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Swelling-induced finite bending of functionally graded pH-responsive hydrogels: a semi-analytical method

  • M. Shojaeifard
  • M. R. Bayat
  • M. BaghaniEmail author
Article
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Abstract

Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation fields, a new semi-analytical approach is developed to predict the swelling induced finite bending for a functionally graded (FG) layer composed of a pH-sensitive hydrogel, in which the cross-link density is continuously distributed along the thickness direction under the plane strain condition. Without considering the intermediary virtual reference, the initial state is mapped into the deformed configuration in a circular shape by utilizing a total deformation gradient tensor stemming from the inhomogeneous swelling of an FG layer in response to the variation of the pH value of the solvent. To enlighten the capability of the presented analytical method, the finite element method (FEM) is used to verify the accuracy of the analytical results in some case studies. The perfect agreement confirms the accuracy of the presented method. Due to the applicability of FG pH-sensitive hydrogels, some design factors such as the semi-angle, the bending curvature, the aspect ratio, and the distributions of deformation and stress fields are studied. Furthermore, the tangential free-stress axes are illustrated in deformed configuration.

Key words

pH-sensitive hydrogel functionally graded (FG) layer finite bending semi-analytical solution finite element method (FEM) 

Chinese Library Classification

O411.1 O648.17 

2010 Mathematics Subject Classification

65M06 65M12 

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References

  1. [1]
    MARCOMBE, R., CAI, S., HONG, W., ZHAO, X., LAPUSTA, Y., and SUO, Z. A theory of constrained swelling of a pH-sensitive hydrogel. Soft Matter, 6, 784–793 (2010)CrossRefGoogle Scholar
  2. [2]
    DROZDOV, A. D., DECLAVILLE CHRISTIANSEN, J., and SANPOREAN, C. G. Inhomogeneous swelling of pH-responsive gels. International Journal of Solids and Structures, 87, 11–25 (2016)CrossRefGoogle Scholar
  3. [3]
    DROZDOV, A. and DECLAVILLE CHRISTIANSEN, J. Modeling the effects of pH and ionic strength on swelling of anionic polyelectrolyte gels. Modelling and Simulation in Materials Science and Engineering, 23, 055005 (2015)CrossRefGoogle Scholar
  4. [4]
    DROZDOV, A. and DECLAVILLE CHRISTIANSEN, J. Swelling of pH-sensitive hydrogels. Physical Review E, 91, 022305 (2015)CrossRefGoogle Scholar
  5. [5]
    LI, H., GO, G., KO, S. Y., PARK, J. O., and PARK, S. Magnetic actuated pH-responsive hydrogel-based soft micro-robot for targeted drug delivery. Smart Materials and Structures, 25, 027001 (2016)CrossRefGoogle Scholar
  6. [6]
    LI, P., KIM, N. H., and LEE, J. H. Swelling behavior of polyacrylamide/laponite clay nanocomposite hydrogels: pH-sensitive property. Composites Part B: Engineering, 40, 275–283 (2009)CrossRefGoogle Scholar
  7. [7]
    MAZAHERI, H., BAGHANI, M., NAGHDABADI, R., and SOHRABPOUR, S. Coupling behavior of the pH/temperature sensitive hydrogels for the inhomogeneous and homogeneous swelling. Smart Materials and Structures, 25, 085034 (2016)CrossRefGoogle Scholar
  8. [8]
    MAZAHERI, H., BAGHANI, M., and NAGHDABADI, R. Inhomogeneous and homogeneous swelling behavior of temperature-sensitive poly-(N -isopropylacrylamide) hydrogels. Journal of Intelligent Material Systems and Structures, 27, 324–336 (2016)CrossRefGoogle Scholar
  9. [9]
    CHESTER, S. A. and ANAND, L. A thermo-mechanically coupled theory for fluid permeation in elastomeric materials: application to thermally responsive gels. Journal of the Mechanics and Physics of Solids, 59, 1978–2006 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    MORIMOTO, T. and ASHIDA, F. Temperature-responsive bending of a bilayer gel. International Journal of Solids and Structures, 56, 20–28 (2015)CrossRefGoogle Scholar
