### Abstract

A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a finite permeable crack subjected to a time-harmonic propagating longitudinal wave in an infinite poroelastic solid. In particular, the effect of the wave-induced fluid flow due to the presence of a liquid-saturated crack on the dynamic stress intensity factor is analyzed. Fourier sine and cosine integral transforms in conjunction with Helmholtz potential theory are used to formulate the mixed boundary-value problem as dual integral equations in the frequency domain. The dual integral equations are reduced to a Fredholm integral equation of the second kind. It is found that the stress intensity factor monotonically decreases with increasing frequency, decreasing the fastest when the crack width and the slow wave wavelength are of the same order. The characteristic frequency at which the stress intensity factor decays the fastest shifts to higher frequency values when the crack width decreases.

Original language | English (US) |
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Pages (from-to) | 356-367 |

Number of pages | 12 |

Journal | Acta Mechanica Sinica/Lixue Xuebao |

Volume | 33 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2017 |

### Fingerprint

### Keywords

- Biot’s theory
- Dynamic stress intensity factor
- Finite crack
- Poroelasticity

### ASJC Scopus subject areas

- Computational Mechanics
- Mechanical Engineering

### Cite this

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*Acta Mechanica Sinica/Lixue Xuebao*, vol. 33, no. 2, pp. 356-367. https://doi.org/10.1007/s10409-016-0633-8

**Normal compression wave scattering by a permeable crack in a fluid-saturated poroelastic solid.** / Song, Yongjia; Hu, Hengshan; Rudnicki, John W.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Normal compression wave scattering by a permeable crack in a fluid-saturated poroelastic solid

AU - Song, Yongjia

AU - Hu, Hengshan

AU - Rudnicki, John W

PY - 2017/4/1

Y1 - 2017/4/1

N2 - A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a finite permeable crack subjected to a time-harmonic propagating longitudinal wave in an infinite poroelastic solid. In particular, the effect of the wave-induced fluid flow due to the presence of a liquid-saturated crack on the dynamic stress intensity factor is analyzed. Fourier sine and cosine integral transforms in conjunction with Helmholtz potential theory are used to formulate the mixed boundary-value problem as dual integral equations in the frequency domain. The dual integral equations are reduced to a Fredholm integral equation of the second kind. It is found that the stress intensity factor monotonically decreases with increasing frequency, decreasing the fastest when the crack width and the slow wave wavelength are of the same order. The characteristic frequency at which the stress intensity factor decays the fastest shifts to higher frequency values when the crack width decreases.

AB - A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a finite permeable crack subjected to a time-harmonic propagating longitudinal wave in an infinite poroelastic solid. In particular, the effect of the wave-induced fluid flow due to the presence of a liquid-saturated crack on the dynamic stress intensity factor is analyzed. Fourier sine and cosine integral transforms in conjunction with Helmholtz potential theory are used to formulate the mixed boundary-value problem as dual integral equations in the frequency domain. The dual integral equations are reduced to a Fredholm integral equation of the second kind. It is found that the stress intensity factor monotonically decreases with increasing frequency, decreasing the fastest when the crack width and the slow wave wavelength are of the same order. The characteristic frequency at which the stress intensity factor decays the fastest shifts to higher frequency values when the crack width decreases.

KW - Biot’s theory

KW - Dynamic stress intensity factor

KW - Finite crack

KW - Poroelasticity

UR - http://www.scopus.com/inward/record.url?scp=85014072521&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014072521&partnerID=8YFLogxK

U2 - 10.1007/s10409-016-0633-8

DO - 10.1007/s10409-016-0633-8

M3 - Article

AN - SCOPUS:85014072521

VL - 33

SP - 356

EP - 367

JO - Acta Mechanica Sinica/Lixue Xuebao

JF - Acta Mechanica Sinica/Lixue Xuebao

SN - 0567-7718

IS - 2

ER -