A hydrogel consists of a cross-linked polymer network and solvent molecules. Depending on its chemical and mechanical environment, the polymer network may undergo enormous volume change. The present work develops a general formulation based on a variational approach, which leads to a set of governing equations coupling mechanical and chemical equilibrium conditions along with proper boundary conditions. A specific material model is employed in a finite element implementation, for which the nonlinear constitutive behavior is derived from a free energy function, with explicit formula for the true stress and tangent modulus at the current state of deformation and chemical potential. Such implementation enables numerical simulations of hydrogels swelling under various constraints. Several examples are presented, with both homogeneous and inhomogeneous swelling deformation. In particular, the effect of geometric constraint is emphasized for the inhomogeneous swelling of surface-attached hydrogel lines of rectangular cross sections, which depends on the width-to-height aspect ratio of the line. The present numerical simulations show that, beyond a critical aspect ratio, creaselike surface instability occurs upon swelling.
Skip Nav Destination
e-mail: ruihuang@mail.utexas.edu
Article navigation
November 2010
Research Papers
A Variational Approach and Finite Element Implementation for Swelling of Polymeric Hydrogels Under Geometric Constraints
Min Kyoo Kang,
Min Kyoo Kang
Department of Aerospace Engineering and Engineering Mechanics,
University of Texas
, Austin, TX 78712
Search for other works by this author on:
Rui Huang
Rui Huang
Department of Aerospace Engineering and Engineering Mechanics,
e-mail: ruihuang@mail.utexas.edu
University of Texas
, Austin, TX 78712
Search for other works by this author on:
Min Kyoo Kang
Department of Aerospace Engineering and Engineering Mechanics,
University of Texas
, Austin, TX 78712
Rui Huang
Department of Aerospace Engineering and Engineering Mechanics,
University of Texas
, Austin, TX 78712e-mail: ruihuang@mail.utexas.edu
J. Appl. Mech. Nov 2010, 77(6): 061004 (12 pages)
Published Online: August 17, 2010
Article history
Received:
August 6, 2009
Revised:
February 7, 2010
Posted:
May 5, 2010
Published:
August 17, 2010
Online:
August 17, 2010
Citation
Kang, M. K., and Huang, R. (August 17, 2010). "A Variational Approach and Finite Element Implementation for Swelling of Polymeric Hydrogels Under Geometric Constraints." ASME. J. Appl. Mech. November 2010; 77(6): 061004. https://doi.org/10.1115/1.4001715
Download citation file:
Get Email Alerts
Related Articles
A Large Strain Material Model for Soft Tissues With Functionally Graded Properties
J Biomech Eng (July,2010)
Effect of Solvent Diffusion on Crack-Tip Fields and Driving Force for Fracture of Hydrogels
J. Appl. Mech (August,2015)
Poro-Viscoelastic Behavior of Gelatin Hydrogels Under Compression-Implications for Bioelasticity Imaging
J Biomech Eng (August,2009)
Related Proceedings Papers
Related Chapters
Static Deformations Budget
Mechanics of Accuracy in Engineering Design of Machines and Robots Volume II: Stiffness and Metrology
Data Tabulations
Structural Shear Joints: Analyses, Properties and Design for Repeat Loading
Subsection NB—Class 1 Components
Companion Guide to the ASME Boiler and Pressure Vessel Code, Volume 1, Third Edition