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Nonlocal Nanoscale Modeling of Shape Memory Alloys Behavior Using Finite Element Method

Soveity, Salem | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48140 (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 smart materials with the ability to recover their original shape. Growing the industrial and laboratory applications of SMAs, the study of their mechanical behavior is extremely important. Recently, the shape memory alloys have been investigated by empirical and experimental methods. The results show that these materials also in nano scale keep up their particular properties to a critical size. Because of the size dependence of the material properties at the nano scale, the constitutive models based on classical continuum mechanics cannot describe phenomena observed in the nano scale. For a successful application of SMAs at nano scale, nonlocal theory can be used, which have the ability to model the material behavior at nano scale. In this study, based on the gradient elasto-plasticity theory, a constitutive equation was presented using the nonlocal theory. Governing equations were presented and the discretized equations were solved using the finite element method. The tangential stiffness matrices were derived based on the nonlocal theory. The finite element approach was implemented by programing codes in MATLAB software. Solving the one-dimensional equations the results were compared with the experimental data, which showed that the presented constitutive equation can well predict the stress-strain response and the distribution of martensite transformation strain in the SMA nano-grain. Several problems were investigated with two-dimensional geometry, it was observed that if the effect of gradient is severe, the length scale effect is significant. The results of the nonlocal modeling were compared to the results obtained by local modeling, where the difference between them was up to 15%. In addition, the results of the nonlocal modeling were in good agreement with the experimental data, which shows the ability of the proposed constitutive model in predicting the behavior of shape memory alloys at the nano scale
  9. Keywords:
  10. Finite Element Method ; Nonlocal Theory ; Constitutive Equations ; Shape Memory Alloy ; Nano-Scale Modeling

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