Total Lagrangian Finite Element Formulation of the Flory-Rehner Free Energy Function

Authors

  • Mario J. Juha University of South Florida

Keywords:

Deformation gradient, incompressibility, network, solvent, gels

Abstract


The total Lagrangian finite element implementation of the Flory-Rehner free-energy function in the framework of a hyperelastic material model is addressed. It is explicitly given all the equations required to implement this material model in an implicit nonlinear finite element analysis, particularly, it is shown how to derive the so-called algorithmic or consistent linearized tangent moduli in the Lagrangian description. Some analytical and numerical results for different boundary-value problems are presented to validate the implementation.

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References

S. DuPont, R. Cates, P. Stroot, R. Toomey, “Swellinginduced instabilities in microscale, surface confined poly(n-isopropylacryamide) hydrogels”. Soft Matter. Vol. 6. 2010. pp. 3876-3882.

R. Jones, “Soft Condensed Matter”. Oxford Master Series in Condensed Matter Physics, 1a Ed., Oxford University Press. Oxford, UK. 2002. pp. 208.

T. Tanaka, D. Fillmore, “Kinetic of swelling of gels”. J. Chem. Phys. Vol. 70. 1979. pp. 1214-1218.

A. Onuki. “Theory of pattern formation in gels: Surface folding in highly compressible elastic bodies”. Physical Review A. Vol. 39. 1988. pp. 5932-5948.

A. Onuki. “Theory of phase transition in polymer gels”. Advances in Polymer Science. I. Vol. 109. 1993. pp. 63-121.

J. Dolbow, E. Fried, H. Ji. “Chemically induced swelling of hydrogels”. Journal of the Mechanics and Physics of Solids. Vol. 52. 2004. pp. 51-84.

J. Dolbow, E. Fried, H. Ji. “A numerical strategy for investigating the kinematic response of stimulusresponsive hydrogels”. Comput. Methods Appl. Engrg. Vol. 194. 2005. pp. 4447-4480.

W. Hong, X. Zhao, J. Zhou, Z. Suo. “A theory of coupled diffusion and large deformation in polymeric gels”. Journal of the Mechanics and Physics of Solids. Vol. 56. 2008. pp. 1779-1793.

W. Hong, Z. Liu, Z. Suo. “Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load”. Int.J.Solids Struct. Vol. 46. 2009. pp. 3282- 3289.

J. Zhang, X. Zhao, Z. Suo, H. Jiang. “A finite element method for transient analysis of concurrent large deformation and mass transport in gels”. Journal of Applied Physics. Vol. 105. 2009. pp. 093522.

M. Kang, R. Huang. “Swell induced surface instability of confined hydrogel layers on substrates”. Journal of the Mechanics and Physics of Solids. Vol. 58. 2010. pp. 1582-1598

M. Kang, R. Huang. “A variational approach and finite element implementation for swelling of polymeric hydrogels under geometric constraints”. J. Appl. Mech. 2010. pp. 1-12.

G. Holzapfel, “Nonlinear Solid Mechanics: A continuum approach for engineers”. John Wiley & Sons, USA, 1a Ed., 2001. pp. 455.

M. Gurtin, E. Fried, L. Anand. The Mechanics and Thermodynamics of Continua. 1sted.Ed. Cambridge University Press. USA. 2009. pp. 716.

T. Hughes. The Finite Element Method: Linear Static and Dynamic Finite element Analysis. 1sted. Dover, USA. 2000. pp. 672.

T. Belytschko, W. Liu, B. Moran. Nonlinear Finite Elements for Continua and Structures. 1sted. Wiley, USA. 2000. pp. 300.

O. Zienkiewicz, R. Taylor. The finite Element Method for Solid and Structural Mechanics. 6thed.Ed. Elsevier. 2005. pp. 736.

Published

2014-01-20

How to Cite

Juha, M. J. (2014). Total Lagrangian Finite Element Formulation of the Flory-Rehner Free Energy Function. Revista Facultad De Ingeniería Universidad De Antioquia, (69), 152–166. Retrieved from https://revistas.udea.edu.co/index.php/ingenieria/article/view/18146