Feeding and dissipative waves in fracture and phase transition. III: Triangular-cellular lattice.

*(English)*Zbl 1140.74535Summary: 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.

Part II, J. Mech. Phys. Solids 49, No. 3, 513–550 (2001) was reviewed jointly with part I.

##### MSC:

74R10 | Brittle fracture |

74N20 | Dynamics of phase boundaries in solids |

74J99 | Waves in solid mechanics |

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\textit{L. I. Slepyan}, J. Mech. Phys. Solids 49, No. 12, 2839--2875 (2001; Zbl 1140.74535)

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