메뉴 건너뛰기




Volumn 77, Issue 6, 2010, Pages

A variational approach and finite element implementation for swelling of polymeric hydrogels under geometric constraints

Author keywords

hydrogel; large deformation; surface instability; swelling

Indexed keywords

CHEMICAL EQUILIBRIUMS; CRITICAL ASPECT RATIO; CROSS-LINKED POLYMERS; EXPLICIT FORMULA; FINITE ELEMENT IMPLEMENTATION; FREE ENERGY FUNCTION; GEOMETRIC CONSTRAINT; GOVERNING EQUATIONS; HEIGHT ASPECT RATIOS; LARGE DEFORMATIONS; MECHANICAL ENVIRONMENT; NONLINEAR CONSTITUTIVE BEHAVIOR; NUMERICAL SIMULATION; POLYMER NETWORKS; POLYMERIC HYDROGELS; RECTANGULAR CROSS-SECTIONS; SOLVENT MOLECULES; SPECIFIC MATERIALS; SURFACE INSTABILITY; SWELLING DEFORMATION; TANGENT MODULI; TRUE STRESS; VARIATIONAL APPROACHES; VOLUME CHANGE;

EID: 78649983783     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.4001715     Document Type: Article
Times cited : (99)

References (53)
  • 1
    • 0033178588 scopus 로고    scopus 로고
    • 'Smart' polymers and what they could do in biotechnology and medicine
    • Galaev, I. Y., and Mattiasson, B., 1999, "'Smart' Polymers and What They Could Do in Biotechnology and Medicine, " Trends Biotechnol., 17(8), pp. 335-340.
    • (1999) Trends Biotechnol. , vol.17 , Issue.8 , pp. 335-340
    • Galaev, I.Y.1    Mattiasson, B.2
  • 2
    • 33745135423 scopus 로고    scopus 로고
    • Hydrogels in biology and medicine: From molecular principles to bionanotechnology
    • Peppas, N. A., Hilt, J. Z., Khademhosseini, A., and Langer, R., 2006, "Hydrogels in Biology and Medicine: From Molecular Principles to Bionanotechnology, " Adv. Mater., 18(11), pp. 1345-1360.
    • (2006) Adv. Mater. , vol.18 , Issue.11 , pp. 1345-1360
    • Peppas, N.A.1    Hilt, J.Z.2    Khademhosseini, A.3    Langer, R.4
  • 4
    • 67649951495 scopus 로고    scopus 로고
    • Stimuli-responsive hydrogel thin films
    • Tokarev, I., and Minko, S., 2009, "Stimuli-Responsive Hydrogel Thin Films, " Soft Matter, 5, pp. 511-524.
    • (2009) Soft Matter. , vol.5 , pp. 511-524
    • Tokarev, I.1    Minko, S.2
  • 5
    • 0034611669 scopus 로고    scopus 로고
    • Functional hydrogel structures for autonomous flow control inside microfluidic channels
    • Beebe, D. J., Moore, J. S., Bauer, J. M., Yu, Q., Liu, R. H., Devadoss, C., and Jo, B.-H., 2000, "Functional Hydrogel Structures for Autonomous Flow Control Inside Microfluidic Channels, " Nature (London), 404, pp. 588-590.
    • (2000) Nature (London) , vol.404 , pp. 588-590
    • Beebe, D.J.1    Moore, J.S.2    Bauer, J.M.3    Yu, Q.4    Liu, R.H.5    Devadoss, C.6    Jo, B.-H.7
  • 6
    • 33746718118 scopus 로고    scopus 로고
    • Adaptive liquid microlenses activated by stimuli-responsive hydrogels
    • Dong, L., Agarwal, A. K., Beebe, D. J., and Jiang, H., 2006, "Adaptive Liquid Microlenses Activated by Stimuli-Responsive Hydrogels, " Nature (London), 442, pp. 551-554.
    • (2006) Nature (London) , vol.442 , pp. 551-554
    • Dong, L.1    Agarwal, A.K.2    Beebe, D.J.3    Jiang, H.4
  • 7
    • 33846590878 scopus 로고    scopus 로고
    • Reversible switching of hydrogel-actuated nanostructures into complex micropatterns
    • Sidorenko, A., Krupenkin, T., Taylor, A., Fratzl, P., and Aizenberg, J., 2007, "Reversible Switching of Hydrogel-Actuated Nanostructures Into Complex Micropatterns, " Science, 315, pp. 487-490.
