J-integral can be obtained using Eshelby's energy-momentum tensor; J-integral for a straight crack is the component of the material (configurational) force along the straight crack. The following references might help.
M. Amestoy, H. D. Bui and R. Labbens, 1981, On the definition of local path independent integrals in 3D crack problems. Mechanics Research Communications 8, 231–236.
K. Eriksson, 2007, Decomposition of Eshelby’s energy momentum tensor and application to path and domain independent integrals for the crack extension force of a plane circular crack in Mode III loading. International Journal of Fracture 144 (4), 215-225.
Re: About J integral for curved crack
J-integral can be obtained using Eshelby's energy-momentum tensor; J-integral for a straight crack is the component of the material (configurational) force along the straight crack. The following references might help.
M. Amestoy, H. D. Bui and R. Labbens, 1981, On the definition of local path independent integrals in 3D crack problems. Mechanics Research Communications 8, 231–236.
K. Eriksson, 2007, Decomposition of Eshelby’s energy momentum tensor and application to path and domain independent integrals for the crack extension force of a plane circular crack in Mode III loading. International Journal of Fracture 144 (4), 215-225.
Regards,
Arash