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Propagating Cracks in Saturated Ionized Porous Media

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Multiscale Methods in Computational Mechanics

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 55))

Abstract

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.

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References

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  3. I. Babuska and J.M. Melenk. The partition of unity method. International Journal for Numerical Methods in Engineering, 40(4):727–758, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  4. G.I. Barenblatt. The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics, (7):55–129, 1962.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  9. D.S. Dugdale. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids, 8(2):100–104, 1960.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Google Scholar 

  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.

    Google Scholar 

  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.

    Google Scholar 

  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.

    Google Scholar 

  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.

    Article  Google Scholar 

  20. N. Moes and T. Belytschko. Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics, 69(7):813–833, 2002.

    Article  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  25. J.G. Rots. Smeared and discrete representation of localized fracture. International Journal of Fracture, 51:45–59, 1991.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  30. L. Simoni and S. Secchi. Cohesive fracture mechanics for a multi-phase porous medium. Engineering Computations, 20(5/6):675–698, 2003.

    Article  MATH  Google Scholar 

  31. K. Terzaghi. Theoretical Soil Mechanics. John Wiley and Sons, New York, 1943.

    Book  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

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Authors and Affiliations

  1. Materials Technology, Eindhoven University of Technology, 513, 5600 MB, Eindhoven, The Netherlands

    F. Kraaijeveld & J. M. Huyghe

Authors
  1. F. Kraaijeveld
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  2. J. M. Huyghe
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Correspondence to F. Kraaijeveld .

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Editors and Affiliations

  1. Dept. Mechanical Engineering, Eindhoven University of Technology, Eindhoven, Netherlands

    René de Borst

  2. Inst. Mechanik, Lehrstuhl II, Univ. Stuttgart, Pfaffenwaldring 7, Stuttgart, 70569, Germany

    Ekkehard Ramm

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Kraaijeveld, F., Huyghe, J.M. (2011). Propagating Cracks in Saturated Ionized Porous Media. In: de Borst, R., Ramm, E. (eds) Multiscale Methods in Computational Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 55. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9809-2_21

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  • DOI: https://doi.org/10.1007/978-90-481-9809-2_21

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