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

TitleA theory of amorphous viscoelastic solids undergoing finite deformations with application to hydrogels
Publication TypeJournal Article
Year of Publication2007
AuthorsV Korchagin, J Dolbow, and D Stepp
JournalInternational Journal of Solids and Structures
Volume44
Issue11-12
Start Page3973
Pagination3973 - 3997
Date Published06/2007
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.

DOI10.1016/j.ijsolstr.2006.11.002
Short TitleInternational Journal of Solids and Structures