@article{banks_hood_medhin_2008, title={A molecular based model for polymer viscoelasticity: Intra- and inter-molecular variability}, volume={32}, ISSN={["1872-8480"]}, DOI={10.1016/j.apm.2007.09.018}, abstractNote={We develop dynamic equations for rubber viscoelasticity based on a stick-slip continuum molecular-based model. The model developed is a continuum tube reptation model in which a chemically cross-linked (CC) system of molecules act as constraint box per unit volume for a physically constrained (PC) system of molecules. The CC-system carries along the PC-system during instantaneous step deformations. The subsequent relaxation of the PC-system is determined by the configuration of the CC-system, its own configuration and confirmation, and external force fields. Conversely, the deformation of the PC-system acts as an internal variable affecting the deformations of the constraining CC-system. We model the relationship between these processes to derive a model of viscoelasticity in rubber deformation. In developing a relaxation process for the PC-system, we start from the fact that the PC-system is composed of long molecular chains. The dynamics of these molecular chains are developed by modelling them as chains of beads connected by springs, which represent inter-molecular potentials. Various segments of the molecular chains relax at different rates. In addition, variability in relaxation times across molecular chains is permitted.}, number={12}, journal={APPLIED MATHEMATICAL MODELLING}, author={Banks, H. T. and Hood, J. B. and Medhin, N. G.}, year={2008}, month={Dec}, pages={2753–2767} }
 @article{banks_hood_medhin_samuels_2008, title={A stick-slip/Rouse hybrid model for viscoelasticity in polymers}, volume={9}, ISSN={["1468-1218"]}, DOI={10.1016/j.nonrwa.2007.06.015}, abstractNote={A Rouse model for polymer chains is incorporated into the linear continuous stick-slip molecular-based tube reptation ideas of Doi–Edwards and Johnson–Stacer. This treats the physically constrained (PC) molecular stretches as internal strain variables for the overall PC/chemically cross-linked (CC) system. It yields an explicit system of stress–strain equations for the system permitting simple calculations of complex stress–strain relations. The model that is developed here treats PC molecule as entrapped within a constraining tube, which is comprised of both CC and PC molecules. The model is compared with experimental data sets from the literature.}, number={5}, journal={NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS}, author={Banks, H. T. and Hood, J. B. and Medhin, N. G. and Samuels, J. S., Jr.}, year={2008}, month={Dec}, pages={2128–2149} }