A new approach to the construction of some path-independent integrals about crack tips
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Ioakimidis, Nikolaos
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Abstract
A new method, based on the complex potentials of Kolosov–Muskhelishvili and Cauchy's theorem in complex analysis, is applied to the establishment of path-independence of some integrals along a curve surrounding the tip of a crack in plane isotropic or anisotropic elasticity. The cases considered are (i) of loaded straight cracks in plane isotropic elasticity, (ii) of unloaded cracks having the shape of a circular arc (circular-arc-shaped cracks) in plane isotropic elasticity and (iii) of unloaded straight cracks in plane anisotropic elasticity. Further generalizations of the proposed method can be easily made.
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Path-independent integrals, Plane isotropic elasticity, Plane anisotropic elasticity, Fracture mechanics, Straight cracks, Circular-arc-shaped cracks, Complex potentials of Kolosov–Muskhelishvili, Holomorphic functions, Cauchy theorem, Boundary conditions