Computational aspects of the determination of the stress intensity factors for two-dimensional elasticity

Abstract

This work is devoted to the investigation of corner and interface singularities in linear elasticity and to the development of a numerical code that computes several quantities associated with those singularities. We compute several terms of the asymptotic expansion of the solution of the elasticity system near the corner or interface, which is of the form $k\sb{n}r\sp{\alpha\sb{n}}f\sb{n}(\theta)$, in particular the $\alpha\sb{n}$ and $f\sb{n}(\theta)$. Those quantities are then used in several extraction techniques to find the stress intensity factors $k\sb{n}$. We treat our problem as a nonlinear eigenvalue problem and we use an approach based on the shooting method for boundary value problems to create an analytic function whose zeros are the $\alpha\sb{n}$ above. The zeros of this function are then found using an iteration method and a global method to make sure that no zero was overlooked. The program works for the general case of anisotropic nonhomogeneous wedge with several general boundary conditions as well as in the case of crossing interfaces in an internal point. We survey several methods that exist in the literature, and are related to the above computations, and we compare them to our method. We test the convergence, accuracy, robustness, efficiency and reliability of the code. From those experiments it can be seen that the code works quite well for the majority of the applications. It is user friendly and its output can be directly incorporated to existing Finite Element Codes such as PROBE to be used in a postprocessing method.