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Research Articles

Two-Dimensional Mode I Crack Propagation in Saturated Ionized Porous Media Using Partition of Unity Finite Elements

[+] Author and Article Information
F. Kraaijeveld

e-mail: famkekraaijeveld@gmail.com

J. M. Huyghe

Mem. ASME
Associate Professor
e-mail: j.m.r.huyghe@tue.nl
Department of Biomedical Engineering,
Eindhoven University of Technology,
Eindhoven, 5600MBThe Netherlands

J. J. C. Remmers

Assistant Professor
e-mail: j.j.c.remmers@tue.nl

R. de Borst

Mem. ASME
Professor
e-mail: r.d.borst@tue.nl
Department of Mechanical Engineering,
Eindhoven University of Technology,
Eindhoven, 5600MBThe Netherlands

1Corresponding author.

Manuscript received December 5, 2010; final manuscript received April 10, 2012; accepted manuscript posted October 25, 2012; published online February 6, 2013. Assoc. Editor: Younane Abousleiman.

J. Appl. Mech 80(2), 020907 (Feb 06, 2013) (12 pages) Paper No: JAM-10-1442; doi: 10.1115/1.4007904 History: Received December 05, 2010; Revised April 10, 2012; Accepted October 25, 2012

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.

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Figures

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Fig. 1

Representation of three types of prestress: free swelling (a) in both directions, (b) in x-direction and (c) in y-direction

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Fig. 2

Schematic representation of the fluid flow at the crack surface with parameter s the distance along the crack

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Fig. 3

Schematic representation of the traction forces at the crack surface

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Fig. 8

Delamination in case of prestress in both directions after 950 time increments (i.e., 9.5e − 2 mm displacement of top boundary). Distribution of (a) chemical potential in (N/mm2) and (b) flow in x-direction in (mm/s).

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Fig. 9

Comparison of the effect mesh and time refinement for delamination at a point just ahead of the initial crack (dx=13.71 mm)

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Fig. 4

Normalized distribution of the exponential cohesive law for tensile loading related traction forces and displacement

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Fig. 5

The mesh and boundary conditions for delamination consisting of 575 elements. Material is pulled at the top and bottom on the left and is on the right in contact with a filter.

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Fig. 13

Distribution for the osmolarity test after 300 increments (i.e., a change in chemical potential of -0.96 MPa) just before damage initiation for prestress in both directions for (a) of chemical potential and (b) of stress component σe,yy

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Fig. 6

The mesh and boundary conditions for pull test: material is pulled at the top with bottom fixed and at sides in contact with a filter

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Fig. 7

The mesh and boundary conditions for the osmolarity test: the material is fixed at bottom, right and top and is in contact with a filter at these sides

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Fig. 10

Distribution of chemical potential in (N/mm2) for delamination in case of prestress in both directions and μΓf=0 after 1100 increments (i.e., displacement of top boundary of du=1.1e − 2 mm) for (a) chemical potential and (b) flow in x-direction

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Fig. 11

Distribution for pull test of (a) chemical potential and (b) stress component σe,yy for the pull test after 1010 increments (i.e., 5.05e − 2mm of pull displacement) in case of prestress in both directions, including cohesive zone

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Fig. 12

Comparison for the pull test of the effect of prestress on crack mouth opening displacement (CMOD), chemical potential and tangential flow in the crack at dx=3.5 mm

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Fig. 14

Distribution at the crack-tip for osmolarity test of flow for prestress in both directions after 306 increments (i.e., a change in chemical potential of -0.98 MPa) just after damage initiation (a) in x-directions and (b) y-direction

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Fig. 15

Evolution for the osmolarity test in plane of crack of chemical potential, tangential flow and crack mouth opening (CMOD) after 130 increments, Δμf=-0.4MPa

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