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Feeding and dissipative waves in fracture and phase transition. III: Triangular-cellular lattice. (English) Zbl 1140.74535
Summary: Wave configurations for modes I and II of crack propagation in an elastic triangular-cell lattice are studied. (Mode III was considered in Part I [J. Mech. Phys. Solids 49, No. 3, 469–511 (2001; Zbl 1003.74007)].) A general solution incorporates a complete set of the feeding and dissipative waves. The solution is based on the wave dispersion dependences obtained in an explicit form. Also some general properties and the long-wave asymptotes of the corresponding Green function are found. This results in the determination of the wavenumbers and modes. The macrolevel-associated solutions exist as the sub-Rayleigh crack speed regime for both modes and as a shear-longitudinal wave-speed intersonic regime for mode II only. In particular, it is shown that any intersonic crack speed is possible, whereas only the speed (shear wave speed multiplied by \(\sqrt 2\)) corresponds to a positive energy release in the cohesive-zone-free homogeneous-material model. This is a manifestation of the fact that the local energy release in the lattice is not connected with the singularity of the macrolevel field. Microlevel solutions, corresponding to a nonzero feeding wavenumber, exist for both modes, at least from the energy point of view, for any, sub- and super-Rayleigh, intersonic and supersonic crack speed regimes. In particular, in the super-Rayleigh regime, a high-frequency wave delivers energy to the crack, while the macrolevel wave carries energy away from the crack.
Part II, J. Mech. Phys. Solids 49, No. 3, 513–550 (2001) was reviewed jointly with part I.

74R10 Brittle fracture
74N20 Dynamics of phase boundaries in solids
74J99 Waves in solid mechanics
Full Text: DOI
[1] Abraham, F.F., Gao, H., 2000. How fast can cracks propagate? Phys. Rev. Lett. 84 (14), 3113-3116.
[2] Broberg, K.B., Cracks and fracture, (1999), Academic Press New York · Zbl 0423.73064
[3] Burridge, R.; Conn, G.; Freund, L.B., The stability of rapid mode II shear crack with finite cohesive traction, J. geophys. res., 84, 2210-2222, (1979)
[4] Freund, L.B., The mechanics of dynamic shear crack propagation, J. geophys. res., 84, 2199-2209, (1979)
[5] Gao, H.; Huan, Y.; Gumbsch, P.; Rosakis, A.J., J. mech. phys. solids, 47, 1941-1961, (1999)
[6] Gerde, E., Marder, M., 2001. Friction and fracture. Nature 391, 37-42.
[7] Kulakhmetova, Sh.A.; Saraikin, V.A.; Slepyan, L.I., Plane problem of a crack in a lattice, Mech. solids, 19, 101-108, (1984)
[8] Marder, M.; Gross, S., Origin of crack tip instabilities, J. mech. phys. solids, 43, 1-48, (1995) · Zbl 0878.73053
[9] Needleman, A.; Rosakis, A.J., The effect of bond strength and loading rate on the conditions governing the attainment of intersonic crack growth along interfaces, J. mech. phys. solids, 47, 2411-2449, (1999) · Zbl 0982.74059
[10] Rosakis, A.J.; Samudrala, O.; Coker, D., Crack faster than the shear wave speed, Science, 284, 1337-1340, (1999)
[11] Rosakis, A.J.; Samudrala, O.; Singh, R.P.; Shukla, A., Intersonic crack propagation in bimaterial systems, J. mech. phys. solids, 46, 1789-1813, (1998) · Zbl 0945.74511
[12] Slepyan, L.I., The problem of the propagation of a cut at transonic velocity. sov. phys. dokl., 26, 1192-1193, (1981) · Zbl 0519.73085
[13] Slepyan, L.I., Dynamic factor in impact, phase transition and fracture, J. mech. phys. solids, 48, 927-960, (2000) · Zbl 0988.74050
[14] Slepyan, L.I., Feeding and dissipative waves in fracture and phase transition. I. some 1D structures and a square-cell lattice, J. mech. phys. solids, 49, 469-511, (2001) · Zbl 1003.74007
[15] Slepyan, L.I., Feeding and dissipative waves in fracture and phase transition. II, Phase-transition waves. J. mech. phys. solids, 49, 513-550, (2001) · Zbl 1003.74007
[16] Slepyan, L.I.; Ayzenberg, M.V.; Dempsey, J.P., A lattice model for viscoelastic fracture, Mech. time-dependent mater., 3, 159-203, (1999)
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