0
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

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

Szymon Leszczynski

Procter & Gamble Service GmbH,
Sulzbacher Straße 40,
Schwalbach am Taunus 65824, Germany
e-mail: leszczynski.s@pg.com

Jacques M. Huyghe

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 October 31, 2017; final manuscript received December 6, 2017; published online December 20, 2017. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 85(2), 021007 (Dec 20, 2017) (12 pages) Paper No: JAM-17-1609; doi: 10.1115/1.4038698 History: Received October 31, 2017; Revised December 06, 2017

Swelling and crack propagation in ionized hydrogels plays an important role in industry application of personal care and biotechnology. Unlike nonionized hydrogel, ionized hydrogel swells up to strain of many 1000's %. In this paper, we present a swelling driven fracture model for ionized hydrogel in large deformation. Flow of fluid within the crack, within the medium, and between the crack and the medium are accounted for. The partition of unity method is used to describe the discontinuous displacement field and chemical potential field, respectively. In order to capture the chemical potential gradient between the gel and the crack, an enhanced local pressure (ELP) model is adopted. The capacity of this numerical model to study the fracture and swelling behaviors of ionized gels with low Young's modulus (< 1 MPa) and low permeability (< 10−16 m4/Ns) is demonstrated. Two numerical examples show the performance of the implemented model (1) swelling with crack opening and (2) swelling with crack propagation. Simulations demonstrate that shrinking of a gel results in decreasing macroscopic stress and simultaneously increasing stress at crack tips. Different scales yield opposite responses, underscoring the need for multiscale modelling. While cracking as a result of external loading can be prevented by reducing the overall stress level in the structure, reducing overall stress levels will not result in reducing the crack initiation and propagation due to swelling.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Cadman, J. E. , Zhou, S. , Chen, Y. , and Li, Q. , 2013, “ On Design of Multi-Functional Microstructural Materials,” J. Mater. Sci, 48(1), pp. 51–66. [CrossRef]
Huyghe, J. M. , and Janssen, J. D. , 1997, “ Quadriphasic Mechanics of Swelling Incompressible Porous Media,” Int. J. Eng. Sci, 35(8), pp. 793–802. [CrossRef]
Lanir, Y. , Seybold, J. , Schneiderman, R. , and Huyghe, J. M. , 1998, “ Partition and Diffusion of Sodium and Chloride Ions in Soft Charged Foam: The Effect of External Salt Concentration and Mechanical Deformation,” Tissue Eng., 4(4), pp. 365–378. [CrossRef] [PubMed]
Frijns, A. J. H. , Huyghe, J. M. , and Wijlaars, M. W. , 2005, “ Measurements of Deformations and Electrical Potentials in a Charged Porous Medium,” IUTAM Symposium on Physicochemical and Electromechanical Interactions in Porous Media (Solid Mechanics and Its Applications), Vol. 125, Springer, Dordrecht, The Netherlands, pp. 133–139. [CrossRef]
Ding , J., Remmers , J. J. C., Malakpoor , K. , and Huyghe , J. M. , eds., 2017, Swelling Driven Cracking in Large Deformation in Porous Media, American Society of Civil Engineers, Reston, VA.
Yu , C., Malakpoor , K., Leszczynski , S. , and Huyghe, J. M. , eds., 2017, A Full 3D Mixed Hybrid Finite Element Model of Superabsorbent Polymers, American Society of Civil Engineers, Reston, VA.
Flory, P. , 1953, “ George Fisher Baker Non-Resident Lectureship in Chemistry at Cornell University,” Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY.
Duda, F. P. , Souza, A. C. , and Fried, E. , 2010, “ A Theory for Species Migration in a Finitely Strained Solid With Application to Polymer Network Swelling,” J. Mech. Phys. Solids, 58(4), pp. 515–529. [CrossRef]
