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Measuring Hyperelastic Properties of Hydrogels Using Cavity Expansion Method

  • W. NafoEmail author
  • A. Al-Mayah
Article
  • 73 Downloads

Abstract

Numerous methods have been proposed to measure the mechanical properties of hyperelastic materials such as hydrogels. Common techniques, such as tension, compression, and indentation test, experience various challenges due to material structure and surface conditions. These challenges affect the measured mechanical properties of the tested material. Therefore, a new technique is proposed to measure the hyperelastic mechanical properties of hydrogels by introducing cavity deformations to the internal solid structure of hydrogels. The data obtained from the cavity test were analyzed mathematically by using three strain energy functions and then were validated numerically through finite element (FE) simulations. Computed Tomography (CT) imaging was implemented to investigate the shape of the cavities, which showed that the proposed technique is capable of applying controlled spherical deformations. The stresses in the cavity test were generated in the radial and hoop directions; therefore, the validation process took into consideration both types of stresses. The numerical simulations considered the two common views about hyperelastic materials: slightly compressible and incompressible. A comparison between experimental results and FE simulations of the cavity test has shown a good agreement in pressure-deformation data.

Keywords

Cavity expansion Hydrogels Hyperelastic FE CT imaging 

Notes

References

  1. 1.
    Yang S-H, Lee Y-SJ, Lin F-H et al (2007) Chitosan/poly(vinyl alcohol) blending hydrogel coating improves the surface characteristics of segmented polyurethane urethral catheters. J Biomed Mater Res B Appl Biomater 83B:304–313.  https://doi.org/10.1002/jbm.b.30796 CrossRefGoogle Scholar
  2. 2.
    Hu X, Hao L, Wang H et al (2011) Hydrogel Contact Lens for Extended Delivery of Ophthalmic Drugs. Int J Polym Sci 2011:1–9.  https://doi.org/10.1155/2011/814163 CrossRefGoogle Scholar
  3. 3.
    Corkhill PH, Hamilton CJ, Tighe BJ (1989) Synthetic hydrogels VI. Hydrogel composites as wound dressings and implant materials. Biomaterials 10:3–10.  https://doi.org/10.1016/0142-9612(89)90002-1 CrossRefGoogle Scholar
  4. 4.
    Lin C-C, Anseth KS (2009) PEG Hydrogels for the Controlled Release of Biomolecules in Regenerative Medicine. Pharm Res 26:631–643.  https://doi.org/10.1007/s11095-008-9801-2 CrossRefGoogle Scholar
  5. 5.
    Oyen ML (2014) Mechanical characterisation of hydrogel materials. Int Mater Rev 59:44–59.  https://doi.org/10.1179/1743280413Y.0000000022 CrossRefGoogle Scholar
  6. 6.
    Oyen ML (2011) Handbook of nanoindentation with biological applications. Pan Stanford Publ, SingaporeGoogle Scholar
  7. 7.
    Jacobs NT, Cortes DH, Vresilovic EJ, Elliott DM (2013) Biaxial Tension of Fibrous Tissue: Using Finite Element Methods to Address Experimental Challenges Arising From Boundary Conditions and Anisotropy. J Biomech Eng 135:021004.  https://doi.org/10.1115/1.4023503 CrossRefGoogle Scholar
  8. 8.
    Mitchell MR, Link RE, Brieu M et al (2007) A New Biaxial Tension Test Fixture for Uniaxial Testing Machine—A Validation for Hyperelastic Behavior of Rubber-like Materials. J Test Eval 35:100688.  https://doi.org/10.1520/JTE100688 CrossRefGoogle Scholar
  9. 9.
    Roberts JJ, Earnshaw A, Ferguson VL, Bryant SJ (2011) Comparative study of the viscoelastic mechanical behavior of agarose and poly(ethylene glycol) hydrogels. J Biomed Mater Res B Appl Biomater 99B:158–169.  https://doi.org/10.1002/jbm.b.31883 CrossRefGoogle Scholar
  10. 10.
    Gu WY, Yao H, Huang CY, Cheung HS (2003) New insight into deformation-dependent hydraulic permeability of gels and cartilage, and dynamic behavior of agarose gels in confined compression. J Biomech 36:593–598CrossRefGoogle Scholar
  11. 11.
    Soden PD, Kershaw I (1974) Tensile testing of connective tissues. Med Biol Eng 12:510–518.  https://doi.org/10.1007/BF02478609 CrossRefGoogle Scholar
  12. 12.
