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Constitutive Modeling & Numerical Implementation of Shape Memory Polymers Based on Continuum Thermodynamics

Baghani, Mostafa | 2012

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 42924 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Naghdabadi, Reza; Sohrabpour, Saeed; Arghavani, Jamal
  7. Abstract:
  8. Shape memory polymers (SMPs) are a class of multi-phase smart materials that have the ability to return from a deformed to their original shape . The origin of SMP material features is a reversible glassy-rubbery phase transformation between a high stiffness glassy phase and a low stiffness rubbery phase . Thus , according to experimental observations , the phase transformation must be considered in the constitutive model development . In most applications , SMPs experience arbitrary thermo-mechanical loadings . Moreover , SMP structures typically undergo large rotations and strains and the use of a finite deformation scheme is preferred. In this thesis , we study the SMP behavior under general loadings at small and finite deformations besides presenting analytical solutions for some SMP structures . Considering storage/release phenomenon accompanied by finite deformations , we derive SMP constitutive models in small and large strain regimes and propose appropriate numerical formulations in an implicit finite element framework. With the aim of properly modeling of the storage/release phenomenon , based on continuum thermodynamics with internal variables, we present a time-independent SMP model in the small strain regime . We also show that the xperimentally observed temperature-shift in shape recovery results can be properly addressed via simultaneously performing heat-transfer analysis. We then extend the proposed model to the time-dependent regime. Using the proposed constitutive models , an analytical solution is presented for torsion of SMP tubes with circular cross section . The analytical solution is also applied to the analysis of SMP helical springs under axial loadings. To capture a more accurate response , curvature effects are also added to the formulation. It is shown that this modification affects the results significantly. It is observed that the solution-time for the analytical method is much less than the computational time in the FE simulations (about 1%). Consequently, the proposed analytical solution can be used as an efficient tool for studying the effects of changing any of the material or geometrical parameters on smart structures consisting of SMP springs for their design and optimization which requires a large number of simulations. Extending the Pandtl solution for modeling of SMP materials, we analytically study the torsion of SMP prismatic bars with rectangular cross-sections. To properly predict the time-dependent behavior of polymers in the rubbery phases, using logarithmic strain we propose a 3D viscoelastic constitutive model in the finite strain framework . Employing the logarithmic mapping, the numerical implementation of the model is also discussed in detail. We also extend the small strain model to the finite deformation regime. A multiplicative decomposition of the deformation gradient into elastic and inelastic stored parts is used within the framework of continuum thermodynamics. A main part of this thesis is devoted to numerical implementation of the proposed constitutive models . Implementing into a user defined subroutine (UMAT) in the software ABAQUS, we simulate several SMP applications, i.e. , SMP springs, tubes, 3D beams , medical stents. It is shown that , the proposed models are useful and appropriate computational tools for design , analysis and optimization of structures made of SMPs
  9. Keywords:
  10. Phase Transition ; Large Deformation ; Constitutive Modeling ; Numerical Integration ; Multiplicative Decomposition ; Shape Memory Polymers

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