Shales, clays, hydrogels, and tissues swell and shrink under changing osmotic conditions, which may lead to failure. The relationship between the presence of cracks and fluid flow has had little attention. The relationship between failure and osmotic conditions has had even less attention. The aim of this research is to study the effect of osmotic conditions on propagating discontinuities under different types of loads for saturated ionized porous media using the finite element method (FEM). Discontinuous functions are introduced in the shape functions of the FEM by partition of unity method, independently of the underlying mesh. Damage ahead of the crack-tip is introduced by a cohesive zone model. Tensile loading of a crack in an osmoelastic medium results in opening of the crack and high pressure gradients between the crack and the formation. The fluid flow in the crack is approximated by Couette flow. Results show that failure behavior depends highly on the load, permeability, (osmotic) prestress and the stiffness of the material. In some cases it is seen that when the crack propagation initiates, fluid is attracted to the crack-tip from the crack rather than from the surrounding medium causing the crack to close. The results show reasonable mesh-independent crack propagation for materials with a high stiffness. Stepwise crack propagation through the medium is seen due to consolidation, i.e., crack propagation alternates with pauses in which the fluid redistributes. This physical phenomenon challenges the numerical scheme. Furthermore, propagation is shown to depend on the osmotic prestressing of the medium. This mechanism may explain the tears observed in intervertebral disks as degeneration progresses.
Issue Section:
Research Articles
References
1.
Urban
, J. P.
, and Roberts
, S.
, 2003
, “Degeneration of the Intervertebral Disc
,” Arthritis Res. Ther.
, 5
(3
), pp. 120
–130
.10.1186/ar6292.
Adams
, M. A.
, and Roughley
, P. J.
, 2006
, “What Is Intervertebral Disc Degeneration, and What Causes It?
” Spine
, 31
(18
), pp. 2151
–2161
.10.1097/01.brs.0000231761.73859.2c3.
Hutton
, W. C.
, Ganey
, T. M.
, Elmer
, W. A.
, Kozlowska
, E.
, Ugbo
, J. L.
, Doh
, E. S.
, and T. E. Whitesides
, J.
, 2000
, “Does Long-Term Compressive Loading on the Intervertebral Disc Cause Degeneration?
” Spine
, 25
(23
), pp. 2993
–3004
.10.1097/00007632-200012010-000064.
Simunic
, D. I.
, Broom
, N. D.
, and Robertson
, P. A.
, 2001
. “Biomechanical Factors Influencing Nuclear Disruption of the Intervertebral Disc,
” Spine
, 26
(11
), pp. 1223
–1230
.10.1097/00007632-200106010-000105.
Simunic
, D. I.
, Robertson
, P. A.
, and Broom
, N. D.
, 2004
, “Mechanically Induced Disruption of the Healthy Bovine Intervertebral Disc
,” Spine
, 29
(9
), pp. 972
–978
.10.1097/00007632-200405010-000056.
Callaghan
, J. P.
, and McGill
, S. M.
, 2001
, “Intervertebral Disc Herniation: Studies on a Porcine Model Exposed to Highly Repetitive Flexion/Extension Motion With Compressive Force
,” Clin. Biomech.
, 16
(1
), pp. 28
–37
.10.1016/S0268-0033(00)00063-27.
Yu
, C. Y.
, Tsai
, K. H.
, Hu
, W. P.
, Lin
, R. M.
, Song
, H. W.
, and Chang
, G. L.
, 2003
, “Geometric and Morphological Changes of the Intervertebral Disc Under Fatigue Testing
,,” Clin. Biomech.
, 18
(6
), pp. S3
–S9
.10.1016/S0268-0033(03)00078-08.
Battie
, M. C.
, Videman
, T.
, and Parent
, E.
, 2004
, “Lumbar Disc Degeneration: Epidemiology and Genetic Influences
,” Spine
, 29
(23
), pp. 2679
–2690
.10.1097/01.brs.0000146457.83240.eb9.
Videman
, T.
, and Battie
, M. C.
, 1999
, “The Influence of Occupation on Lumbar Degeneration
,” Spine
, 24
(11
), pp. 1164
–1168
.10.1097/00007632-199906010-0002010.
Wognum
, S.
, Huyghe
, J. M.
, and Baaijens
, F. P.
, 2006
, “Influence of Osmotic Pressure Changes on the Opening of Existing Cracks in 2 Intervertebral Disc Models
,” Spine
, 31
(16
), pp. 1783
–1788
.10.1097/01.brs.0000227267.42924.bb11.
Huang
, N. C.
, and Russell
, S. G.
, 1985
, “Hydraulic Fracturing of a Saturated Porous Medium—I: General Theory
,” Theoret. Appl. Fract. Mech.