Baek, S. , and Pence, T. J. , 2011, “ Inhomogeneous Deformation of Elastomer Gels in Equilibrium Under Saturated and Unsaturated Conditions,” J. Mech. Phys. Solids, 59(3), pp. 561–582. [CrossRef]
Chester, S. A. , and Anand, L. , 2011, “ A Thermo-Mechanically Coupled Theory for Fluid Permeation in Elastomeric Materials: Application to Thermally Responsive Gels,” J. Mech. Phys. Solids, 59(10), pp. 1978–2006. [CrossRef]
Selvadurai, A. P. , and Suvorov, A. P. , 2016, “ Coupled Hydro-Mechanical Effects in a Poro-Hyperelastic Material,” J. Mech. Phys. Solids, 91, pp. 311–333. [CrossRef]
Peppas, N. , and Mikos, A. , 1986, Preparation Methods and Structure of Hydrogels, Vol. 1, CRC Press, Boca Raton, FL.
Wognum, S. , Huyghe, J. M. , and Baaijens, F. P. T. , 2006, “ Influence of Osmotic Pressure Changes on the Opening of Existing Cracks in 2 Intervertebral Disc Models,” Spine, 31(16), pp. 1783–1788. [CrossRef] [PubMed]
Lee, J. N. , Park, C. , and Whitesides, G. M. , 2003, “ Solvent Compatibility of Poly(Dimethylsiloxane)-Based Microfluidic Devices,” Anal. Chem, 75(23), pp. 6544–6554. [CrossRef] [PubMed]
Bertrand, T. , Peixinho, J. , Mukhopadhyay, S. , and Macminn, C. W. , 2016, “ Dynamics of Swelling and Drying in a Spherical Gel,” e-print arXiv:1605.00599. https://arxiv.org/abs/1605.00599
Tanaka, T. , Sun, S.-T. , Hirokawa, Y. , Katayama, S. , Kucera, J. , Hirose, Y. , and Amiya, T. , 1987, “ Mechanical Instability of Gels at the Phase Transition,” Nature, 325, pp. 796–798. [CrossRef]
Holmes, D. P. , Roché, M. , Sinha, T. , and Stone, H. A. , 2011, “ Bending and Twisting of Soft Materials by Non-Homogenous Swelling,” Soft Matter, 7(11), p. 5188. [CrossRef]
Kraaijeveld, F. , 2009, “ Propagating Discontinuities in Ionized Porous Media,” Ph.D. thesis, Technische Universiteit Eindhoven, Eindhoven, The Netherlands. http://repository.tue.nl/652157
Moulinet, S. , and Adda-Bedia, M. , 2015, “ Popping Balloons: A Case Study of Dynamical Fragmentation,” Phys. Rev. Lett., 115(18), p. 184301.
Tjeerdsma, B. F. , Boonstra, M. , Pizzi, A. , Tekely, P. , and Militz, H. , 1998, “ Characterisation of Thermally Modified Wood: Molecular Reasons for Wood Performance Improvement,” Holz Als Roh-Werkstoff, 56, pp. 149–153. [CrossRef]
Jurkovich, G. J. , 2007, “ Environmental Cold-Induced Injury,” Surg. Clin. North Am., 87(1), pp. 247–267. [CrossRef] [PubMed]
Miller, S. A. , Collettini, C. , Chiaraluce, L. , Cocco, M. , Barchi, M. , and Kaus, B. J. P. , 2004, “ Aftershocks Driven by a High-Pressure CO2 Source at Depth,” Nature, 427(6976), pp. 724–727. [CrossRef] [PubMed]
Battié, M. C. , Videman, T. , and Parent, E. , 2004, “ Lumbar Disc Degeneration Epidemiology and Genetic Influences,” Spine, 29(23), pp. 2679–2690. [CrossRef] [PubMed]
Battié, M. C. , Videman, T. , Levalahti, E. , Gill, K. , and Kaprio, J. , 2007, “ Heritability of Low Back Pain and the Role of Disc Degeneration,” Pain, 131(3), pp. 272–280. [CrossRef] [PubMed]
Battié, M. C. , Videman, T. , Levälahti, E. , Gill, K. , and Kaprio, J. , 2008, “ Genetic and Environmental Effects on Disc Degeneration by Phenotype and Spinal Level: A Multivariate Twin Study,” Spine, 33(25), pp. 2801–2808. [CrossRef] [PubMed]
Huyghe, J. M. , Molenaar, M. M. , and Baajens, F. P. T. , 2007, “ Poromechanics of Compressible Charged Porous Media Using the Theory of Mixtures,” J. Biomech. Eng, 129(5), pp. 776–785. [CrossRef] [PubMed]
Eringen, A. C. , 1994, “ A Continuum Theory of Swelling Porous Elastic Soils,” Int. J. Eng. Sci, 32(8), pp. 1337–1349. [CrossRef]
Mijnlieff, P. F. , and Jaspers, W. J. M. , 1969, “ Thermodynamics of Swelling of Polymer-Network Gels. Analysis of Excluded Volume Effects in Polymer Solutions and Polymer Networks,” J. Polym. Sci. Part B: Polym. Phys., 7(2), pp. 357–375. [CrossRef]
Wilson, W. , van Donkelaar, C. C. , and Huyghe , J. M. , 2005, “ A Comparison Between Mechano-Electrochemical and Biphasic Swelling Theories for Soft Hydrated Tissues,” ASME J. Biomech. Eng., 127(1), pp. 158–165. [CrossRef]
