Fracture analysis of functionally graded materials by the method of fundamental solutions

• Published in: Theoretical and applied fracture mechanics 2023-02, Vol.123, p.103724, Article 103724
• Main Authors: Wen, J.C., Sladek, J., Sladek, V., Aliabadi, M.H., Wen, P.H.
• Format: Article
• Language: English
• Subjects: Erdogan’s fundamental solution; Finite block method; Fracture mechanics; Functionally graded materials; Laplace transform; Method of fundamental solutions; Stress intensity factors
• ISSN: 0167-8442; 1872-7638
• DOI: 10.1016/j.tafmec.2022.103724

•Erdogan fundamental solutions are employed in the method of fundamental solution for cracked body in functionally graded materials.•The accuracy and convergence of MFS have been observed;•Dynamic problem is solved without dynamic fundamental solutions;•Mapping method is applied in the domain integral. In this paper the Method of Fundamental Solutions (MFS) incorporating Erdogan’s solutions for Functionally Graded Materials (FGM) is presented for analysis of 2D fracture problems subjected to static and dynamics loads. Erdogan derived analytical solutions for a pair of static concentrated force in an infinite isotropic plate with a straight cut. Based on homogenous isotropic analysis, the contribution from non-homogeneity in equilibrium equations is treated as body forces and domain integrals based on the Erdogan’s fundamental solutions are required. In the domain integrals, all singularities are cancelled by introduction of a polar coordinate system at collocation points and crack tips. In the dynamic cases, the Laplace transformation with the Durbin inversion technique is adopted to determine the time-dependent variables such as the stress intensity factors at crack tips. The domain integrals are obtained numerically with the sub-region technique. The accuracy of the MFS is demonstrated with four numerical examples and comparisons are implemented with different numerical approaches.