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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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  • Abstract
  • Acknowledgments
  • List of Tables
  • List of Figures
  • Introduction to shape memory alloys
    • Smart materials
    • Shape memory Alloys
      • Shape memory effect
      • Pseudo-elasticity
      • SMA behavior under multiaxial loading
      • Classification of SMA behaviors
    • Applications
      • Couplings and Fasteners
      • Actuators
      • Adaptive materials and hybrid composites
      • Biomedical applications
      • Other applications
  • Literature review and research outline
    • Constitutive modeling approaches
    • Phenomenological SMA models
      • Models without internal variables
      • Models with internal variables
    • Literature review: models based on the continuum thermodynamics with internal variables
      • SMA modeling activities between 1980–1995
      • SMA modeling activities after 1995
      • Experimental studies on mechanical behavior of SMAs
    • Outline of the research
  • Preliminaries from nonlinear solid mechanics
    • Introduction
    • Kinematics
    • Balance equations
    • Constitutive equations
    • Weak form of equilibrium.
      • Weak form of linear momentum in the initial configuration
      • Weak form of linear momentum in the current configuration
    • Linearizations
      • Linearization of kinematical quantities
      • Linearization of constitutive equations
      • Linearization of weak form
    • Finite element formulation
  • Constitutive modeling: small deformation regime
    • Introduction
    • Some models available in the literature
      • Model proposed by Souza98
      • Model proposed by Panico2007
      • A basic model extracted from Panico-Brinson model
      • A modified Panico-Brinson model
      • Model proposed by Lagoudas2008
    • Proposing a class of SMA constitutive models
      • Constitutive model development
      • Identification and comparison of some models in terms of formulation
    • Comparison of models in terms of numerical results
      • Uniaxial tests
      • Multiaxial proportional tests
      • Multiaxial non-proportional tests
    • Summary
  • Constitutive modeling: finite deformation regime
    • Introduction
    • Literature review: finite strain SMA constitutive models
    • Kinematics description
    • Finite strain extension of Panico and Brinson model
      • Representation with respect to the reference configuration
      • Linearization of the finite deformation SMA model
    • Finite strain extension of Souza model
      • Representation with respect to the reference configuration.
      • A singularity-free, continuous definition of the model
    • An approach to fully symmetrize constitutive models
    • A kinematic hardening model based on Hencky strain
      • Motivation
      • Constitutive model development
      • Representation with respect to the reference configuration
      • Proposing a Hencky-based SMA constitutive model
    • Extension into large rotation, small strain regime
      • Introduction
      • Kinematics description
      • Extension of Souza model to large rotation regime: Lagrangian formulation
      • Extension of Souza model to large rotation regime: Eulerian formulation
    • Summary
  • Numerical implementation: time-discretization and solution algorithms
    • Introduction
    • Numerical implementation of GLUS model
      • Time integration.
      • Solution algorithm.
      • Considerations on nucleation-completion condition.
      • Consistent tangent matrix.
    • Numerical implementation of GLSY model
    • Numerical implementation of HSGF model
      • Time integration.
    • Numerical implementation of HSSY model
      • Solution algorithm.
      • Considerations on nucleation-completion condition.
      • Consistent tangent matrix.
    • Numerical implementation of SSSR model
      • Consistent tangent matrix.
    • Numerical implementation of SSLR model
      • Method 1: Time-discretization based on Lagrangian formulation
      • Method 2: Time-discretization based on Eulerian formulation
    • Summary
  • Numerical examples and simulation of SMA-based applications
    • Introduction
    • Robustness study of different integration algorithms for GLUS model
      • Numerical examples: Gauss point level investigations
      • Numerical examples: Boundary value problems
      • Investigation of computational efficiency
    • Comparison of GLUS and GLSY models in terms of computational efficiency
    • Simulation of some BVPs using HSSY formulation
      • Uniaxial test
      • Pseudo-elastic stent
      • Spring actuator
    • Comparison of SSSR, SSLR and GLUS models
      • Simple tension test
      • Bending of a straight beam
      • Out-of-plane bending of a curved beam
    • Simulation of SMA-based devices: an SMA micro-gripper
    • Summary
  • Summary and conclusions
    • Summary
    • Conclusions
    • Future research directions
  • References
  • Appendices
  • Model derivation considering bold0mu mumu CCanchorcolorCCCC as control variable
  • Details of derivations for Hencky-based model
  • Linearization of the asymmetric finite strain Souza model
  • Publications
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