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A finite elastic body with a curved crack loaded in anti-plane shear. (English) Zbl 0786.73081
The paper deals with an indirect boundary integral equation formulation for the stress analysis of linearly elastic, homogeneous and isotropic body with a curved crack loaded in anti-plane shear. The crack must be an arc of a circle and wholly inside the solid. Making use of complex variables and conformal mapping, the singular kernels for an infinite domain are augmented such that the new kernels are singular solutions for a point source in an infinite domain containing a traction-free curved crack. All the unknowns of the problem are localized only on the outer boundary of the body. Integral expressions for the mode III stress intensity factors at each crack tip is derived. These integral representations require far field boundary data, available from a numerical solution of a boundary value problem without any special treatment of the crack surfaces. A rigorous mathematical formulation is developed, the main aspects of the numerical implementation are discussed, and several representative examples are presented.

74S15 Boundary element methods applied to problems in solid mechanics
74R99 Fracture and damage
74B05 Classical linear elasticity
74S30 Other numerical methods in solid mechanics (MSC2010)
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