TY - JOUR
T1 - Crack in a lattice waveguide
AU - Slepyan, Leonid I.
AU - Movchan, Alexander B.
AU - Mishuris, Gennady S.
PY - 2010/3
Y1 - 2010/3
N2 - We consider some structures where the harmonic 'feeding' wave localized at the crack faces can force the crack to grow. First, we present some results related to a lattice with a high-contrast layer, where the wave speed is larger than in the ambient matrix. The analytical solution obtained for the steady-state regime, where the crack speed is independent of the wave amplitude, is used to determine the energy relations and the wave-amplitude-dependent position of the crack front relative to the feeding wave. The corresponding numerical simulations confirmed the existence of the steady-state regime within a range of the wave amplitude. For lager amplitudes the simulations revealed a set of ordered crack-speed oscillation regimes, where the average crack speed is characterized by a stepwise dependence on the wave amplitude. We show that the related cluster-type wave representation allows the average crack speeds to be determined analytically. We also show the connection between the cluster representation and the 'local' crack-speeds within the cluster. As an example of a continuous system, where the crack can uniformly grow under the localized harmonic wave, an elastic flexural plate is considered. Both symmetric and antisymmetric fracture modes are examined.
AB - We consider some structures where the harmonic 'feeding' wave localized at the crack faces can force the crack to grow. First, we present some results related to a lattice with a high-contrast layer, where the wave speed is larger than in the ambient matrix. The analytical solution obtained for the steady-state regime, where the crack speed is independent of the wave amplitude, is used to determine the energy relations and the wave-amplitude-dependent position of the crack front relative to the feeding wave. The corresponding numerical simulations confirmed the existence of the steady-state regime within a range of the wave amplitude. For lager amplitudes the simulations revealed a set of ordered crack-speed oscillation regimes, where the average crack speed is characterized by a stepwise dependence on the wave amplitude. We show that the related cluster-type wave representation allows the average crack speeds to be determined analytically. We also show the connection between the cluster representation and the 'local' crack-speeds within the cluster. As an example of a continuous system, where the crack can uniformly grow under the localized harmonic wave, an elastic flexural plate is considered. Both symmetric and antisymmetric fracture modes are examined.
KW - Dynamic fracture
KW - Inhomogeneous material
KW - Integral transforms
KW - Supersonic crack
KW - Vibrations
UR - http://www.scopus.com/inward/record.url?scp=77953807549&partnerID=8YFLogxK
U2 - 10.1007/s10704-009-9389-5
DO - 10.1007/s10704-009-9389-5
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AN - SCOPUS:77953807549
SN - 0376-9429
VL - 162
SP - 91
EP - 106
JO - International Journal of Fracture
JF - International Journal of Fracture
IS - 1-2
ER -