A theory of amorphous viscoelastic solids undergoing finite deformations with application to hydrogels

We consider a hydrogel in the framework of a continuum theory for the viscoelastic deformation of amorphous solids developed by Anand and Gurtin [Anand, L., Gurtin, M., 2003. A theory of amorphous solids undergoing large deformations, with application to polymeric glasses. International Journal of Solids and Structures, 40, 1465-1487.] and based on (i) a system of microforces consistent with a microforce balance, (ii) a mechanical version of the second law of thermodynamics and (iii) a constitutive theory that allows the free energy to depend on inelastic strain and the microstress to depend on inelastic strain rate. We adopt a particular (neo-Hookean) form for the free energy and restrict kinematics to one dimension, yielding a classical problem of expansion of a thick-walled cylinder. Considering both Dirichlet and Neumann boundary conditions, we arrive at stress relaxation and creep problems, respectively, which we consider, in turn, locally, at a point, and globally, over the interval. We implement the resulting equations in a finite element code, show analytical and/or numerical solutions to some representative problems, and obtain viscoelastic response, in qualitative agreement with experiment. © 2006 Elsevier Ltd. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Korchagin, V; Dolbow, J; Stepp, D

Published Date

  • 2007

Published In

Volume / Issue

  • 44 / 11-12

Start / End Page

  • 3973 - 3997

International Standard Serial Number (ISSN)

  • 0020-7683

Digital Object Identifier (DOI)

  • 10.1016/j.ijsolstr.2006.11.002

Citation Source

  • SciVal