The identification of cracks stress intensity factors (SIFs) in elastics solids from full-field in-plane displacement field measurements via optic method is a quickly increasing subject with the development of precise digital cameras and image correlation algorithms. Nevertheless, due to the availability of only surface displacements, most of the identification methods rely on the hypothesis of plane elasticity, and geometric invariance of the crack front inside the solid. It is however known that significant three dimensional effects alter the values of plane stress computed SIFs, and that the overall geometry of the crack front plays also a role. The problem of SIFs identification is tackled here in the full three-dimensional framework by first deriving a data completion method in elasticity [1, 2, 3] enabling the determination of the elastic displacement and stress fields inside the solid, or in the part where the behavior remain elastic, from surface displacements including the case of only in-plane displacement fields measurements over a traction-free surface. Then usual numerical methods for the computation of SIF or energy release rates can be used. Numerical applications in three-dimensional elasticity with emphasis on the comparison with plane stress or plane strain results are described.


[1] S.Andrieux, T. N. Baranger, 2008, An energy error-based method for the resolution of the Cauchy problem in 3D linear elasticity, Computer Methods in Applied Mechanics and Engineering, 197, 9-12, 902-920.
[2] T. N. Baranger and S. Andrieux, Data completion for linear symmetric operators as a Cauchy problem: and efficient method via energy-like error minimization, Vietnam journal of Mechanics, Issues 3-4, to appear, 2009.
[3] T. N. Baranger and S. Andrieux, An optimization approach for the Cauchy problem in linear elasticity, J. Multidisciplinary optimization, 35 (2008), 141-152.