    • (2007) Science , vol.315 , pp. 487-490
    • Sidorenko, A.1    Krupenkin, T.2    Taylor, A.3    Fratzl, P.4    Aizenberg, J.5
  • 8
    • 35448999809 scopus 로고
    • Reversible dilation and contraction by changing the state of ionization of high-polymer acid networks
    • Kuhn, W., Hargitay, B., Katchalsky, A., and Eisenberg, H., 1950, "Reversible Dilation and Contraction by Changing the State of Ionization of High-Polymer Acid Networks, " Nature (London), 165, pp. 514-516.
    • (1950) Nature (London) , vol.165 , pp. 514-516
    • Kuhn, W.1    Hargitay, B.2    Katchalsky, A.3    Eisenberg, H.4
  • 9
    • 0001319020 scopus 로고
    • Effect of constraints on the equilibrium swelling of rubber vulcanizates
    • Southern, E., and Thomas, A. G., 1965, "Effect of Constraints on the Equilibrium Swelling of Rubber Vulcanizates, " J. Polym. Sci. A, 3, pp. 641-646.
    • (1965) J. Polym. Sci. A , vol.3 , pp. 641-646
    • Southern, E.1    Thomas, A.G.2
  • 11
    • 11944260761 scopus 로고
    • Patterns in shrinking gels
    • Matsuo, E. S., and Tanaka, T., 1992, "Patterns in Shrinking Gels, " Nature (London), 358, pp. 482-485.
    • (1992) Nature (London) , vol.358 , pp. 482-485
    • Matsuo, E.S.1    Tanaka, T.2
  • 12
    • 4243678480 scopus 로고
    • Surface-pattern evolution in a swelling gel under a geometrical constraint: Direction observation of fold structure and its coarsening dynamics
    • Tanaka, H., and Sigehuzi, T., 1994, "Surface-Pattern Evolution in a Swelling Gel Under a Geometrical Constraint: Direction Observation of Fold Structure and Its Coarsening Dynamics, " Phys. Rev. E, 49, pp. R39-R42.
    • (1994) Phys. Rev. E , vol.49
    • Tanaka, H.1    Sigehuzi, T.2
  • 13
    • 29044441675 scopus 로고    scopus 로고
    • Direct-write E-beam patterning of stimuli-responsive hydrogel nanostructures
    • Tirumala, V. R., Divan, R., Ocola, L. E., and Mancini, D. C., 2005, "Direct-Write E-Beam Patterning of Stimuli-Responsive Hydrogel Nanostructures, " J. Vac. Sci. Technol. B, 23(6), pp. 3124-3128.
    • (2005) J. Vac. Sci. Technol. B. , vol.23 , Issue.6 , pp. 3124-3128
    • Tirumala, V.R.1    Divan, R.2    Ocola, L.E.3    Mancini, D.C.4
  • 14
    • 33745713668 scopus 로고    scopus 로고
    • Buckling of swelling gels
    • Mora, T., and Boudaoud, A., 2006, "Buckling of Swelling Gels, " Eur. Phys. J. E, 20(2), pp. 119-124.
    • (2006) Eur. Phys. J. E , vol.20 , Issue.2 , pp. 119-124
    • Mora, T.1    Boudaoud, A.2
  • 15
    • 52649091857 scopus 로고    scopus 로고
    • The buckling of a swollen thin gel layer bound to a compliant substrate
    • Sultan, E., and Boudaoud, A., 2008, "The Buckling of a Swollen Thin Gel Layer Bound to a Compliant Substrate, " ASME J. Appl. Mech., 75, p. 051002.
    • (2008) ASME J. Appl. Mech. , vol.75 , pp. 051002
    • Sultan, E.1    Boudaoud, A.2
  • 16
    • 39749091638 scopus 로고    scopus 로고
    • Creasing instability of surface-attached hydrogels
    • Trujillo, V., Kim, J., and Hayward, R. C., 2008, "Creasing Instability of Surface-Attached Hydrogels, " Soft Matter, 4, pp. 564-569.
    • (2008) Soft Matter. , vol.4 , pp. 564-569
    • Trujillo, V.1    Kim, J.2    Hayward, R.C.3
  • 17
    • 46749106127 scopus 로고    scopus 로고
    • One-step nanoscale assembly of complex structures via harnessing of an elastic instability
    • Zhang, Y., Matsumoto, E. A., Peter, A., Lin, P.-C., Kamien, R. D., and Yang, S., 2008, "One-Step Nanoscale Assembly of Complex Structures Via Harnessing of an Elastic Instability, " Nano Lett., 8, pp. 1192-1196.
