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Thermo-Mechanical Behavior of Shape Memory Alloys Under Multiaxial Loadings: Constitutive Modeling and Numerical Implementation at Small and Finite Strains

Arghavani Hadi, Jamal | 2010

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 40885 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Naghdabadi, Reza; Sohrabpour, Saeed
  7. Abstract:
  8. Shape memory alloys (SMAs) are a type of smart materials which have unique features known as pseudo-elasticity, one-way and two-way shape memory eects. The interest in the mechanical behavior of SMAs is rapidly growing with the increasing number of potential industrial applications. The origin of SMA material features is a reversible thermo-elastic martensitic phase transformation between a high symmetry, austenitic phase and a low symmetry, martensitic phase. In most applications, SMAs experience general non-proportional thermo-mechanical loads. Thus, according to experimental observations, the so-called variant reorientation should be considered in the constitutive model development. Moreover, SMA structures typically undergo very large rotations and moderate strains (in the range of 10-15%) and the use of a nite deformation scheme is preferred. In this thesis, we have studied the SMA behavior under multiaxial loadings at small and nite deformations. Considering variant reorientation accompanied by nite deformations, we have derived several SMA constitutive models and have proposed a robust and ecient numerical formulation. With the aim of properly modeling of the variant reorientation, based on continuum thermodynamics with internal variables, we have presented a class of SMA models in the small strain regime. We have shown that several available models can be identied as members of the proposed class of models. With emphasis on non-proportional loading and reorientation, we specically have introduced a model which has the property of decoupling pure reorientation from pure phase transformation. In addition, we have shown that most available SMA models are basically the same under proportional loadings while they yield dierent results under non-proportional loading conditions. We have also proposed nite deformation SMA constitutive models, which are extensions of available small strain models. The approach is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts. The derived constitutive models are well-dened, singularity-free and fully-symmetric. In addition, we have proposed a model which utilizes interesting properties of the logarithmic strain. A main part of this thesis has been devoted to numerical implementation of the proposed constitutive models. To this end, we have proposed a logarithmic mapping, and dening a nucleation-completion condition, we have also proposed a robust and ecient integration algorithm. We have compared dierent models as well as integration algorithms in terms of robustness and computational eciency. Implementing into a user dened subroutine (UMAT) in the commercial software ABAQUS, we have simulated several SMA-based applications, i.e., an SMA spring, a nitinol stent and a smart micro-gripper. It has been shown that, comparing with the algorithms available in the literature, the proposed integration algorithm reduces the computational cost about 35%
  9. Keywords:
  10. Shape Memory Alloy ; Numerical Integration ; Large Deformation ; Multiplicative Decomposition ; Constitutive Modeling ; Superelasticity

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