Research Papers

Simulation of the Transient Behavior of Gels Based on an Analogy Between Diffusion and Heat Transfer

[+] Author and Article Information
Hanqing Jiang

e-mail: hanqing.jiang@asu.edu
Mechanical Engineering,
School for Engineering of Matter,
Transport and Energy,
Arizona State University,
Tempe, AZ 85287

1Corresponding author.

Manuscript received July 24, 2012; final manuscript received September 30, 2012; accepted manuscript posted October 8, 2012; published online May 16, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(4), 041017 (May 16, 2013) (5 pages) Paper No: JAM-12-1347; doi: 10.1115/1.4007789 History: Received July 24, 2012; Revised September 30, 2012; Accepted October 08, 2012

The transient behaviors of the swelling and deswelling of gels involve concurrent mechanical deformation and solvent diffusion and exhibit a fascinating phenomenon. In this paper, a simple numerical tool is developed by using an analogy between diffusion and heat transfer when large deformation presents for gels. Using this analogy, a finite element method is developed in the framework of a commercial finite element package ABAQUS via two material-specific user subroutines to describe the mechanical and mass diffusion behaviors of gels. The present method is not limited to any specific materials; therefore, this method can be extended to other materials that featured with coupled deformation and diffusion. This method is expected to be able to serve as a useful numerical tool to study related materials and problems due to its simplicity.

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Fig. 1

(a) Schematic of a cubic gel swelling under no constraint. Three points A, B, and C are marked. (b) Normalized vertical displacements w/L of three characteristic points (A, B, and C) versus normalized time Dt/L2 for both scaling factors α = 1 and α = 100. The inset shows the max principal strain contour at Dt/L2 = 160.

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Fig. 2

(a) Schematic of a gel bar swelling in X3 direction. (b) Stretch in X3 direction λ3 as a function of X3 when Dt/L2 = 560 using both COMSOL and the present method.

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Fig. 3

(a) Schematic of gel indentation. (b) Evolution of indentation force F(t) with time t for two gels with different material parameters. The fitting curve based on F(t) = F(0)+ [F(∞)-F(0)][1-exp(-tτind)] is also given.

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Fig. 4

(a) Schematic of a swellable elastomer inside a pipe. (b) The contour plots of pipe pressure p(t) at different times. (c) Evolution of average pipe pressure p(t) with time t for different elastomers.




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