It is shown that the energy-release rates associated with the translation, rotation, self-similar expansion and distortion of the fracture process region are expressed by the newly introduced integrals, Jˆ, Lˆ, Mˆ, and Iˆ. These integrals can be defined even if there exist plastic deformation, thermal strains, body forces, and inertia forces. They include as special cases the J, L, and M integrals which have been defined by Knowles and Sternberg and discussed by Budiansky and Rice.

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