    • (2008) Nano. Lett. , vol.8 , pp. 1192-1196
    • Zhang, Y.1    Matsumoto, E.A.2    Peter, A.3    Lin, P.-C.4    Kamien, R.D.5    Yang, S.6
  • 18
    • 0000590441 scopus 로고
    • Phase transitions of gels
    • Li, Y., and Tanaka, T., 1992, "Phase Transitions of Gels, " Annu. Rev. Mater. Sci., 22, pp. 243-277.
    • (1992) Annu. Rev. Mater. Sci. , vol.22 , pp. 243-277
    • Li, Y.1    Tanaka, T.2
  • 19
    • 24444435692 scopus 로고
    • Theory of pattern formation in gels: Surface folding in highly compressible elastic bodies
    • Onuki, A., 1989, "Theory of Pattern Formation in Gels: Surface Folding in Highly Compressible Elastic Bodies, " Phys. Rev. A, 39(11), pp. 5932-5948.
    • (1989) Phys. Rev. A , vol.39 , Issue.11 , pp. 5932-5948
    • Onuki, A.1
  • 20
    • 0001542206 scopus 로고
    • Three-dimensional computer modeling for pattern formation on the surface of an expanding polymer gel
    • Suematsu, N., Sekimoto, N., and Kawasaki, K., 1990, "Three- Dimensional Computer Modeling for Pattern Formation on the Surface of an Expanding Polymer Gel, " Phys. Rev. A, 41(10), pp. 5751-5754.
    • (1990) Phys. Rev. A , vol.41 , Issue.10 , pp. 5751-5754
    • Suematsu, N.1    Sekimoto, N.2    Kawasaki, K.3
  • 21
    • 33749227620 scopus 로고
    • Nonlinear swelling of polymer gels
    • Durning, C. J., and Morman, K. N., Jr., 1993, "Nonlinear Swelling of Polymer Gels, " J. Chem. Phys., 98(5), pp. 4275-4293.
    • (1993) J. Chem. Phys. , vol.98 , Issue.5 , pp. 4275-4293
    • Durning, C.J.1    Morman Jr., K.N.2
  • 22
    • 0001300309 scopus 로고    scopus 로고
    • Elasticity in strongly interacting soft solids: A polyelectolyte network
    • Wilder, J., and Vilgis, T. A., 1998, "Elasticity in Strongly Interacting Soft Solids: A Polyelectolyte Network, " Phys. Rev. E, 57, pp. 6865-6874.
    • (1998) Phys. Rev. E , vol.57 , pp. 6865-6874
    • Wilder, J.1    Vilgis, T.A.2
  • 23
    • 0001172071 scopus 로고    scopus 로고
    • Theory and numerical calculation of pattern formation in shrinking gels
    • Maskawa, J., Takeuchi, T., Maki, K., Tsujii, K., and Tanaka, T., 1999, "Theory and Numerical Calculation of Pattern Formation in Shrinking Gels, " J. Chem. Phys., 110(22), pp. 10993-10999.
    • (1999) J. Chem. Phys. , vol.110 , Issue.22 , pp. 10993-10999
    • Maskawa, J.1    Takeuchi, T.2    Maki, K.3    Tsujii, K.4    Tanaka, T.5
  • 24
    • 37649029144 scopus 로고    scopus 로고
    • Mechanical phase diagram of shrinking cylindrical gels
    • Boudaoud, A., and Chaieb, S., 2003, "Mechanical Phase Diagram of Shrinking Cylindrical Gels, " Phys. Rev. E, 68, p. 021801.
    • (2003) Phys. Rev. E , vol.68 , pp. 021801
    • Boudaoud, A.1    Chaieb, S.2
  • 25
    • 0346724506 scopus 로고    scopus 로고
    • Chemically induced swelling of hydrogels
    • Dolbow, J., Fried, E., and Jia, H. D., 2004, "Chemically Induced Swelling of Hydrogels, " J. Mech. Phys. Solids, 52, pp. 51-84.
    • (2004) J. Mech. Phys. Solids , vol.52 , pp. 51-84
    • Dolbow, J.1    Fried, E.2    Jia, H.D.3
  • 26
    • 34250664687 scopus 로고    scopus 로고
    • Modeling of multiphase smart hydrogels responding to pH and electric voltage coupled stimuli
    • Li, H., Luo, R., Birgersson, E., and Lam, K. Y., 2007, "Modeling of Multiphase Smart Hydrogels Responding to pH and Electric Voltage Coupled Stimuli, " J. Appl. Phys., 101(11), p. 114905.
