Finite element method for coupled diffusion-deformation theory in polymeric gel based on slip-link model. (English) Zbl 1390.74055
Summary: A polymeric gel is an aggregate of polymers and solvent molecules, which can retain its shape after a large deformation. The deformation behavior of polymeric gels was often described based on the Flory-Rehner free energy function without considering the influence of chain entanglements on the mechanical behavior of gels. In this paper, a new hybrid free energy function for gels is formulated by combining the Edwards-Vilgis slip-link model and the Flory-Huggins mixing model to quantify the time-dependent concurrent process of large deformation and mass transport. The finite element method is developed to analyze examples of swelling-induced deformation. Simulation results are compared with available experimental data and show good agreement. The influence of entanglements on the time-dependent deformation behavior of gels is also demonstrated. The study of large deformation kinetics of polymeric gel is useful for diverse applications.
MSC:
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
polymeric gel; finite element method; slip-link model; large deformation; mass transport; kineticsSoftware:
FEAPpvReferences:
| [1] | Wichterle, O. and Lim, D. Hydrophilic gels for biological use. nature, 185(4706), 117-118 (1960) · doi:10.1038/185117a0 |
| [2] | Peppas, N. A., Bures, P., Leobandung, W., and Ichikawa, H. Hydrogels in pharmaceutical formu-lations. European Journal of Pharmaceutics and Biopharmaceutics, 50(1), 27-46 (2000) · doi:10.1016/S0939-6411(00)00090-4 |
| [3] | Luo, Y. and Shoichet, M. S. A photolabile hydrogel for guided three-dimensional cell growth and migration. Nature Materials, 3(4), 249-254 (2004) · doi:10.1038/nmat1092 |
| [4] | 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(6778), 588-590 (2000) · doi:10.1038/35007047 |
| [5] | Dong, L., Agarwal, A. K., Beebe, D. J., and Jiang, H. Adaptive liquid microlenses activated by stimuli-responsive hydrogels. nature, 442(7102), 551-554 (2006) · doi:10.1038/nature05024 |
| [6] | Gibbs, J. W.; Bumstead, H. A., The Scientific Papers of J, 184-184 (1906) |
| [7] | Biot, M. A. General theory of three-dimensional consolidation. Journal of Applied Physics, 12(2), 155-164 (1941) · JFM 67.0837.01 · doi:10.1063/1.1712886 |
| [8] | Flory, P. J. and Rehner, J. Statistical mechanics of cross-linked polymer networks II: swelling. The Journal of Chemical Physics, 11(11), 521-526 (1943) · doi:10.1063/1.1723792 |
| [9] | Baek, S. and Pence, T. Inhomogeneous deformation of elastomer gels in equilibrium under satu-rated and unsaturated conditions. Journal of the Mechanics and Physics of Solids, 59(3), 561-582 (2011) · Zbl 1270.74080 · doi:10.1016/j.jmps.2010.12.013 |
| [10] | 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(5), 1779-1793 (2008) · Zbl 1162.74313 · doi:10.1016/j.jmps.2007.11.010 |
| [11] | Zhang, H. Strain-stress relation in macromolecular microsphere composite hydro-gel. Applied Mathematics and Mechanics (English Edition), 37(11), 1539-1550 (2016) https://doi.org/10.1007/s10483-016-2110-9 · doi:10.1007/s10483-016-2110-9 |
| [12] | 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(11), 2259-2278 (2011) · Zbl 1270.74163 · doi:10.1016/j.jmps.2011.08.008 |
| [13] | Hong, W., Liu, Z., and Suo, Z. Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load. International Journal of Solids and Structures, 46(17), 3282-3289 (2009) · Zbl 1167.74333 · doi:10.1016/j.ijsolstr.2009.04.022 |
| [14] | Hong, W., Zhao, X., and Suo, Z. Large deformation and electrochemistry of polyelectrolyte gels. Journal of the Mechanics and Physics of Solids, 58(4), 558-577 (2010) · Zbl 1244.82089 · doi:10.1016/j.jmps.2010.01.005 |
| [15] | Liu, Z. S., Swaddiwudhipong, S., Cui, F. S., Hong, W., Suo, Z., and Zhang, Y. W. Analytical solutions of polymeric gel structures under buckling and wrinkle. International Journal of Applied Mechanics, 3(2), 235-257 (2012) · doi:10.1142/S1758825111000968 |
| [16] | Wineman, A. and Rajagopal, K. R. Shear induced redistribution of fluid within a uniformly swollen nonlinear elastic cylinder. International Journal of Engineering Science, 30(11), 1583-1595 (1992) · Zbl 0764.73056 · doi:10.1016/0020-7225(92)90127-3 |
