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Conservation laws in dynamic fracture tasks. (Ukrainian. English summary) Zbl 1463.74023

Summary: Two fracture model under elastic wave action are considered: with energy dissipation while fracturing and without energy dissipation. The conservation of integrals of the complete mechanical energy and the quantities of motion of the fragments of the rod are investigated. For the model of fracture without energy dissipation, the complete mechanical energy is stored. For a fracture model involving energy dissipation, the complete mechanical energy decreases, although the motion of the inertia center remains. Therefore, dynamic fracture occurs due to the dissipation of the energy of the wave process in the rod. Applications of the models are illustrated by example of a study of quasistatic fracture by the propagation of a brittle crack. The dependence of the fracture energy on the crack size as well as the complete fracture energy are obtained.

MSC:

74A45 Theories of fracture and damage
74R10 Brittle fracture
76S05 Flows in porous media; filtration; seepage
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