Summary
The apparent contradiction between the Eshelby formulation (consideration of a material force on the material manifold) and the more usual global-dissipation analysis (essentially, the balance of energy about the moving singular point represented by the tip of the crack) of theJ-integral and energy-release rate in dynamical fracture is resolved in both pure finite-strain elasticity and Galilean-invariant electrodynamics of electro-magneto-elastic media. The solution uses the notions of mechanical and electromagnetic pseudomomenta (canonical momenta) in finitely deformable continua with cracks.
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Maugin, G.A. On the J-integral and energy-release rates in dynamical fracture. Acta Mechanica 105, 33–47 (1994). https://doi.org/10.1007/BF01183940
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DOI: https://doi.org/10.1007/BF01183940