We study the short time transient stress and pore pressure fields near the tip of a stationary crack when a sudden load is applied to a poroelastic solid. These fields are determined using a small scale “yielding” (SSY) analysis where the stress relaxation due to fluid flow is confined to a small region near the crack tip. They are found to exhibit the usual inverse square root singularity characteristic of cracks in linear elastic solids. Analysis shows that these fields are self-similar; the region of stress relaxation that propagates outward from the crack tip is proportional to , where is the cooperative diffusion coefficient and t is time. The pore pressure at the crack tip vanishes immediately after loading. The stress intensity factor at the crack tip is found to be reduced by a factor of , where is the Poisson's ratio of the drained solid. Closed form approximations are found for the pore pressure and the trace of the effective stress. These approximate analytical solutions compare well with finite element results.
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March 2013
Research-Article
Stress Relaxation Near the Tip of a Stationary Mode I Crack in a Poroelastic Solid
Chung-Yuen Hui,
Chung-Yuen Hui
Field of Theoretical and Applied Mechanics,
Ithaca, NY 14853
Cornell University
,Ithaca, NY 14853
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Rong Long,
Rong Long
Department of Mechanical Engineering,
Boulder, CO 80303
University of Colorado
,Boulder, CO 80303
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Jing Ning
Jing Ning
Department of Mechanical and Aerospace Engineering,
Ithaca, NY 14853
Cornell University
,Ithaca, NY 14853
Search for other works by this author on:
Chung-Yuen Hui
Field of Theoretical and Applied Mechanics,
Ithaca, NY 14853
Cornell University
,Ithaca, NY 14853
Rong Long
Department of Mechanical Engineering,
Boulder, CO 80303
University of Colorado
,Boulder, CO 80303
Jing Ning
Department of Mechanical and Aerospace Engineering,
Ithaca, NY 14853
Cornell University
,Ithaca, NY 14853
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 5, 2012; final manuscript received June 29, 2012; accepted manuscript posted July 25, 2012; published online January 22, 2013. Assoc. Editor: Chad Landis.
J. Appl. Mech. Mar 2013, 80(2): 021014 (9 pages)
Published Online: January 22, 2013
Article history
Received:
March 5, 2012
Revision Received:
June 29, 2012
Accepted:
July 25, 2012
Citation
Hui, C., Long, R., and Ning, J. (January 22, 2013). "Stress Relaxation Near the Tip of a Stationary Mode I Crack in a Poroelastic Solid." ASME. J. Appl. Mech. March 2013; 80(2): 021014. https://doi.org/10.1115/1.4007228
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