Finite deformation swelling of a temperature-sensitive hydrogel cylinder under combined extension-torsion

doi:10.1007/s10483-020-2585-6

摘要/Abstract

摘要： The swelling behavior of a temperature-sensitive poly-N-isopropylacrylamide (PNIPAM) hydrogel circular cylinder is studied subjected to combined extension-torsion and varied temperature. In this regard, a semi-analytical solution is proposed for general combined loading. A finite element (FE) analysis is conducted, subjecting a hydrogel cylinder to the combined extension-torsion and the varied temperature to evaluate the validity and accuracy of the solution. A user-defined UHYPER subroutine is developed and verified under free and constrained swelling conditions. The FE results illustrate excellent agreement with the semi-analytical solution. Due to the complexity of the problem, some compositions and applied loading factors are analyzed. It is revealed that for larger cross-linked density and larger ending temperature, the cylinder yields higher stresses and smaller radial swelling deformation. Besides, the radial and hoop stresses increase by applying larger twist and axial stretch. The hoop stresses intersect at approximately R/R_out=0.58, where the hoop stress vanishes. Besides, the axial force has direct and inverse relationships with the axial stretch and the twist, respectively. However, the resultant torsional moment behavior is complex, and the position of the maximum point varies significantly by altering the axial stretch and the twist.

关键词: extension-torsion of the circular cylinder, temperature variation, finite element (FE) analysis, temperature-sensitive poly-N-isopropylacrylamide (PNIPAM) hydrogel, semi-analytical solution

Abstract: The swelling behavior of a temperature-sensitive poly-N-isopropylacrylamide (PNIPAM) hydrogel circular cylinder is studied subjected to combined extension-torsion and varied temperature. In this regard, a semi-analytical solution is proposed for general combined loading. A finite element (FE) analysis is conducted, subjecting a hydrogel cylinder to the combined extension-torsion and the varied temperature to evaluate the validity and accuracy of the solution. A user-defined UHYPER subroutine is developed and verified under free and constrained swelling conditions. The FE results illustrate excellent agreement with the semi-analytical solution. Due to the complexity of the problem, some compositions and applied loading factors are analyzed. It is revealed that for larger cross-linked density and larger ending temperature, the cylinder yields higher stresses and smaller radial swelling deformation. Besides, the radial and hoop stresses increase by applying larger twist and axial stretch. The hoop stresses intersect at approximately R/R_out=0.58, where the hoop stress vanishes. Besides, the axial force has direct and inverse relationships with the axial stretch and the twist, respectively. However, the resultant torsional moment behavior is complex, and the position of the maximum point varies significantly by altering the axial stretch and the twist.

Key words: extension-torsion of the circular cylinder, temperature variation, finite element (FE) analysis, temperature-sensitive poly-N-isopropylacrylamide (PNIPAM) hydrogel, semi-analytical solution

中图分类号:

65M06

M. SHOJAEIFARD, M. BAGHANI. Finite deformation swelling of a temperature-sensitive hydrogel cylinder under combined extension-torsion[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(3): 409-424.