  11. [11]
    DEHGHANY, M., ZHANG, H., NAGHDABADI, R., and HU, Y. A thermodynamically-consistent large deformation theory coupling photochemical reaction and electrochemistry for light-responsive gels. Journal of the Mechanics and Physics of Solids, 116, 239–266 (2018)MathSciNetCrossRefGoogle Scholar
  12. [12]
    TOH, W., NG, T. Y., HU, J., and LIU, Z. Mechanics of inhomogeneous large deformation of photo-thermal sensitive hydrogels. International Journal of Solids and Structures, 51, 4440–4451 (2014)CrossRefGoogle Scholar
  13. [13]
    ATTARAN, A., BRUMMUND, J., and WALLMERSPERGER, T. Modeling and simulation of the bending behavior of electrically-stimulated cantilevered hydrogels. Smart Materials and Structures, 24, 035021 (2015)CrossRefGoogle Scholar
  14. [14]
    LIU, T. Y., HU, S. H., LIU, T. Y., LIU, D. M., and CHEN, S. Y. Magnetic-sensitive behavior of intelligent ferrogels for controlled release of drug. Langmuir, 22, 5974–5978 (2006)CrossRefGoogle Scholar
  15. [15]
    IONOV, L. Biomimetic hydrogel-based actuating systems. Advanced Functional Materials, 23, 4555–4570 (2013)CrossRefGoogle Scholar
  16. [16]
    BEEBE, D. J., MOORE, J. S., BAUER, J. M., YU, Q., LIU, R. H., DEVADOSS, C., and JO, B. H. Functional hydrogel structures for autonomous flow control inside microfluidic channels. nature, 404, 588–590 (2000)CrossRefGoogle Scholar
  17. [17]
    WONG, A. P., PEREZ-CASTILLEJOS, R., LOVE, J. C., and WHITESIDES, G. M. Partitioning microfluidic channels with hydrogel to construct tunable 3-D cellular microenvironments. Biomaterials, 29, 1853–1861 (2008)CrossRefGoogle Scholar
  18. [18]
    NIKOLOV, S., FERNANDEZ-NIEVES, A., and ALEXEEV, A. Mesoscale modeling of microgel mechanics and kinetics through the swelling transition. Applied Mathematics and Mechanics (English Edition), 39(1), 47–62 (2018) https://doi.org/10.1007/s10483-018-2259-6 MathSciNetCrossRefGoogle Scholar
  19. [19]
    SU, H., YAN, H., and JIN, B. Finite element method for coupled diffusion-deformation theory in polymeric gel based on slip-link model. Applied Mathematics and Mechanics (English Edition), 39(4), 581–596 (2018) https://doi.org/10.1007/s10483-018-2315-7 MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    ZHANG, H. Strain-stress relation in macromolecular microsphere composite hydrogel. Applied Mathematics and Mechanics (English Edition), 37(11), 1539–1550 (2016) https://doi.org/10.1007/s10483-016-2110-9 MathSciNetCrossRefGoogle Scholar
  21. [21]
    FLORY, P. J. Thermodynamics of high polymer solutions. The Journal of Chemical Physics, 10, 51–61 (1942)CrossRefGoogle Scholar
  22. [22]
    CAI, S. and SUO, Z. Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels. Journal of the Mechanics and Physics of Solids, 59, 2259–2278 (2011)CrossRefzbMATHGoogle Scholar
  23. [23]
    HONG, W., ZHAO, X., ZHOU, J., and SUO, Z. A theory of coupled diffusion and large deformation in polymeric gels. Journal of the Mechanics and Physics of Solids, 56, 1779–1793 (2008)CrossRefzbMATHGoogle Scholar
  24. [24]
    LUCANTONIO, A., NARDINOCCHI, P., and TERESI, L. Transient analysis of swelling-induced large deformations in polymer gels. Journal of the Mechanics and Physics of Solids, 61, 205–218 (2013)MathSciNetCrossRefGoogle Scholar
  25. [25]
    ZHANG, Y., LIU, Z., SWADDIWUDHIPONG, S., MIAO, H., DING, Z., and YAND, Z. pH-sensitive hydrogel for micro-fluidic valve. Journal of Functional Biomaterials, 3, 464–479 (2012)CrossRefGoogle Scholar
  26. [26]
    ZALACHAS, N., CAI, S., SUO, Z., and LAPUSTA, Y. Crease in a ring of a pH-sensitive hydrogel swelling under constraint. International Journal of Solids and Structures, 50, 920–927 (2013)CrossRefGoogle Scholar
  27. [27]
    HE, T., LI, M., and ZHOU, J. Modeling deformation and contacts of pH sensitive hydrogels for microfluidic flow control. Soft Matter, 8, 3083–3089 (2012)CrossRefGoogle Scholar
  28. [28]
