A finite deformation constitutive model for shape memory polymers based on Hencky strain |
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| Affiliation: | 1. School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran;2. Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran;3. Institute for Nano-Science and Technology, Sharif University of Technology, Tehran, Iran;1. South China University of Technology, Guangzhou 510640, China;2. China Building Material Test and Certification Center, Beijing 100024, China;3. PPG Industries, Inc., Glass Business and Discovery Center, Pittsburgh 15024, USA;1. School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran;2. Mechanical Engineering Department, Sharif University of Technology, Tehran, Iran;3. Institute for Nano Science and Technology, Sharif University of Technology, Tehran, Iran;1. Université Lille 1 Sciences et Technologies, Laboratoire de Mécanique de Lille (LML), UMR CNRS 8107, F-59650 Villeneuve d’Ascq, France;2. Mechanical Engineering Program, Texas A&M University at Qatar, Doha, Qatar;3. Pôle de neurochirurgie, Hôpital Universitaire de Lille, rue Emile-Laine, F-59037 Lille, France |
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| Abstract: | In many engineering applications, shape memory polymers (SMPs) usually undergo arbitrary thermomechanical loadings at finite deformation. Thus, development of 3D constitutive models for SMPs within the finite deformation regime has attracted a great deal of interest. In this paper, based on the classical framework of thermodynamics of irreversible processes, employing the logarithmic (or Hencky) strain as a more physical measure of strain, a 3D large-strain macromechanical model is presented. In the constitutive model development, we adopt a multiplicative decomposition of the deformation gradient into elastic and stored parts. In addition, employing the averaging scheme, the logarithmic elastic strain tensor is decomposed into the rubbery and glassy parts. The evolution equations for internal variables are introduced for both cooling and heating processes. The time-discrete form of the proposed model in the implicit form is also presented. Comparing the predicted results with experimental data reported in the literature, the model is validated. Finally, using the finite element method, two boundary value problems e.g., a 3D beam and a medical stent made of SMPs are numerically simulated. |
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| Keywords: | Shape memory polymer Finite deformation Hencky strain tensor Continuum thermodynamics Finite element |
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