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Propagating cracks in saturated ionized porous media. (English) Zbl 1323.74076
de Borst, René (ed.) et al., Multiscale methods in computational mechanics. Progress and accomplishments. Selected papers based on the presentations at the international colloquium (MMCM 2009), Rolduc, The Netherlands, March 11–13, 2009. New York, NY: Springer (ISBN 978-90-481-9808-5/hbk; 978-94-007-3386-2/pbk; 978-90-481-9809-2/ebook). Lecture Notes in Applied and Computational Mechanics 55, 425-442 (2011).
Summary: Ionized porous media swell or shrink under changing osmotic conditions. Examples of such materials are shales, clays, hydrogel and biological tissues. The presence of the fixed charges causes an osmotic pressure difference between the material and surrounding fluid and concomitantly prestressing of the material. Understanding the mechanisms for fracture and failure of these materials are important for design of oil recovery, medical treatment and materials. The aim has therefore been to study with the Finite Element Method the effect of osmotic conditions on propagating discontinuities. The work uses the partition of unity modeling of a crack in a swelling medium. The modeling of the fluid flow around the crack is essentially different for mode-I compared to mode-II. In mode-I, the pressure is assumed continuous in the crack area, while in mode-II the pressure is assumed discontinuous across the crack. Step-wise crack propagation through the medium is observed both for mode-II as for mode-I. Furthermore, propagation is shown to depend on the osmotic prestressing of the medium. In mode-II the prestressing has an influence on the angle of growth. In mode-I, the prestressing is found to enhance crack propagation or protect against failure depending on the load and material properties.
For the entire collection see [Zbl 1202.74012].

74R99 Fracture and damage
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics
76S05 Flows in porous media; filtration; seepage
Full Text: DOI
[1] R. Al-Khoury and L.J. Sluys. A computational model for fracturing porous media. \(International Journal for Numerical Methods in Engineering\), 70(4):423-444, 2007. · Zbl 1194.74057 · doi:10.1002/nme.1886
[2] F. Armero and C. Callari. An analysis of strong discontinuities in a saturated poro-plastic solid. \(International Journal for Numerical Methods in Engineering\), 46(10):1673-1698, 1999. · Zbl 0971.74029 · doi:10.1002/(SICI)1097-0207(19991210)46:10<1673::AID-NME719>3.0.CO;2-S
[3] I. Babuska and J.M. Melenk. The partition of unity method. \(International Journal for Numerical Methods in Engineering\), 40(4):727-758, 1997. · Zbl 0949.65117 · doi:10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N
[4] G.I. Barenblatt. The mathematical theory of equilibrium cracks in brittle fracture. \(Advances in Applied Mechanics\), (7):55-129, 1962. · doi:10.1016/S0065-2156(08)70121-2
[5] T. Belytschko and T. Black. Elastic crack growth in finite elements with minimal remeshing. \(International Journal for Numerical Methods in Engineering\), 45(5):601-620, 1999. · Zbl 0943.74061 · doi:10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S
[6] T.J. Boone and A.R. Ingraffea. A numerical procedure for simulation of hydraulicallydriven fracture propagation in poroelastic media. \(International Journal for Numerical and Analytical Methods in Geomechanics\), 14(1):27-47, 1990. · doi:10.1002/nag.1610140103
[7] T.J. Boone, A.R. Ingraffea, and J.C. Roegiers. Simulation of hydraulic fracture propagation in poroelastic rock with application to stress measurement techniques. \(International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts\), 28(1):1-14, 1991. · doi:10.1016/0148-9062(91)93228-X
[8] R. de Borst, J.J.C. Remmers, A. Needleman, andM.A. Abellan. Discrete vs smeared crack models for concrete fracture: Bridging the gap. \(International Journal for Numerical and Analytical Methods in Geomechanics\), 28(7/8):583-607, 2004. · Zbl 1086.74044 · doi:10.1002/nag.374
[9] D.S. Dugdale. Yielding of steel sheets containing slits. \(Journal of the Mechanics and Physics of Solids\), 8(2):100-104, 1960. · doi:10.1016/0022-5096(60)90013-2
[10] S.H. Emerman, D.L. Turcotte, and D.A. Spence. Transport of magma and hydrothermal solutions by laminar and turbulent fluid fracture. \(Physics of the Earth and Planetary Interiors\), 41(4):249-259, 1986. · doi:10.1016/0031-9201(86)90004-X
[11] T.C. Gasser and G.A. Holzapfel. Modeling plaque fissuring and dissection during balloon angioplasty intervention. \(Annals of Biomedical Engineering\), 35(5):711-723, 2007. · doi:10.1007/s10439-007-9258-1
[12] T. Hettich, A. Hund, and E. Ramm. Modeling of failure in composites by x-fem and level sets within a multiscale framework. \(Computer Methods in Applied Mechanics and Engineering\), 197(5):414-424, 2008. · Zbl 1169.74543 · doi:10.1016/j.cma.2007.07.017
[13] T. Hettich and E. Ramm. Interface material failure modeled by the extended finiteelement method and level sets. \(Computer Methods in Applied Mechanics and Engineering\), 195(37-40):4753-4767, 2006. · Zbl 1154.74386 · doi:10.1016/j.cma.2005.09.022
[14] A. Hillerborg, M. Modeér, and P.E. Petersson. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. \(Cement and Concrete Research\), (6):773-782, 1976. · doi:10.1016/0008-8846(76)90007-7
[15] F. Kraaijeveld, J.M. Huyghe, and F.P.T. Baaijens. Singularity solution of Lanir’s osmoelasticity: Verification of discontinuity simulations in soft tissues. \(Journal of Biomechenical Engineering\), 2009.
