Stress intensity factor calculation in orthotropic functionally graded layers using element-free Galerkin method

Production methods of functionally graded materials cause anisotropic behavior. In this paper, the element-free Galerkin method is used to study of fracture behavior of orthotropic functionally graded materials. In this method, numerical calculation of the main and auxiliary strain fields is simply done while, in finite element and extended finite element methods, it is associated with difficulties. In addition to in this paper, a path-independent integral is presented to compute the fracture parameters in heterogeneous materials which has a unique form for mechanical and thermal loading. This new form of interaction integral includes terms with the certain physical interpretation. Also, the presented form of interaction integral has fixed term for interaction of linear fields on elastic field and it is systematically extensible. In this paper, the stress intensity factors in orthotropic functionally graded materials are obtained by using this interaction integral formula. The element-free Galerkin method is implemented to discrete the governing equations. The effect of materials characteristics on the stress intensity factors is studied in several examples. The obtained results are in good agreement with reported ones in existence papers.