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In the thermodynamic framework of fracture processes, a solid made of a material obeying nonlocal elasticity and standard plasticity is considered, in which fracture is preceded by damage phenomena localized in rigid-decohesive interfaces.
Basing on the second principle of thermodynamics, a stability criterion for three-dimensional fracture is formulated, which turns out to be a generalization of the
classical Griáth's one, and in which a decisive role is played by the fracture driving force vector, the fracture resistance vector and the (symmetric) fracture stiÞness matrix, all being deßned on the fracture front (either continuously, or for discrete modes). The Griáth's fracture energy concept is met. Nonlocal elasticity renders applicable the classical stress-based safety criteria.