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Research Papers

Swelling-Driven Crack Propagation in Large Deformation in Ionized Hydrogel

[+] Author and Article Information
Jingqian Ding

Department of Mechanical Engineering,
Eindhoven University of Technology,
P.O. BOX 513,
Eindhoven 5600 MB, The Netherlands
e-mail: j.ding@tue.nl

Ernst W. Remij

Department of Mechanical Engineering,
Eindhoven University of Technology,
P.O. BOX 513,
Eindhoven 5600 MB, The Netherlands
e-mail: ernst_remij@hotmail.com

Joris J. C. Remmers

Department of Mechanical Engineering,
Eindhoven University of Technology,
P.O. BOX 513,
Eindhoven 5600 MB, The Netherlands
e-mail: j.j.c.remmers@tue.nl

Jacques M. Huyghe

Department of Biomedical Engineering,
Bernal Institute,
University of Limerick,
Limerick V94 T9PX, Ireland
e-mail: Jacques.huyghe@ul.ie

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 12, 2018; final manuscript received May 14, 2018; published online July 12, 2018. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 85(10), 101011 (Jul 12, 2018) (7 pages) Paper No: JAM-18-1209; doi: 10.1115/1.4040334 History: Received April 12, 2018; Revised May 14, 2018

Stepwise crack propagation is evidently observed in experiments both in geomaterials and in hydrogels. Pizzocolo et al. (2012, “Mode I Crack Propagation in Hydrogels is Step Wise,” Eng. Fract. Mech., 97(1), pp. 72–79) show experimental evidence that mode I crack propagation in hydrogel is stepwise. The pattern of the intermittent crack growth is influenced by many factors, such as porosity of the material, the permeability of the fluid, the stiffness of the material, etc. The pause duration time is negatively correlated with the stiffness of the material, while the average propagation length per step is positively correlated. In this paper, we integrate extended finite element method (XFEM) and enhanced local pressure (ELP) method, and incorporate cohesive relation to reproduce the experiments of Pizzocolo et al. in the finite deformation regime. We investigate the stepwise phenomenon in air and in water, respectively, under mode I fracture. Our simulations show that despite the homogeneous material properties, the crack growth under mode I fracture is stepwise, and this pattern is influenced by the hydraulic permeability and the porosity of the material. Simulated pause duration is negatively correlated with stiffness, and the average propagating length is positively correlated with stiffness. In order to eliminate the numerical artifacts, we also take different time increments into consideration. The staccato propagation does not disappear with smaller time increments, and the pattern is approximately insensitive to the time increment. However, we do not observe stepwise crack growth scheme when we simulate fracture in homogeneous rocks.

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References

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Figures

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Fig. 2

Tip displacement over time

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Fig. 3

Final crack paths with the tests in air and in water

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Fig. 4

Crack propagation at time-step 14

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Fig. 5

Crack propagation at time-step 15

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Fig. 6

Crack propagation at time-step 56

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Fig. 7

Crack propagation at time-step 70 (final state)

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Fig. 1

Sketch of the single edge notch specimen with tensile loading

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Fig. 8

Tip displacement with three different time increments in air

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Fig. 9

Tip displacement versus time in water with different porosities

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Fig. 14

Relation between the stiffness of the hydrogel and the time span during pause in air of experimental results from Pizzocolo et al. [1] (Reprinted with permission from Elsevier copyright 2012)

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Fig. 15

Relation between the stiffness of the hydrogel and the average propagation length in air (numerical results)

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Fig. 10

Tip displacements with different specific lengths in air (element size = 0.3 mm)

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Fig. 11

The pressure at the crack tip during crack propagation

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Fig. 12

The opening at the end of the cohesive zone during crack propagation

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Fig. 13

Relation between the stiffness of the hydrogel and the time span during pause in air (numerical results)

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Fig. 16

Relation between the stiffness of the hydrogel and the average propagation length in air of experimental results from Pizzocolo et al. [1] (Reprinted with permission from Elsever copyright 2012)

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Fig. 17

Tip displacement in water with stiffer porous material. No staccato crack propagation is observed.

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