| [17] | Chester, S. A. and Anand, L. A coupled theory of fluid permeation and large deformations for elastomeric materials. Journal of the Mechanics and Physics of Solids, 58(11), 1879-1906 (2010) · Zbl 1225.74034 · doi:10.1016/j.jmps.2010.07.020 |
| [18] | Mergell, B. and Everaers, R. Tube models for rubber-elastic systems. Macromolecules, 34(16), 5675-5686 (2001) · doi:10.1021/ma002228c |
| [19] | Flory, P. J. Theory of elasticity of polymer networks-effect of local constraints on junctions. Journal of Chemical Physics, 66(12), 5720-5729 (1977) · doi:10.1063/1.433846 |
| [20] | Ronca, G. and Allegra, G. Approach to rubber elasticity with internal constraints. Journal of Chemical Physics, 63(11), 4990-4997 (1975) · doi:10.1063/1.431245 |
| [21] | Edwards, S. F. Theory of rubber elasticity. British Polymer Journal, 9(2), 140-143 (1977) · doi:10.1002/pi.4980090209 |
| [22] | Kloczkowski, A., Mark, J. E., and Erman, B. A diffused-constraint theory for the elasticity of amorphous polymer networks I: fundamentals and stress-strain isotherms in elongation. Macro-molecules, 28(14), 5089-5096 (1995) · doi:10.1021/ma00118a043 |
| [23] | Edwards, S. and Vilgis, T. The effect of entanglements in rubber elasticity. Polymer, 27(4), 483-492 (1986) · doi:10.1016/0032-3861(86)90231-4 |
| [24] | Higgs, P. G. and Gaylord, R. J. Slip-links, hoops and tubes: tests of entanglement models of rubber elasticity. Polymer, 31(1), 70-74 (1990) · doi:10.1016/0032-3861(90)90351-X |
| [25] | Urayama, K. Network topology-mechanical properties relationships of model elastomers. Polymer Journal, 40(8), 669-678 (2008) · doi:10.1295/polymj.PJ2008033 |
| [26] | Meissner, B. and Matejka, L. Comparison of recent rubber-elasticity theories with biaxial stress-strain data: the slip-link theory of Edwards and Vilgis. Polymer, 43(13), 3803-3809 (2002) · doi:10.1016/S0032-3861(02)00150-7 |
| [27] | Yan, H. X. and Jin, B. Influence of microstructural parameters on mechanical behavior of polymer gels. International Journal of Solids and Structures, 49(3), 436-444 (2012) · doi:10.1016/j.ijsolstr.2011.10.026 |
| [28] | Yan, H. X. and Jin, B. Influence of environmental solution pH and microstructural parameters on mechanical behavior of amphoteric pH-sensitive hydrogels. European Physical Journal E, 35(5), 36-46 (2012) · doi:10.1140/epje/i2012-12036-7 |
| [29] | Yan, H. X. and Jin, B. Equilibrium swelling of a polyampholytic pH-sensitive hydrogel. European Physical Journal E, 36(3), 27-33 (2013) · doi:10.1140/epje/i2013-13027-x |
| [30] | Yan, H. X., Jin, B., Gao, S. H., and Chen, L. W. Equilibrium swelling and electrochemistry of polyampholytic pH-sensitive hydrogel. International Journal of Solids and Structures, 51(23/24), 4149-4156 (2014) · doi:10.1016/j.ijsolstr.2014.08.016 |
| [31] | Chester, S. A., Di Leo, C. V., and Anand, L. A finite element implementation of a coupled diffusion-deformation theory for elastomeric gels. International Journal of Solids and Structures, 52, 1-18 (2015) · doi:10.1016/j.ijsolstr.2014.08.015 |
| [32] | Flory, P. J. Thermodynamics of high polymer solutions. The Journal of Chemical Physics, 10(1), 51-61 (1942) · doi:10.1063/1.1723621 |
| [33] | Huggins, M. L. Solutions of long chain compounds. The Journal of Chemical Physics, 9(5), 440-440 (1941) · doi:10.1063/1.1750930 |
| [34] | Zienkiewicz, O. C., Taylor, R. L., and Fox, D. The Finite Element Method for Solid and Structural Mechanics, Butterworth-Heinemann Elsevier Ltd., Oxford, 17-19 (2014) · Zbl 1307.74003 |
| [35] | Zienkiewicz, O. C., Taylor, R. L., and Zhu, J. Z. The Finite Element Method: Its Basis and Fundamentals, Butterworth-Heinemann Elsevier Ltd., Oxford, 64-66 (2013) · Zbl 1307.74005 |
| [36] | Yoon, J., Cai, S., Suo, Z., and Hayward, R. C. Poroelastic swelling kinetics of thin hydrogel layers: comparison of theory and experiment. Soft Matter, 6(23), 6004-6012 (2010) · doi:10.1039/c0sm00434k |
| [37] | Bouklas, N. and Huang, R. Swelling kinetics of polymer gels: comparison of linear and nonlinear theories. Soft Matter, 8(31), 8194-8203 (2012) · doi:10.1039/c2sm25467k |
| [38] | Achilleos, E. C., Prud’homme, R. K., Christodoulou, K. N., Gee, K. R., and Kevrekidis, I. G. Dynamic deformation visualization in swelling of polymer gels. Chemical Engineering Science, 55(17), 3335-3340 (2000) · doi:10.1016/S0009-2509(00)00002-6 |
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