The difference in the potential energy in an elastic three-dimensional domain with a V-notch with and without a small crack (δΠ) under a general mixed mode I. +. II. +. III loading is provided as an asymptotic series. It involves the V-notch edge stress intensity functions, the area of the formed crack, and special geometrical functions that can be pre-computed and tabulated. Importantly, the stress intensity functions along the crack front and the solution for the V-notched domain with the presence of the crack are un-necessary. The analytical formulation is verified by finite element methods, demonstrating the accuracy of the obtained expressions.
- 3D singularities
- Edge stress intensity functions
- Potential energy