参考文献 31

[1]	DOI, M. Gel dynamics. Journal of the Physical Society of Japan, 78, 052001(2009)
[2]	CAI, S. and SUO, Z. Mechanics and chemical thermodynamics of phase transition in temperaturesensitive hydrogels. Journal of the Mechanics and Physics of Solids, 59, 2259-2278(2011)
[3]	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)
[4]	SHOJAEIFARD, M., ROUHANI, F., and BAGHANI, M. A combined analytical-numerical analysis on multidirectional finite bending of functionally graded temperature-sensitive hydrogels. Journal of Intelligent Material Systems and Structures, 30, 1882-1895(2019)
[5]	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)
[6]	SHOJAEIFARD, M. and BAGHANI, M. On the finite bending of functionally graded lightsensitive hydrogels. Meccanica, 54, 841-854(2019)
[7]	OSADA, Y. and GONG, J. P. Soft and wet materials:polymer gels. Advanced Materials, 10, 827-837(1998)
[8]	LIU, Q., LI, H., and LAM, K. Y. Development of a multiphysics model to characterize the responsive behavior of magnetic-sensitive hydrogels with finite deformation. The Journal of Physical Chemistry B, 121, 5633-5646(2017)
[9]	RANDALL, C. L., GULTEPE, E., and GRACIAS, D. H. Self-folding devices and materials for biomedical applications. Trends in Biotechnology, 30, 138-146(2012)
[10]	HOARE, T. R. and KOHANE, D. S. Hydrogels in drug delivery:progress and challenges. Polymer, 49, 1993-2007(2008)
[11]	IONOV, L. Biomimetic hydrogel-based actuating systems. Advanced Functional Materials, 23, 4555-4570(2013)
[12]	DONG, L., AGARWAL, A. K., BEEBE, D. J., and JIANG, H. Adaptive liquid microlenses activated by stimuli-responsive hydrogels. nature, 442, 551-554(2006)
[13]	MAJIDI, C. Soft robotics:a perspective-current trends and prospects for the future. Soft Robotics, 1, 5-11(2014)
[14]	SHOJAEIFARD, M., BAYAT, M. R., and BAGHANI, M. Swelling-induced finite bending of functionally graded pH-responsive hydrogels:a semi-analytical method. Applied Mathematics and Mechanics (English Edition), 40(5), 679-694(2019) https://doi.org/10.1007/s10483-019-2478-6
[15]	JI, H., MOURAD, H., FRIED, E., and DOLBOW, J. Kinetics of thermally induced swelling of hydrogels. International Journal of Solids and Structures, 43, 1878-1907(2006)
[16]	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)
[17]	KHAJEHSAEID, H., BAGHANI, M., and NAGHDABADI, R. Finite strain numerical analysis of elastomeric bushings under multi-axial loadings:a compressible visco-hyperelastic approach. International Journal of Mechanics and Materials in Design, 9, 385-399(2013)
[18]	BOYCE, P. H. and TRELOAR, L. R. G. The thermoelasticity of natural rubber in torsion. Polymer, 11, 21-30(1970)
[19]	ALLEN, G., PRICE, C., and YOSHIMURA, N. Thermomechanical studies on natural rubber in torsion and simple extension. Journal of the Chemical Society, Faraday Transactions 1:Physical Chemistry in Condensed Phases, 71, 548-557(1975)
[20]	RIVLIN, R. S. Large elastic deformations of isotropic materials, VI:further results in the theory of torsion, shear and flexure. Philosophical Transactions of the Royal Society of London Series A, Mathematical and Physical Sciences, 242, 173-195(1949)
[21]	RIVLIN, R. S. Large elastic deformations of isotropic materials, III:some simple problems in cyclindrical polar coordinates. Philosophical Transactions of the Royal Society of London Series A, Mathematical and Physical Sciences, 240, 509-525(1948)
[22]	HUMPHREY, J. D. Cardiovascular Solid Mechanics:Cells, Tissues, and Organs, Springer-Verlag, New York (2002)
[23]	HUMPHREY, J. D., BARAZOTTO JR, R. L., and HUNTER, W. C. Finite extension and torsion of papillary muscles:a theoretical framework. Journal of Biomechanics, 25, 541-547(1992)
[24]	SHOJAEIFARD, M., TAHMASIYAN, S., and BAGHANI, M. Swelling response of functionally graded temperature-sensitive hydrogel valves:analytic solution and finite element method. Journal of Intelligent Material Systems and Structures, 1045389X19891544(2019)
[25]	KANNER, L. M. and HORGAN, C. O. On extension and torsion of strain-stiffening rubber-like elastic circular cylinders. Journal of Elasticity, 93, 39-61(2008)
[26]	VALIOLLAHI, A., SHOJAEIFARD, M., and BAGHANI, M. Closed form solutions for large deformation of cylinders under combined extension-torsion. International Journal of Mechanical Sciences, 157, 336-347(2019)
[27]	GANDHI, M. V., USMAN, M., WINEMAN, A. S., and RAJAGOPAL, K. R. Combined extension and torsion of a swollen cylinder within the context of mixture theory. Acta Mechanica, 79, 81-95(1989)
[28]	MOLLICA, F., LAROBINA, D., and AMBROSIO, L. Combined extension and torsion of a swollen cylinder in unsteady conditions for the mechanical characterization of a hydrogel:an application of the continuum theory of mixtures. International Journal of Engineering Science, 57, 90-101(2012)
[29]	AFROZE, F., NIES, E., and BERGHMANS, H. Phase transitions in the system poly (Nisopropylacrylamide)/water and swelling behaviour of the corresponding networks. Journal of Molecular Structure, 554, 55-68(2000)
[30]	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)
[31]	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, 3282-3289(2009)