    Blake A (1985) Handbook of mechanics, materials, and structures. Wiley, New YorkzbMATHGoogle Scholar
  13. 13.
    Doerner MF, Nix WD (1986) A method for interpreting the data from depth-sensing indentation instruments. J Mater Res 1:601–609.  https://doi.org/10.1557/JMR.1986.0601 CrossRefGoogle Scholar
  14. 14.
    Nix WD (1989) Mechanical properties of thin films. Metall Trans A 20:2217.  https://doi.org/10.1007/BF02666659 CrossRefGoogle Scholar
  15. 15.
    Burnett PJ, Rickerby DS (1987) The mechanical properties of wear-resistant coatings. Thin Solid Films 148:41–50.  https://doi.org/10.1016/0040-6090(87)90119-2 CrossRefGoogle Scholar
  16. 16.
    Farges G, Degout D (1989) Interpretation of the indentation size effect in vickers microhardness measurements-absolute hardness of materials. Thin Solid Films 181:365–374.  https://doi.org/10.1016/0040-6090(89)90505-1 CrossRefGoogle Scholar
  17. 17.
    Menčík J, Swain MV (1995) Errors associated with depth-sensing microindentation tests. J Mater Res 10:1491–1501.  https://doi.org/10.1557/JMR.1995.1491 CrossRefGoogle Scholar
  18. 18.
    Stone D, LaFontaine WR, Alexopoulos P et al (1988) An investigation of hardness and adhesion of sputter-deposited aluminum on silicon by utilizing a continuous indentation test. J Mater Res 3:141–147.  https://doi.org/10.1557/JMR.1988.0141 CrossRefGoogle Scholar
  19. 19.
    Wan WK, Campbell G, Zhang ZF et al (2002) Optimizing the tensile properties of polyvinyl alcohol hydrogel for the construction of a bioprosthetic heart valve stent. J Biomed Mater Res 63:854–861.  https://doi.org/10.1002/jbm.10333 CrossRefGoogle Scholar
  20. 20.
    Li W, Wang D, Yang W, Song Y (2016) Compressive mechanical properties and microstructure of PVA–HA hydrogels for cartilage repair. RSC Adv 6:20166–20172.  https://doi.org/10.1039/C6RA02166B CrossRefGoogle Scholar
  21. 21.
    Lin DC, Shreiber DI, Dimitriadis EK, Horkay F (2009) Spherical indentation of soft matter beyond the Hertzian regime: numerical and experimental validation of hyperelastic models. Biomech Model Mechanobiol 8:345–358.  https://doi.org/10.1007/s10237-008-0139-9 CrossRefGoogle Scholar
  22. 22.
    Chen F, Kang D-J, Park J-H (2013) New measurement method of Poisson’s ratio of PVA hydrogels using an optical flow analysis for a digital imaging system. Meas Sci Technol 24:055602.  https://doi.org/10.1088/0957-0233/24/5/055602 CrossRefGoogle Scholar
  23. 23.
    Ogden RW (1997) Non-linear elastic deformations. Dover Publications, MineolaGoogle Scholar
  24. 24.
    Lev Y, Volokh KY (2016) On Cavitation in Rubberlike Materials. J Appl Mech 83:044501.  https://doi.org/10.1115/1.4032377 CrossRefGoogle Scholar
  25. 25.
    Faye A, Rodríguez-Martínez JA, Volokh KY (2017) Spherical void expansion in rubber-like materials: The stabilizing effects of viscosity and inertia. Int J Non-Linear Mech 92:118–126.  https://doi.org/10.1016/j.ijnonlinmec.2017.04.005 CrossRefGoogle Scholar
  26. 26.
    Fond C (2001) Cavitation criterion for rubber materials: A review of void-growth models. J Polym Sci Part B Polym Phys 39:2081–2096.  https://doi.org/10.1002/polb.1183 CrossRefGoogle Scholar
  27. 27.
    Li J, Mayau D, Song F (2007) A constitutive model for cavitation and cavity growth in rubber-like materials under arbitrary tri-axial loading. Int J Solids Struct 44:6080–6100.  https://doi.org/10.1016/j.ijsolstr.2007.02.016 CrossRefzbMATHGoogle Scholar
  28. 28.
    deBotton G, Bustamante R, Dorfmann A (2013) Axisymmetric bifurcations of thick spherical shells under inflation and compression. Int J Solids Struct 50:403–413.  https://doi.org/10.1016/j.ijsolstr.2012.10.004 CrossRefGoogle Scholar
  29. 29.
    Sasso M, Palmieri G, Chiappini G, Amodio D (2008) Characterization of hyperelastic rubber-like materials by biaxial and uniaxial stretching tests based on optical methods. Polym Test 27:995–1004.  https://doi.org/10.1016/j.polymertesting.2008.09.001 CrossRefGoogle Scholar
  30. 30.
    Shahzad M, Kamran A, Siddiqui MZ, Farhan M (2015) Mechanical Characterization and FE Modelling of a Hyperelastic Material. Mater Res 18:918–924.  https://doi.org/10.1590/1516-1439.320414 CrossRefGoogle Scholar
  31. 31.