Griffith, A. A. , 1921, “ The Phenomena of Rupture and Flow in Solids,” Philos. Trans. R. Soc. London, Ser. A., 221(582–593), pp. 163–198. [CrossRef]
Ingraffea, A. R. , and Saouma, V. , 1985, Fracture Mechanics of Concrete, Martinus Nijhoff Publishers, Leiden, The Netherlands.
Knops, H. A. J. , 1994, “ Numerical Simulation of Crack Growth in Pressurized Fuselages,” Ph.D. thesis, Delft University of Technology, Delft, The Netherlands.
Dugdale, D. , 1960, “ Yielding of Steel Sheets Containing Slits,” J. Mech. Phys. Solids, 8(2), pp. 100–104. [CrossRef]
Barenblatt, G. , 1962, “ The Mathematical Theory of Equilibrium Cracks in Brittle Fracture,” Advan. Appl. Mech., 7, pp. 55–129. [CrossRef]
Needleman, A. , 1987, “ A Finite Element Method for Localized Failure Analysis,” Comput. Methods Appl. Mech. Eng., 61(2), pp. 189–214. [CrossRef]
Schrefler, B. A. , Secchi, S. , and Simoni, L. , 2006, “ On Adaptive Refinement Techniques in Multi-Field Problems Including Cohesive Fracture,” Comput. Methods Appl. Mech. Eng., 195(4–6), pp. 444–461. [CrossRef]
Belytschko, T. , and Black, T. , 1999, “ Elastic Crack Growth in Finite Elements With Minimal Remeshing,” Int. J. Numer. Methods Eng., 45(5), pp. 601–620. [CrossRef]
Moës, N. , Dolbow, J. , and Belytschko, T. , 1999, “ A Finite Element Method for Crack Growth Without Remeshing,” Int. J. Numer. Methods Eng., 46(1), pp. 131–150. [CrossRef]
Wells, G. , and Sluys, L. , 2001, “ A New Method for Modelling Cohesive Cracks Using Finite Elements,” Int. J. Numer. Methods Eng., 50(12), pp. 2667–2682. [CrossRef]
Larsson, J. , and Larsson, R. , 2000, “ Localization Analysis of a Fluid-Saturated Elastoplastic Porous Medium Using Regularized Discontinuities,” Mech. Cohes.-Frict. Mater., 5(7), pp. 565–582. [CrossRef]
Leonhart, D. , and Meschke, G. , 2011, “ Extended Finite Element Method for Hygro-Mechanical Analysis of Crack Propagation in Porous Materials,” Proc. Appl. Math. Mech, 11(1), pp. 161–162. [CrossRef]
Irzal, F. , Remmers, J. J. , Huyghe, J. M. , and De Borst, R. , 2013, “ A Large Deformation Formulation for Fluid Flow in a Progressively Fracturing Porous Material,” Comput. Methods Appl. Mech. Eng., 256, pp. 29–37. [CrossRef]
Remij, E. W. , Remmers, J. J. C. , Huyghe, J. M. , and Smeulders, D. M. J. , 2015, “ The Enhanced Local Pressure Model for the Accurate Analysis of Fluid Pressure Driven Fracture in Porous Materials,” Comput. Methods Appl. Mech. Eng., 286, pp. 293–312. [CrossRef]
Terzaghi, K. , 1943, Theoretical Soil Mechanics, Wiley, Hoboken, NJ. [CrossRef]
Kraaijeveld, F. , Huyghe, J. M. , Remmers, J. J. C. , and de Borst, R. , 2013, “ Two-Dimensional Mode I Crack Propagation in Saturated Ionized Porous Media Using Partition of Unity Finite Elements,” ASME J. Appl. Mech., 80(2), p. 020907. [CrossRef]
Boone, T. J. , and Ingraffea, A. R. , 1990, “ A Numerical Procedure for Simulation of Hydraulically-Driven Fracture Propagation in Poroelastic Media,” Int. J. Numer. Anal. Methods, 14(1), pp. 27–47. [CrossRef]
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. [CrossRef]
Vermeer, P. , and Verruijt, A. , 1981, “ An Accuracy Condition for Consolidation by Finite Elements,” Int. J. Numer. Anal. Methods, 5(1), pp. 1–14. [CrossRef]
Booker, J. R. , and Small, J. C. , 1975, “ An Investigation of the Stability of Numerical Solutions of Biot's Equations of Consolidation,” Int. J. Solids Struct., 11(7–8), pp. 907–917. [CrossRef]
Faulkner, D. R. , Mitchell, T. M. , Healy, D. , and Heap, M. J. , 2006, “ Slip on ‘Weak’ Faults by the Rotation of Regional Stress in the Fracture Damage Zone,” Nature, 444(7121), pp. 922–925. [CrossRef] [PubMed]
Thomas, A. M. , Nadeau, R. M. , and Bürgmann, R. , 2009, “ Tremor-Tide Correlations and Near-Lithostatic Pore Pressure on the Deep San Andreas Fault,” Nature, 462(7276), pp. 1048–1051. [CrossRef] [PubMed]
Nolet, G. , 2009, “ Geophysics. Slabs Do Not Go Gently,” Science, 324(5931), pp. 1152–1153. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

