The crack problem for nonhomogeneous materials under antiplane shear loading — a displacement based formulation

On an Antiplane Crack Problem for Functionally Graded Elastic Materials

“…The equilibrium equation governing small antiplane deformations of a functionally graded elastic material that exhibits elastic symmetry with respect to the coordinate [3] On an antiplane crack problem 71…”

“…Some of the earlier studies include the work of Clements et al [8] and Erdogan [10] while other examples include papers by Erdogan and Ozturk [11], Konda and Erdogan [16], Chen and Erdogan [4] and Jin and Batra [15]. More recent studies include papers by Chan et al [3], Dag and Erdogan [9], Noda and Wang [18], Bohr [2], Clements and Ang [7] and Chen et al [5].…”

An antiplane crack between bonded dissimilar functionally graded isotropic elastic materials

“…For many of the problems considered the functional gradation is represented by exponential functions (see for example Erdogan (1), Chan et al (2) and Chen and Erdogan (3)). Crack problems for materials in which the functional gradation is represented by polynomials or other analytic functions have been considered in several papers (see for example Clements et al (4), Ang and Clements (5), Erdogan and Ozturk (6) and Clements (7)).…”

Fracture analysis of functionally graded materials by a BEM

“…In recent years, a new class of composite materials, the so-called functionally graded [3][4][5][6][7], the classical finite element method (FEM) [8][9][10][11][12][13][14][15], the graded finite element method [16][17][18][19], the extended finite element method (XFEM) [20], the element-free Galerkin method (EFG) [21,22], the boundary integral equation method (BIEM) or boundary element method (BEM) [23][24][25][26][27], and the meshless Petrov-Galerkin method (MLPG) [28][29][30][31].…”