Title | A theory of amorphous viscoelastic solids undergoing finite deformations with application to hydrogels |
Publication Type | Journal Article |
Year of Publication | 2007 |
Authors | V Korchagin, J Dolbow, and D Stepp |
Journal | International Journal of Solids and Structures |
Volume | 44 |
Issue | 11-12 |
Start Page | 3973 |
Pagination | 3973 - 3997 |
Date Published | 06/2007 |
Abstract | 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. |
DOI | 10.1016/j.ijsolstr.2006.11.002 |
Short Title | International Journal of Solids and Structures |