A new eigenfunction expansion method is developed to obtain hitherto unavailable explicit expressions for three-dimensional asymptotic singular stress fields int he vicinity of (a) an interior point (edge), (b) the surface corner point (vertex) and (c) the transition region located at the front of a a semi-infinite crack. In comparison with the existing asymptotic methods valid for the interior region, the present method is considerably easier to implement, and is also computationally more efficient in the sense that it does not need to resort to iterative schemes to solve the system of three coupled partial differential equations of three-dimensional elasticity theory.
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