A Thermoviscoelastic Approach for Modeling Shape Memory Polymers
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A Thermoviscoelastic Approach for Modeling Shape Memory Polymers Thao D. Nguyen Department of Mechanical Engineering, The Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218. ABSTRACT This paper presents a thermoviscoelastic model for shape memory polymers (SMPs). The model has been developed based on the hypothesis that structural and stress relaxation are the primary shape memory mechanisms of crosslinked glassy SMP, and that consideration of these mechanisms is essential for predicting the time-dependence of the shape memory response. Comparisons with experiments show that the model can reproduce the rate-dependent straintemperature and stress-strain response of a crosslinked glassy SMP. The model also captures many important features of the temperature and time dependence of the free strain recovery and constrained stress recovery response. INTRODUCTION Thermally activated shape memory polymers are active materials that respond to a specific temperature range by changing shape [1]. The permanent shape of a crosslinked, glassy SMP device is manufactured using conventional processes for thermoset polymers, while the temporary shape can be programmed using a thermomechanical cycle as described in [1]. The majority of constitutive models for SMPs treat the shape memory mechanism as a phase transition mechanism (e.g., [2-4]). These models depict the SMP as a mixture of glassy and rubbery phases. The volume fractions of the phases evolve with temperature to produce shape storage and recovery. In this work, we hypothesize that structural and stress relaxation are the primary shape memory mechanisms of crosslinked glassy SMPs. Structural relaxation refers to the time-dependent process in which the macromolecular structure and structure-dependent properties (e.g., the viscosity) evolve to equilibrium in response to a temperature and/or pressure change. Similarly, stress relaxation describes the time-dependent process in which the stress response evolves to equilibrium in response to a change in the deformation state. To examine the relative importance of the structural and stress relaxation mechanisms, we have developed a constitutive model that exhibits structural relaxation in the glass transition region, viscoelasticity in the rubbery and transition regions, and viscoplasticity in the glassy region. A detailed development of the model and discussion of the results below can be found in [5]. MODEL FORMULATION Let Ω0 denote the equilibrium configuration of an undeformed continuum body at time t0 and temperature T0, and F denote the deformation gradient that maps Ω0 to the heated/cooled deformed configuration Ω. It is assumed that the deformation gradient can be split multiplicatively into thermal and mechanical components, F = FMFT, where FT = ΘT1/31 and ΘT is the thermal dilatation. The mechanical deformation gradient is split further into elastic and viscous parts, FM = FeMFvM. We also assume that the mechanical deformation gradient and its components can be split multiplicatively into dev
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