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Finite Element Simulation of Shape Memory Based Structures Using Beam Elements

Poorasadion, Saeed | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 43596 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Sohrabpour, Saeed; Arghavani Hadi, Jamal
  7. Abstract:
  8. Having unique characteristic behaviors of Shape memory alloys (SMAs) known as shape memory effect (SME), and superelasticity (SE), make them an appropriate choice for innovative engineering applications. Optimum design of SMA applications, calls for constitutive models and finite element simulations. It is evident that using structural elements (bar, beam, plate, shell) considerably reduces computational cost (CPU time) when compared to continuum elements. Therefore, structural elements are usually preferred in the early stages of design process. In this thesis, we simulate shape memory based structures using beam elements.Up to now, we have studied phenomenological constitutive models that have the characteristics of simplicity and low number of material parameters which make them appropriate candidate for beam element formulation. The well-known SMA models, we have chosen a model proposed by Brinson (BM) because this model is simple formulation, good agreement with experimental data and capability to predict primary effects (superelasticity and shape memory effect). But, the Brinson model is unable to capture secondary effects such as hysteresis loops, asymmetric behavior in tension and compression and reorientation effect. In the present study, we have improved the Brinson model to predict secondary effects while these improvements have been kept the simplicity of the BM. Because the phenomenological models, especially the Brinson model, are inherently 1D dimensional model, we have used a microplane theory to define 3D beam element. In this approach, a 1D constitutive law for one stress component and the associated strain component on each microplane is sufficient to generate a macroscopic 3D model. Thus, we have presented a 3D microplane constitutive model based on the modified Brinson model. Using these proposed models, we then implement the proposed model in a user-defined subroutine (UMAT) in the nonlinear finite element software ABAQUS/Standard to simulate SMA devices based on 2D and 3D Euler-Bernoulli beam elements. To evaluate the 1D and 3D proposed models and the proposed beam elements of SMAs, we have simulated several standard examples and have compared with experimental data and exiting models in literature. The results show that the predictions of proposed model have good agreement with the experimental data and the proposed model is also able to predict accurately SMA behaviors. We have finally simulated a SMA staple used in idiopathic scoliosis treatment.
  9. Keywords:
  10. Shape Memory Alloy ; Constitutive Model ; Microplane Model ; Finite Element Simulation ; Brinson Model ; Beam Element

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