, 4
(3
), pp. 201
–213
.10.1016/0167-8442(85)90005-912.
Rice
, J. R.
, and Cleary
, M. P.
, 1976
, “Some Basic Stress Diffusion Solutions for Fluid-Saturated Elastic Porous Media With Compressible Constituents
,” Rev. Geophys. Space Phys.
, 14
(2
), pp. 227
–241
.10.1029/RG014i002p0022713.
Detournay
, E.
, and Cheng
, A. H. D.
, 1991
, “Plane Strain Analysis of a Stationary Hydraulic Fracture in a Poroelastic Medium
,” Int. J. Solids Struct.
, 27
(13
), pp. 1645
–1662
.10.1016/0020-7683(91)90067-P14.
Emerman
, S. H.
, Turcotte
, D. L.
, and Spence
, D. A.
, 1986
, “Transport of Magma and Hydrothermal Solutions by Laminar and Turbulent Fluid Fracture
,” Phys. Earth Planet. Inter.
, 41
(4
), pp. 249
–259
.10.1016/0031-9201(86)90004-X15.
Boone
, T. J.
, Ingraffea
, A. R.
, and Roegiers
, J. C.
, 1991
, “Simulation of Hydraulic Fracture Propagation in Poroelastic Rock With Application to Stress Measurement Techniques
,” International J. Rock Mech.
, 28
(1
), pp. 1
–14
.10.1016/0148-9062(91)93228-X16.
Detournay
, E.
, and Garagash
, D. I.
, 2003
“The Near-Tip Region of a Fluid-Driven Fracture Propagating in a Permeable Elastic Solid
,” J. Fluid Mech.
, 494
, pp. 1
–32
.10.1017/S002211200300527517.
Kfoury
, M.
, Ababou
, R.
, Noetinger
, B.
, and Quintard
, M.
, 2006
, “Upscaling Fractured Heterogeneous Media: Permeability and Mass Exchange Coefficient
,” ASME J. Appl. Mech.
, 73
(1
), pp. 41
–46
.10.1115/1.199186418.
Dormieux
, L.
, Kondo
, D.
, and Ulm
, F. J.
, 2006
, “A Micromechanical Analysis of Damage Propagation in Fluid-Saturated Cracked Media
,” Comptes Rendus Mecanique
, 334
(7
), pp. 440
–446
.10.1016/j.crme.2006.05.00719.
Dugdale
, D. S.
, 1960
, “Yielding of Steel Sheets Containing Slits
,” J. Mech. Phys. Solid.
, 8
(2
), pp. 100
–104
.10.1016/0022-5096(60)90013-220.
Barenblatt
, G. I.
, 1962
. “The Mathematical Theory of Equilibrium Cracks in Brittle Fracture
,” Adv. Appl. Mech.
, (7
), pp. 55
–129
.10.1016/S0065-2156(08)70121-221.
Simoni
, L.
, and Secchi
, S.
, 2003
, “Cohesive Fracture Mechanics for a Multi-Phase Porous Medium
,”. Eng. Computat.
, 20
(5–6
), pp. 675
–698
.10.1108/0264440031048881722.
Schrefler
, B. A.
, Secchi
, S.
, and Simoni
, L.
, 2006
, “On Adaptive Refinement Techniques in Multi-Field Problems Including Cohesive Fracture
,” Comput. Meth. Appl. Mech. Eng.
, 195
(4–6
), pp. 444
–461
.10.1016/j.cma.2004.10.01423.
Secchi
, S.
, Simoni
, L.
, and Schrefler
, B. A.
, 2007
, “Mesh Adaptation and Transfer Schemes for Discrete Fracture Propagation in Porous Materials
,” Int. J. Numer. Anal. Meth. Geomech.
, 31
(2
), pp. 331
–345
.10.1002/nag.58124.
Babuska
, I.
, and Melenk
, J. M.
, 1997
, “The Partition of Unity Method
,” Int. J. Numer. Meth. Eng.
, 40
(4
), pp. 727
–758
.10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N25.
Belytschko
, T.
, and Black
, T.
, 1999
, “Elastic Crack Growth in Finite Elements With Minimal Remeshing
,” Int. J. Numer. Meth. Eng.
, 45
(5
), pp. 601
–620
.10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S26.
Wells
, G. N.
, 2001
, “Discontinuous Modelling of Strain Localisation and Failure
,” Ph.D. thesis, Delft University of Technology, Delft, The Netherlands.27.
Moes
, N.
, and Belytschko
, T.
, 2002
, “Extended Finite Element Method for Cohesive Crack Growth
,” Eng. Fract. Mech.
