Development of a finite strain two-network model for shape memory polymers using QR decomposition

Abstract

The aim of this paper is to develop a thermodynamically consistent finite deformation continuum model to simulate the thermomechanical response of shape memory polymers (SMPs). The SMP is modeled as a thermoviscoelastic material whose response in a thermomechanical cycle is modeled as a combination of a rubbery (viscoelastic) and a glassy (elastic) network in series. The activation criterion for the breakage of temporary network junctions is governed by a temperature dependent rate equation (akin to a thermal Bauschinger effect). We further show how the decomposition of the deformation gradient into an upper triangular matrix and a rotation (the QR) decomposition can be used instead of the more traditional polar (RU) decomposition in the development of models for such materials with persistent configurational changes. Such a decomposition has both physical meaning as well as computational advantages due to their convenient structure. Using these assumptions, we propose a specific form for the Helmholtz potential and the rate of dissipation. The model is simple (deliberately ignoring some aspects such as anisotropy that affect the quantitative but not the qualitative response features) and is able to capture the major phenomena of interest in SMPs. The efficacy of the resulting model, which is in a state evolution form, is demonstrated by comparing with published experimental data for simple shear. We study the response of the SMP model for monotonic shear deformation, different deformation rates as well as cyclic shear deformation at different temperatures. Comparisons with experiments show good agreement. Finally, we implement the thermomechanical cycle under shear deformations and study the behavior of the model.