Normal compression wave scattering by a permeable crack in a fluid-saturated poroelastic solid |
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| Authors: | Yongjia Song Hengshan Hu John W. Rudnicki |
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| Affiliation: | 1. Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin 150001, China;Department of Civil and Environmental Engineering, Northwestern University, Evanston, Illinois 60208, USA;2. Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin 150001, China;3. Department of Civil and Environmental Engineering, Northwestern University, Evanston, Illinois 60208, USA;Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, USA |
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| 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 longitudi-nal 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 fac-tor 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 inte-gral 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 mono-tonically 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. |
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| Keywords: | Poroelasticity Biot's theory Finite crack Dynamic stress intensity factor |
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