, 69
(7
), pp. 813
–833
.10.1016/S0013-7944(01)00128-X28.
Remmers
, J. J. C.
, de Borst
, R.
, and Needleman
, A.
, 2003
, “A Cohesive Segments Method for the Simulation of Crack Growth
,” Comput. Mech.
, 31
(1–2
), pp. 69
–77
.10.1007/s00466-002-0394-z29.
Larsson
, R.
, Runesson
, K.
, and Ottosen
, N. S.
, 1993
, “Discontinuous Displacement Approximation for Capturing Plastic Localization
,” Int. J. Numer. Meth. Eng.
, 36
(12
), pp. 2087
–2105
.10.1002/nme.162036120930.
Larsson
, J.
, and Larsson
, R.
, 2000
, “Localization Analysis of a Fluid-Saturated Elastoplastic Porous Medium Using Regularized Discontinuities
,” Mech. Co.-Frict. Mater.
, 5
(7
), pp. 565
–582
.10.1002/1099-1484(200010)5:7<565::AID-CFM107>3.0.CO;2-W31.
Armero
, F.
, and Callari
, C.
, 1999
, “An Analysis of Strong Discontinuities in a Saturated Poro-Plastic Solid
,” Int. J. Numer. Meth. Eng.
, 46
(10
), pp. 1673
–1698
.10.1002/(SICI)1097-0207(19991210)46:10<1673::AID-NME719>3.0.CO;2-S32.
Roels
, S.
, Moonen
, P.
, Proft
, K. D.
, and Carmeliet
, J.
, 2006
, “A Coupled Discrete-Continuum Approach to Simulate Moisture Effects on Damage Processes in Porous Materials
,” Comput. Meth. Appl. Mech. Eng.
, 195
(52
), pp. 7139
–7153
.10.1016/j.cma.2005.05.05133.
Al-Khoury
, R.
, and Sluys
, L. J.
, 2007
, “A Computational Model for Fracturing Porous Media
,” Int. J. Numer. Meth. Eng.
, 70
(4
), pp. 423
–444
.10.1002/nme.188634.
Rethore
, J.
, de Borst
, R.
, and Abellan
, M. A.
, 2007
, “A Two-Scale Approach for Fluid Flow in Fractured Porous Media
,” Int. J. Numer. Meth. Eng.
, 71
(7
), pp. 780
–800
.10.1002/nme.196235.
de Borst
, R.
, 2008
, “Challenges in Computational Materials Science: Multiple Scales, Multi-Physics and Evolving Discontinuities
,” Comput. Mater. Sci.
, 43
(1
), pp. 1
–15
.10.1016/j.commatsci.2007.07.02236.
Lanir
, Y.
, 1987
, “Biorheology and Fluid Flux in Swelling Tissues. 1. Bicomponent Theory for Small Deformations, Including Concentration Effects
,” Biorheology
, 24
(2
), pp. 173
–187
.37.
Camacho
, G. T.
, and Ortiz
, M.
, 1996
, “Computational Modelling of Impact Damage in Brittle Materials
,” Int. J. Solids Struct.
, 33
(20–22
), pp. 2899
–2938
.10.1016/0020-7683(95)00255-338.
Vermeer
, P. A.
, and Verruijt
, A.
, 1981
, “An Accuracy Condition for Consolidation by Finite Elements
,” Int. J. Numer. Anal. Meth. Geomech.
, 5
(1
), pp. 1
–14
.10.1002/nag.161005010339.
Remmers
, J. J. C.
, 2006
, “Discontinuities in Materials and Structures. A Unifying Computational Approach
,” Ph.D. thesis, University of Technology Delft, The Netherlands.40.
Remmers
, J. J. C.
, de Borst
, R.
, and Needleman
, A.
, 2008
, “The Simulation of Dynamic Crack Propagation Using the Cohesive Segments Method
,” J. Mech. Phys. Solids
, 56
(1
), pp. 70
–92
.10.1016/j.jmps.2007.08.00341.
Kraaijeveld
, F.
, Huyghe
, J. M.
, Remmers
, J. J. C.
, de Borst
, R.
, and Baaijens
, F. P. T.
, 2013
, “Shear Fracture in Osmoelastic Saturated Porous Media: A Mesh-Independent Model
,” Eng. Fract. Mech.
(submitted).42.
Zienkiewicz
, O. C.
, Qu
, S.
, Taylor
, R. L.
, and Nakazawa
, S.
, 1986
, “The Patch Test for Mixed Formulations
,” Int. J. Numer. Meth. Eng.
, 23
(10
), pp. 1873
–1883
.10.1002/nme.1620231007Copyright © 2013 by ASME
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