    ARBABI, N., BAGHANI, M., ABDOLAHI, J., MAZAHERI, H., and MASHHADI, M. M. Finite bending of bilayer pH-responsive hydrogels: a novel analytic method and finite element analysis. Composites Part B: Engineering, 110, 116–123 (2017)CrossRefGoogle Scholar
  29. [29]
    ABDOLAHI, J., BAGHANI, M., ARBABI, N., and MAZAHERI, H. Analytical and numerical analysis of swelling-induced large bending of thermally-activated hydrogel bilayers. International Journal of Solids and Structures, 99, 1–11 (2016)CrossRefGoogle Scholar
  30. [30]
    HU, Z., ZHANG, X., and LI, Y. Synthesis and application of modulated polymer gels. Science, 269, 525–527 (1995)CrossRefGoogle Scholar
  31. [31]
    TIMOSHENKO, S. Analysis of bi-metal thermostats. Journal of the Optical Society of America, 11, 233–255 (1925)CrossRefGoogle Scholar
  32. [32]
    ABDOLAHI, J., BAGHANI, M., ARBABI, N., and MAZAHERI, H. Finite bending of a temperature-sensitive hydrogel tri-layer: an analytical and finite element analysis. Composite Structures, 164, 219–228 (2017)CrossRefGoogle Scholar
  33. [33]
    ZHANG, J., WU, J., SUN, J., and ZHOU, Q. Temperature-sensitive bending of bigel strip bonded by macroscopic molecular recognition. Soft Matter, 8, 5750–5752 (2012)CrossRefGoogle Scholar
  34. [34]
    GUVENDIREN, M., BURDICK, J. A., and YANG, S. Kinetic study of swelling-induced surface pattern formation and ordering in hydrogel films with depth-wise crosslinking gradient. Soft Matter, 6, 2044–2049 (2010)CrossRefGoogle Scholar
  35. [35]
    GUVENDIREN, M., BURDICK, J. A., and YANG, S. Solvent induced transition from wrinkles to creases in thin film gels with depth-wise crosslinking gradients. Soft Matter, 6, 5795–5801 (2010)CrossRefGoogle Scholar
  36. [36]
    GUVENDIREN, M., YANG, S., and BURDICK, J. A. Swelling-induced surface patterns in hydrogels with gradient crosslinking density. Advanced Functional Materials, 19, 3038–3045 (2009)CrossRefGoogle Scholar
  37. [37]
    WU, Z., BOUKLAS, N., and HUANG, R. Swell-induced surface instability of hydrogel layers with material properties varying in thickness direction. International Journal of Solids and Structures, 50, 578–587 (2013)CrossRefGoogle Scholar
  38. [38]
    WU, Z., BOUKLAS, N., LIU, Y., and HUANG, R. Onset of swell-induced surface instability of hydrogel layers with depth-wise graded material properties. Mechanics of Materials, 105, 138–147 (2017)CrossRefGoogle Scholar
  39. [39]
    WU, Z., MENG, J., LIU, Y., LI, H., and HUANG, R. A state space method for surface instability of elastic layers with material properties varying in thickness direction. Journal of Applied Mechanics, 81, 081003 (2014)CrossRefGoogle Scholar
  40. [40]
    ROCCABIANCA, S., GEI, M., and BIGONI, D. Plane strain bifurcations of elastic layered structures subject to finite bending: theory versus experiments. IMA Journal of Applied Mathematics, 75, 525–548 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    LUCANTONIO, A., NARDINOCCHI, P., and PEZZULLA, M. Swelling-induced and controlled curving in layered gel beams. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 470, 20140467 (2014)CrossRefGoogle Scholar
  42. [42]
    KIERZENKA, J. and SHAMPINE, L. F. A BVP solver that controls residual and error. Journal of Numerical Analysis Industrial and Applied Mathematics, 3, 27–41 (2008)MathSciNetzbMATHGoogle Scholar
  43. [43]
    BYRD, R. H., GILBERT, J. C., and NOCEDAL, J. A trust region method based on interior point techniques for nonlinear programming. Mathematical Programming, 89, 149–185 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    ALMASI, A., BAGHANI, M., MOALLEMI, A., BANIASSADI, M., and FARAJI, G. Investigation on thermal stresses in FGM hyperelastic thick-walled cylinders. Journal of Thermal Stresses, 41, 204–221 (2018)CrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical Engineering, College of EngineeringUniversity of TehranTehranIran

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