Swollen SAP particle showing cracking cross-linked surface during swelling

Grahic Jump Location
Fig. 2

A domain is crossed by a discontinuity Γd (dashed line) with two resulting subdomains Ω+ and Ω. nΓd is defined as the normal of the discontinuity surface Γd pointing to the subdomain Ω+.

Grahic Jump Location
Fig. 3

Schematic representation of the enhanced local chemical potential. The dark gray area represents the crack. The chemical potential variation across the crack is composed of two parts: (1) the chemical potential degree-of-freedom which is discontinuous over both boundaries of the crack (bold continuous line); (2) the analytical solution of consolidation (dotted line) from which the flux of the fluid between crack and hydrogel is calculated.

Grahic Jump Location
Fig. 4

Sketch of the dry, swollen reference and current state of the gel. Xd, X, and x are points of the dry, swollen reference, and current state, respectively.

Grahic Jump Location
Fig. 12

Traction versus opening of the crack

Grahic Jump Location
Fig. 6

The height change at the top is caused by the change of salt concentration at the bottom. The curve denotes the transient numerical solution and the horizontal line is the equilibrium analytical solution.

Grahic Jump Location
Fig. 7

The left side of the sample and crack are in contact with a salt solution of concentration cex. The right side is a symmetry plane. The crack (0.5 mm) is placed in the middle of the right side (length: 1 mm height: 0.5 mm).

Grahic Jump Location
Fig. 5

The geometry and boundary condition of swelling verification test

Grahic Jump Location
Fig. 8

Simulated normal Second Piola–Kirchhoff stress distribution S22 (MPa) after an increase of external salt concentration from 0.15 M to 0.2 M

Grahic Jump Location
Fig. 9

Macroscopic stress (above) and local stress of the crack tip (below) (MPa)

Grahic Jump Location
Fig. 10

Displacement plots of the middle point of left side (above) and the top surface of the crack (below) (mm)

Grahic Jump Location
Fig. 11

The geometry and boundary conditions of the sample. A changing chemical potential is applied along the outer surface. (ROuter = 0.5 mm, RCore = 0.2 mm).

Grahic Jump Location
Fig. 13

Crack propagation over time

Grahic Jump Location
Fig. 14

Initial state of the sample

Grahic Jump Location
Fig. 15

Displacement distribution of the sample at 15 s

Grahic Jump Location
Fig. 16

Displacement distribution of the sample at 30 s

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In