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Temperature-Dependent Hierarchical Multi-Scale Modeling of Nano-Materials Considering Surface Effect

Ghahremani, Pegah | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 41781 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Khoei, Amir Reza
  7. Abstract:
  8. In continuum mechanics, the constitutive models are usually based on the Cauchy-Born (CB) hypothesis which seeks the intrinsic characteristics of the material via the atomistic information and it is valid in small deformation. The main purpose of this thesis is to investigate the temperature effect on the stability and size dependency of Cauchy-Born hypothesis and a novel temperature-dependent multi-scale method is developed to investigate the role of temperature on surface effects in the analysis of nano-scale materials. Three-dimensional temperature-related Cauchy-Born formulation are developed for crystalline structure and the stability and size dependency of temperature-related Cauchy-Born hypothesis is investigated by means of direct comparison between atomistic and continuous mediums. Since the Helmholtz free energy is temperature dependent; the first Piola-Kirchhoff stresses are explicitly computed as the first derivative of the Helmholtz free energy density to the deformation gradient. It is numerically shown that the validity surfaces become smaller at higher temperature, which is significant in larger specimen. In multiclae model, the first Piola-Kirchhoff stress and tangential stiffness tensor are computed, as the first and second derivatives of the free energy density to the deformation gradient, which are transferred to the macro-scale level. The Lagrangian finite element formulation is incorporated into the heat transfer analysis to develop the thermo-mechanical finite element model, and an intrinsic function is employed to model the surface and temperature effects in macro-scale level. The stress and tangential stiffness tensors are derived at each quadrature point by interpolating the data from nearby representative atom. The Boundary Cauchy-Born (BCB) elements are introduced to capture the surface, edge and corner effects. Finally, the numerical simulation of proposed model together with the direct comparison with fully atomistic model illustrates that the technique provides promising results for facile modeling of boundary effect on thermo-mechanical behavior of metallic nano-scale devices
  9. Keywords:
  10. Computational Nanomechanics ; Molecular Dynamics ; Surface Effect ; Temperature Related Cauchy ; Temperature Related Hierarchial Multiscale Model

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