Alternative solution methods for crack problems in plane anisotropic elasticity, with examples

Two-dimensional crack problems of homogeneous, anisotropic, linear elastici ty are solved using the Riemann-Hilbert method. To this end, the Riemann-Hi lbert problem of line-discontinuity is formulated for anisotropic plane pro blems and the necessary parameters and functions are identified. For illust ration, the method is applied to obtain the complete stress field and the s tress intensity factors for a crack in an infinite anisotropic plate which is loaded on a part of one of its faces. Then, the well-established method of continuously distributed edge-dislocations is considered and illustrated via some example problems; e.g., an infinite anisotropic plate under unifo rm farfield loads containing: 1. a closed frictional crack and a pair of ar bitrarily-located single edge-dislocations, and 2. an infinite row of equal ly-spaced parallel open cracks. The illustrative examples reveal that the first method offers an effective solution technique for problems where unbalanced tractions are applied on c rack surfaces, whereas for problems with self-equilibrating loads applied o n the crack faces, the second method is generally well suited. In addition, the method of resultant forces along the crock is discussed and its formul ation in terms of the dislocation density functions and also the crack-open ing displacements (which is new) is presented. The solutions to some of the example problems are provided in some detail, and for others, just the key formulae (e.g., stress functions and stress intensity factors) are calcula ted and analyzed. In brief, this paper presents the generalization of the R iemann-Hilbert method from isotropic to anisotropic in-plane elasticity pro blems, and also provides a collection of certain basic two-dimensional anis otropic crack problems; some of the results here are also new. (C) 2000 Els evier Science Ltd. All rights reserved.