Bifurcation of a Swelling Gel with a Mechanical Load and Geometric Constraint
XUE Feng, YONG Hua-Dong, ZHOU You-He**
Key Laboratory of Mechanics on Disaster and Environment in Western China (Ministry of Education of China), and Department of Mechanics, Lanzhou University, Lanzhou 730000
Bifurcation of a Swelling Gel with a Mechanical Load and Geometric Constraint
XUE Feng, YONG Hua-Dong, ZHOU You-He**
Key Laboratory of Mechanics on Disaster and Environment in Western China (Ministry of Education of China), and Department of Mechanics, Lanzhou University, Lanzhou 730000
摘要We present an analysis of the bifurcation phenomenon of a gel in contact with a solvent. When a Mooney–Rivlin form-free energy function is introduced, an asymmetric swelling may appear for a gel swelling under uniaxial constraint or subjected to equal dead loads, which results in an interesting pitchfork bifurcation phenomenon. We present an analytical investigation of this problem based on the classical theory of continuum mechanics. The bifurcation points are obtained for different values of the chemical potential of the solvent molecules. The results demonstrate that the free swelling of the gel under uniaxial constraint will not result in the bifurcation unless further mechanical loads are applied.
Abstract：We present an analysis of the bifurcation phenomenon of a gel in contact with a solvent. When a Mooney–Rivlin form-free energy function is introduced, an asymmetric swelling may appear for a gel swelling under uniaxial constraint or subjected to equal dead loads, which results in an interesting pitchfork bifurcation phenomenon. We present an analytical investigation of this problem based on the classical theory of continuum mechanics. The bifurcation points are obtained for different values of the chemical potential of the solvent molecules. The results demonstrate that the free swelling of the gel under uniaxial constraint will not result in the bifurcation unless further mechanical loads are applied.
XUE Feng;YONG Hua-Dong;ZHOU You-He**
. Bifurcation of a Swelling Gel with a Mechanical Load and Geometric Constraint[J]. 中国物理快报, 2011, 28(11): 118301-118301.
XUE Feng, YONG Hua-Dong, ZHOU You-He**
. Bifurcation of a Swelling Gel with a Mechanical Load and Geometric Constraint. Chin. Phys. Lett., 2011, 28(11): 118301-118301.
[1] Guth E and Mark H 1934 Monatshefte 65 93
[2] Flory P J and Rehner J 1943 J. Chem. Phys. 11 521
[3] Flory P J 1953 Principles of Polymer Chemistry (New York: Cornell University Press)
[4] Liu Z et al 2010 Comp. Mater. Sci. 49 S60
[5] Hong W et al 2009 Int. J. Solids. Struct. 46 3282
[6] Zhao X, Hong W and Suo Z 2008 Appl. Phys. Lett. 92 051904
[7] Hong W, Zhao X and Suo Z 2008 J. Appl. Phys. 104 084905
[8] Wichterle O and Lim D 1960 Nature 185 117
[9] Lee K Y and Mooney D J 2001 Chem. Rev. 101 1869
[10] Beebe D J et al 2000 Nature 404 588
[11] Dong L et al 2006 Nature 442 551
[12] Rivlin R S 1948 Philos. Trans. R. Soc. A 241 379
[13] Treloar L R G 1975 The Physics of Rubber Elasticity (Oxford: Clarendon)
[14] Mooney M 1940 J. Appl. Phys. 11 582
[15] Zhang Y et al 2008 Nano Lett. 8 1192
[16] Díaz-Calleja R et al 2009 Eur. Phys. J. E 30 417
[17] Díaz-Calleja R et al 2009 J. Electrostatics 67 158
[18] Doi M 1996 Introduction to Polymer Physics (Oxford: Clarendon)
[19] Doi M 2009 J. Phys. Soc. Jpn. 78 052001
2011, Vol. 28 