    • (2007) J. Appl. Phys. , vol.101 , Issue.11 , pp. 114905
    • Li, H.1    Luo, R.2    Birgersson, E.3    Lam, K.Y.4
  • 27
    • 41749089776 scopus 로고    scopus 로고
    • A theory of coupled diffusion and large deformation in polymeric gels
    • Hong, W., Zhao, X., Zhou, J., and Suo, Z., 2008, "A Theory of Coupled Diffusion and Large Deformation in Polymeric Gels, " J. Mech. Phys. Solids, 56, pp. 1779-1793.
    • (2008) J. Mech. Phys. Solids , vol.56 , pp. 1779-1793
    • Hong, W.1    Zhao, X.2    Zhou, J.3    Suo, Z.4
  • 28
    • 43049093032 scopus 로고    scopus 로고
    • Stretching and polarizing a dielectric gel immersed in a solvent
    • Zhao, X., Hong, W., and Suo, Z., 2008, "Stretching and Polarizing a Dielectric Gel Immersed in a Solvent, " Int. J. Solids Struct., 45, pp. 4021-4031.
    • (2008) Int. J. Solids Struct. , vol.45 , pp. 4021-4031
    • Zhao, X.1    Hong, W.2    Suo, Z.3
  • 29
    • 67249152749 scopus 로고    scopus 로고
    • Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load
    • Hong, W., Liu, Z., and Suo, Z., 2009, "Inhomogeneous Swelling of a Gel in Equilibrium With a Solvent and Mechanical Load, " Int. J. Solids Struct., 46, pp. 3282-3289.
    • (2009) Int. J. Solids Struct. , vol.46 , pp. 3282-3289
    • Hong, W.1    Liu, Z.2    Suo, Z.3
  • 30
    • 67249085163 scopus 로고    scopus 로고
    • A finite element method for transient analysis of concurrent large deformation and mass transport in gels
    • Zhang, J., Zhao, X., Suo, Z., and Jiang, H., 2009, "A Finite Element Method for Transient Analysis of Concurrent Large Deformation and Mass Transport in Gels, " J. Appl. Phys., 105, p. 093522.
    • (2009) J. Appl. Phys. , vol.105 , pp. 093522
    • Zhang, J.1    Zhao, X.2    Suo, Z.3    Jiang, H.4
  • 32
    • 0345643551 scopus 로고
    • General theory of three-dimensional consolidation
    • Biot, M. A., 1941, "General Theory of Three-Dimensional Consolidation, " J. Appl. Phys., 12, pp. 155-164.
    • (1941) J. Appl. Phys. , vol.12 , pp. 155-164
    • Biot, M.A.1
  • 33
    • 0001098982 scopus 로고
    • Nonlinear and semilinear rheology of porous solids
    • Biot, M. A., 1973, "Nonlinear and Semilinear Rheology of Porous Solids, " J. Geophys. Res., 78, pp. 4924-4937.
    • (1973) J. Geophys. Res. , vol.78 , pp. 4924-4937
    • Biot, M.A.1
  • 36
    • 36849140573 scopus 로고
    • Statistical mechanics of swelling of network structures
    • Flory, P. J., 1950, "Statistical Mechanics of Swelling of Network Structures, " J. Chem. Phys., 18, pp. 108-111.
    • (1950) J. Chem. Phys. , vol.18 , pp. 108-111
    • Flory, P.J.1
  • 38
    • 0000298336 scopus 로고
    • Large elastic deformations of isotropic materials. I. Fundamental concepts
    • Rivlin, R. S., 1948, "Large Elastic Deformations of Isotropic Materials. I. Fundamental Concepts, " Philos. Trans. R. Soc. London, Ser. A, 240, pp. 459-490.
    • (1948) Philos. Trans. R. Soc. London, Ser. A , vol.240 , pp. 459-490
    • Rivlin, R.S.1
  • 39
    • 0021515714 scopus 로고
    • Remarks on rate constitutive equations for finite deformation problems: Computational implications
    • Simo, J. C., and Pister, K. S., 1984, "Remarks on Rate Constitutive Equations for Finite Deformation Problems: Computational Implications, " Comput. Methods Appl. Mech. Eng., 46, pp. 201-215.
    • (1984) Comput. Methods Appl. Mech. Eng. , vol.46 , pp. 201-215
    • Simo, J.C.1    Pister, K.S.2
  • 40
    • 0001567544 scopus 로고
    • Volume changes associated with the deformation of rubber-like solids
    • Ogden, R. W., 1976, "Volume Changes Associated With the Deformation of Rubber-Like Solids, " J. Mech. Phys. Solids, 24(6), pp. 323-338.
