Strain-stress relation in macromolecular microsphere composite hydrogel

doi:10.1007/s10483-016-2110-9

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (11): 1539-1550.doi: https://doi.org/10.1007/s10483-016-2110-9

Strain-stress relation in macromolecular microsphere composite hydrogel

Hui ZHANG

School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

收稿日期:2016-01-25 修回日期:2016-09-13 出版日期:2016-11-01 发布日期:2016-11-01
通讯作者: Hui ZHANG E-mail:hzhang@bnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos.11471046 and 11571045),the Funds for the International Cooperation and Exchange of the National Natural Science Foundation of China and Hong Kong Research Grant Council (No.11261160486),the Ministry of Education Program for New Century Excellent Talents Project (No.NCET-12-0053),and the Fundamental Research Funds for the Central Universities

Strain-stress relation in macromolecular microsphere composite hydrogel

Hui ZHANG

School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Received:2016-01-25 Revised:2016-09-13 Online:2016-11-01 Published:2016-11-01
Supported by:
Project supported by the National Natural Science Foundation of China (Nos.11471046 and 11571045),the Funds for the International Cooperation and Exchange of the National Natural Science Foundation of China and Hong Kong Research Grant Council (No.11261160486),the Ministry of Education Program for New Century Excellent Talents Project (No.NCET-12-0053),and the Fundamental Research Funds for the Central Universities

摘要/Abstract

摘要：

This paper investigates the strain-stress relation for the macromolecular microsphere composite (MMC) hydrogel.The novel point is to present the strain-stress model,which is based on the microscopic mixed entropy set up in the previous work and the Flory-Rehner elastic energy.Then,the numerical result of the strain-stress model is shown,which is completely consistent with the chemical experiment.Moreover,the theoretical relation of the strain-stress depends on the microscopic parameters of the MMC hydrogel.Therefore,it is a way to investigate the relation of macroscopic properties and microscopic structures of soft matters.This approach can be extended to other soft matters.

关键词: large deformation, free energy functional, microscopic parameter, strain-stress model

Abstract:

Key words: free energy functional, microscopic parameter, strain-stress model, large deformation

中图分类号:

Hui ZHANG. Strain-stress relation in macromolecular microsphere composite hydrogel[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(11): 1539-1550.

参考文献

[1] Cai, S. Q. and Suo, Z. G. Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels. Journal of the Mechanics and Physics of Solids, 59, 2259-2278(2011)
[2] During, C. J. and Morman, K. N. Nonlinear swelling of polymer gels. Journal of Chemical Physics, 98, 4275-4293(1993)
[3] Flory, P. J. and Rehner, J. Statistical mechanics of cross-linked polymer networks swelling. Journal of Chemical Physics, 11, 521-526(1943)
[4] Huang, T., Xu, H. G., Jiao, K. X., Zhu, L. P., Brown, H. R., and Wang, H. L. A novel hydrogel with high mechanical strength:a macromolecular microsphere composite hydrogel. Advanced Materials, 19, 1622-1626(2007)
[5] Kang, M. K. and Huang, R. Swell-induced surface instability of confined hydrogel layers on substrates. Journal of the Mechanics and Physics of Solids, 58, 1582-1598(2010)
[6] Sun, S. and Mak, A. F. T. The dynamical response of a hydrogel fiber to electrochemical stimulation. Journal of Applied Physics Science, 39, 236-246(2000)
[7] Cai, S. Q., Lou, Y. C., Partha, G., Agathe, R., and Suo, Z. G. Force generated by a swelling elastomer subject to constraint. Journal of the Mechanics and Physics of Solids, 107, 103535(2010)
[8] Hong, W., Zhao, X. H., and Suo, Z. G. Drying-induced bifurcation in a hydrogel-actuated nanostructures. Journal of Applied Physics, 104, 084905(2008)
[9] Hong, W., Zhao, X. H., and Suo, Z. G. Large deformation and electrochemistry of polyelectrolyte gels. Journal of the Mechanics and Physics of Solids, 58, 558-577(2010)
[10] Hong, W., Zhao, X. H., Zhou, J. X., and Suo, Z. G. A theory of coupled diffusion and large deformation in polymeric gels. Journal of the Mechanics and Physics of Solids, 56, 1779-1793(2008)
[11] Hong, W., Liu, Z. S., and Suo, Z. G. Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load. International Journal of Solid and Structures, 46, 3282-3289(2009)
[12] Huang, Y. Z., Hong, W., and Suo, Z. G. Nonlinear analysis of wrinkles in a film bonded to a compliant substrate. Journal of the Mechanics and Physics, 53, 2101-2118(2005)
[13] Liu, Z. S., Hong, W., Suo, Z. G., Swaddiwudhipong, S., and Zhang, Y. W. Modeling and simulation of buckling of polymeric membrane thin film gel. Computational Materials Science, 49, 60-64(2010)
[14] Liu, Z. S., Swaddiwudhipong, S., Cui, F. S., Hong, W., Suo, Z. G., and Zhang, Y. W. Analytical solutions of polymeric gel structures under buckling and wrinkle. International Journal of Applied Mechanics, 2, 235-257(2011)
[15] Li, H. Smart Hydrogel Modeling, Springer Verlag, Berlin (2009)
[16] Yao, X. M. and Zhang, H. Kinetic model for the large deformation of cylindrical gels. Journal of Theoretical and Computational Chemistry, 13(4), 1450032(2014)
[17] Zhang, J. P., Zhao, X. H., Suo, Z. G., and Jiang, H. Q. A finite element method for transient analysis of concurrent large deformation and mass transport in gels. Journal of Applied Physics, 105, 093522(2009)
[18] Zhao, X. H., Wei, H., and Suo, Z. G. Inhomogeneous and anisotropic equilibrium state of a swollen hydrogel containing a hard core. Applied Physics Letters, 92, 051904(2008)
[19] Zhou, X., Hon, Y. C., Sun, S., and Mak, A. F. T. Numerical simulation of the steady-state deformation of a smart hydrogel under an external electric field. Institute of Physics Publishing, 11, 459-467(2002)
[20] Li, X., Ji, G. H., and Zhang, H. Phase transitions of macromolecular microsphere composite hydrogels based on the stochastic Cahn-Hilliard equation. Journal of Computational Physics, 283, 81-97(2015)
[21] Yuan, C. H. and Zhang, H. Self-consistent mean field model of hydrogel and its numerical simulation. Journal of Theoretical and Computational Chemistry, 12(6), 1350048(2013)
[22] Chen, R., Ji, G. H., Yang, X. F., and Zhang, H. Decoupled energy stable schemes for phase-field vesicle membrane model. Journal of Computational Physics, 302, 509-523(2015)
[23] Zhai, D. and Zhang, H. Investigation on the application of the TDGL equation in macromolecular microsphere composite hydrogel. Soft Matter, 9, 820-825(2013)
[24] Mooney, M. A theory of large elastic deformation. Journal of Applied Physics, 11, 582-592(1940)
[25] Rivlin, R. S. Large elastic deformations of isotropic materials, IV, further developments of the general theory. Philosophical Transactions of the Royal Society of London A, 241, 379-397(1948)
[26] Miquelard-Garnier, G., Hourdet, D., and Creton, C. Large stain behaviour of nanostructured polyelectrolyte hydrogels. Polymer, 50, 481-490(2009)
[27] Webber, R. E. and Creton, C. Large strain hysteresis and mullins effect of tough double-network hydrogels. Macromolecules, 40, 2919-2927(2007)

Strain-stress relation in macromolecular microsphere composite hydrogel

Strain-stress relation in macromolecular microsphere composite hydrogel

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