[16] F. Kraaijeveld, J.M. Huyghe, J.J.C. Remmers, R. de Borst, and F.P.T. Baaijens. A meshindependent model for mode-\(i\) fracture in osmoelastic saturated porous media. \(International Journal for Numerical Methods in Engineering\), 2009.
[17] F. Kraaijeveld, J.M. Huyghe, J.J.C. Remmers, R. de Borst, and F.P.T. Baaijens. Shear fracture in osmoelastic saturated porous media: A mesh-independent model. \(Engineering Fracture Mechanics\), 2009.
[18] Y. Lanir. Biorheology and fluid flux in swelling tissues. 1. Bicomponent theory for small deformations, including concentration effects. \(Biorheology\), 24(2):173-187, 1987.
[19] J. Larsson and R. Larsson. Localization analysis of a fluid-saturated elastoplastic porous medium using regularized discontinuities. \(Mechanics of Cohesive-Frictional Materials\), 5(7):565-582, 2000. · Zbl 0995.74069 · doi:10.1002/1099-1484(200010)5:7<565::AID-CFM107>3.0.CO;2-W
[20] N. Moes and T. Belytschko. Extended finite element method for cohesive crack growth. \(Engineering Fracture Mechanics\), 69(7):813-833, 2002. · doi:10.1016/S0013-7944(01)00128-X
[21] J.J.C. Remmers, R. de Borst, and A. Needleman. A cohesive segments method for the simulation of crack growth. \(Computational Mechanics\), 31(1-2):69-77, 2003. · Zbl 1038.74679 · doi:10.1007/s00466-002-0394-z
[22] J. Rethore, R. de Borst, and M.A. Abellan. A discrete model for the dynamic propagation of shear bands in a fluid-saturated medium. \(International Journal for Numerical and Analytical Methods in Geomechanics\), 31(2):347-370, 2007. · Zbl 1112.74055 · doi:10.1002/nag.575
[23] J. Rethore, R. de Borst, and M. A. Abellan. A two-scale approach for fluid flow in fractured porous media. \(International Journal for Numerical Methods in Engineering\), 71(7):780-800, 2007. · Zbl 1194.76139 · doi:10.1002/nme.1962
[24] S. Roels, P. Moonen, K. De Proft, and J. Carmeliet. A coupled discrete-continuum approach to simulate moisture effects on damage processes in porous materials. \(Computer Methods in Applied Mechanics and Engineering\), 195(52):7139-7153, 2006. · Zbl 1331.76118 · doi:10.1016/j.cma.2005.05.051
[25] J.G. Rots. Smeared and discrete representation of localized fracture. \(International Journal of Fracture\), 51:45-59, 1991. · doi:10.1007/BF00020852
[26] F.J. Santarelli, D. Dahen, H. Baroudi, and K.B. Sliman. Mechanisms of borehole instability in heavily fractured rock media. \(International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts\), 29(5):457-467, 1992. · doi:10.1016/0148-9062(92)92630-U
[27] J.C.J. Schelleken and R. de Borst. Free edge delamination in carbon-epoxy laminates: a novel numerical/experimental approach. \(Composite Structures\), 28:357-373, 1994. · doi:10.1016/0263-8223(94)90118-X
[28] B.A. Schrefler, S. Secchi, and L. Simoni. On adaptive refinement techniques in multifield problems including cohesive fracture. \(Computer Methods in Applied Mechanics and Engineering\), 195(4-6):444-461, 2006. · Zbl 1193.74158 · doi:10.1016/j.cma.2004.10.014
[29] S. Secchi, L. Simoni, and B.A. Schrefler. Mesh adaptation and transfer schemes for discrete fracture propagation in porous materials. \(International Journal for Numerical and Analytical Methods in Geomechanics\), 31(2):331-345, 2007. · Zbl 1114.74061 · doi:10.1002/nag.581
[30] L. Simoni and S. Secchi. Cohesive fracture mechanics for a multi-phase porous medium. \(Engineering Computations\), 20(5/6):675-698, 2003. · Zbl 1060.74065 · doi:10.1108/02644400310488817
[31] K. Terzaghi. \(Theoretical Soil Mechanics\). John Wiley and Sons, New York, 1943. · doi:10.1002/9780470172766
[32] G.N. Wells and L.J. Sluys. Discontinuous analysis of softening solids under impact loading. \(International Journal for Numerical and Analytical Methods in Geomechanics\), 25(7):691-709, 2001. · Zbl 1052.74564 · doi:10.1002/nag.148
[33] S. Wognum, J.M. Huyghe, and F.P.T. Baaijens. Influence of osmotic pressure changes on the opening of existing cracks in 2 intervertebral disc models. \(Spine\), 31(16):1783-1788, 2006. · doi:10.1097/01.brs.0000227267.42924.bb
[34] X.P. Xu and A. Needleman. Void nucleation by inclusion debonding in a crystal matrix. \(Modelling and Simulation in Materials Science and Engineering\), 1(2):111-132, 1993. · doi:10.1088/0965-0393/1/2/001
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