    • (1976) J. Mech. Phys. Solids , vol.24 , Issue.6 , pp. 323-338
    • Ogden, R.W.1
  • 41
    • 0000353991 scopus 로고    scopus 로고
    • A new constitutive model for the compressibility of elastomers at finite deformations
    • Bischoff, J. E., Arruda, E. M., and Grosh, K., 2001, "A New Constitutive Model for the Compressibility of Elastomers at Finite Deformations, " Rubber Chem. Technol., 74(4), pp. 541-559.
    • (2001) Rubber Chem. Technol. , vol.74 , Issue.4 , pp. 541-559
    • Bischoff, J.E.1    Arruda, E.M.2    Grosh, K.3
  • 42
    • 0034216714 scopus 로고    scopus 로고
    • Constitutive models of rubber elasticity: A review
    • Boyce, M. C., and Arruda, E. M., 2000, "Constitutive Models of Rubber Elasticity: A Review, " Rubber Chem. Technol., 73(3), pp. 504-523.
    • (2000) Rubber Chem. Technol. , vol.73 , Issue.3 , pp. 504-523
    • Boyce, M.C.1    Arruda, E.M.2
  • 43
    • 84982060196 scopus 로고
    • Mechanische und optische eigenschaften von gequollenem kautschuk
    • Kuhn, W., Pasternak, R., and Kuhn, H., 1947, "Mechanische und optische eigenschaften von gequollenem kautschuk, " Helv. Chim. Acta, 30, pp. 1705-1740.
    • (1947) Helv. Chim. Acta , vol.30 , pp. 1705-1740
    • Kuhn, W.1    Pasternak, R.2    Kuhn, H.3
  • 44
    • 0006280870 scopus 로고
    • Deformation and swelling of polymer networks containing comparatively long chains
    • Hermans, J. J., 1947, "Deformation and Swelling of Polymer Networks Containing Comparatively Long Chains, " Trans. Faraday Soc, 43, pp. 591-600.
    • (1947) Trans. Faraday Soc. , vol.43 , pp. 591-600
    • Hermans, J.J.1
  • 45
    • 16544364675 scopus 로고
    • Solutions of long chain compounds
    • Huggins, M. L., 1941, "Solutions of Long Chain Compounds, " J. Chem. Phys., 9(5), p. 440.
    • (1941) J. Chem. Phys. , vol.9 , Issue.5 , pp. 440
    • Huggins, M.L.1
  • 47
    • 77955519078 scopus 로고    scopus 로고
    • abaqus version 6.8, Providence, RI
    • abaqus version 6.8, 2008, Dassault Systémes Simulia Corp., Providence, RI.
    • (2008) Dassault Systémes Simulia Corp.
  • 49
    • 0011010370 scopus 로고    scopus 로고
    • Surface instabilities in compressed or bent rubber blocks
    • Gent, A. N., and Cho, I. S., 1999, "Surface Instabilities in Compressed or Bent Rubber Blocks, " Rubber Chem. Technol., 72, pp. 253-262.
    • (1999) Rubber Chem. Technol. , vol.72 , pp. 253-262
    • Gent, A.N.1    Cho, I.S.2
  • 50
    • 34547949538 scopus 로고    scopus 로고
    • Kink instability of a highly deformable elastic cylinder
    • Ghatak, A., and Das, A. L., 2007, "Kink Instability of a Highly Deformable Elastic Cylinder, " Phys. Rev. Lett., 99, p. 076101.
    • (2007) Phys. Rev. Lett. , vol.99 , pp. 076101
    • Ghatak, A.1    Das, A.L.2
  • 51
    • 0011012068 scopus 로고
    • Surface instability of rubber in compression
    • Biot, M. A., 1963, "Surface Instability of Rubber in Compression, " Appl. Sci. Res., Sect. A, 12, pp. 168-182.
    • (1963) Appl. Sci. Res., Sect. A , vol.12 , pp. 168-182
    • Biot, M.A.1
  • 53
    • 70349479058 scopus 로고    scopus 로고
    • Formation of creases on the surfaces of elastomers and gels
    • Hong, W., Zhao, X., and Suo, Z., 2009, "Formation of Creases on the Surfaces of Elastomers and Gels, " Appl. Phys. Lett., 95, p. 111901.
    • (2009) Appl. Phys. Lett. , vol.95 , pp. 111901
    • Hong, W.1    Zhao, X.2    Suo, Z.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.