    Ogden RW (1972) Large Deformation Isotropic Elasticity - On the Correlation of Theory and Experiment for Incompressible Rubberlike Solids. Proc R Soc Math Phys Eng Sci 326:565–584.  https://doi.org/10.1098/rspa.1972.0026 CrossRefzbMATHGoogle Scholar
  32. 32.
    Rashid B, Destrade M, Gilchrist MD (2014) Mechanical characterization of brain tissue in tension at dynamic strain rates. J Mech Behav Biomed Mater 33:43–54.  https://doi.org/10.1016/j.jmbbm.2012.07.015 CrossRefGoogle Scholar
  33. 33.
    Yeoh OH (1993) Some Forms of the Strain Energy Function for Rubber. Rubber Chem Technol 66:754–771.  https://doi.org/10.5254/1.3538343 CrossRefGoogle Scholar
  34. 34.
    Hackett RM (2016) Hyperelasticity Primer. Springer International Publishing, ChamCrossRefGoogle Scholar
  35. 35.
    Arruda EM, Boyce MC (1993) A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J Mech Phys Solids 41:389–412.  https://doi.org/10.1016/0022-5096(93)90013-6 CrossRefzbMATHGoogle Scholar
  36. 36.
  37. 37.
    ABAQUS/CAE (2013) Abaqus/CAE v6.13 User’s ManualGoogle Scholar
  38. 38.
    Mohan C, Ramanathan J, Kumar S, Gupta A (2011) Characterisation of Materials used in Flex Bearings of Large Solid Rocket Motors. Def Sci J 61:264–269.  https://doi.org/10.14429/dsj.61.52 CrossRefGoogle Scholar
  39. 39.
    Charlton DJ, Yang J, Teh KK (1994) A Review of Methods to Characterize Rubber Elastic Behavior for Use in Finite Element Analysis. Rubber Chem Technol 67:481–503.  https://doi.org/10.5254/1.3538686 CrossRefGoogle Scholar
  40. 40.
    Agoras M, Lopez-Pamies O, Ponte Castañeda P (2009) A general hyperelastic model for incompressible fiber-reinforced elastomers. J Mech Phys Solids 57:268–286.  https://doi.org/10.1016/j.jmps.2008.10.014 CrossRefzbMATHGoogle Scholar
  41. 41.
    Elshazly T (2004) Characterization of PVA hydrogels with regards to vascular graft development. Georgia Institute of Technology, AtlantaGoogle Scholar
  42. 42.
    Urayama K, Takigawa T, Masuda T (1993) Poisson’s ratio of poly(vinyl alcohol) gels. Macromolecules 26:3092–3096.  https://doi.org/10.1021/ma00064a016 CrossRefGoogle Scholar
  43. 43.
    Lee J-H, Lee S-S, Chang J-D et al (2013) A Novel Method for the Accurate Evaluation of Poisson’s Ratio of Soft Polymer Materials. Sci World J 2013:1–7.  https://doi.org/10.1155/2013/930798 Google Scholar
  44. 44.
    Leibinger A, Forte AE, Tan Z et al (2016) Soft Tissue Phantoms for Realistic Needle Insertion: A Comparative Study. Ann Biomed Eng 44:2442–2452.  https://doi.org/10.1007/s10439-015-1523-0 CrossRefGoogle Scholar
  45. 45.
    Urrea FA, Casanova F, Orozco GA, García JJ (2016) Evaluation of the friction coefficient, the radial stress, and the damage work during needle insertions into agarose gels. J Mech Behav Biomed Mater 56:98–105.  https://doi.org/10.1016/j.jmbbm.2015.11.024 CrossRefGoogle Scholar
  46. 46.
    Casanova F, Carney PR, Sarntinoranont M (2014) Effect of Needle Insertion Speed on Tissue Injury, Stress, and Backflow Distribution for Convection-Enhanced Delivery in the Rat Brain. PLoS One 9:e94919.  https://doi.org/10.1371/journal.pone.0094919 CrossRefGoogle Scholar
  47. 47.
    Ní Annaidh A, Destrade M, Gilchrist MD, Murphy JG (2013) Deficiencies in numerical models of anisotropic nonlinearly elastic materials. Biomech Model Mechanobiol 12:781–791.  https://doi.org/10.1007/s10237-012-0442-3 CrossRefGoogle Scholar
  48. 48.
    Gilchrist MD, Murphy JG, Parnell W, Pierrat B (2014) Modelling the slight compressibility of anisotropic soft tissue. Int J Solids Struct 51:3857–3865.  https://doi.org/10.1016/j.ijsolstr.2014.06.018 CrossRefGoogle Scholar
  49. 49.
    Weiss JA, Maker BN, Govindjee S (1996) Finite Element Implementation of Incompressible, Transversely Isotropic Hyperelasticity. Comput Methods Appl Mech Eng 135:107–128.  https://doi.org/10.1016/0045-7825(96)01035-3 CrossRefzbMATHGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2019

Authors and Affiliations

  1. 1.Civil and Environmental Engineering DepartmentUniversity of WaterlooWaterlooCanada
  2. 2.Mechanical and Mechatronics Engineering DepartmentUniversity of WaterlooWaterlooCanada

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