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A Gradient-Enhanced Computational Homogenization Technique for Multi-Scale Modeling of Heterogeneous Materials with Softening Behavior

Raisi, Alireza | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51177 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Khoei, Amir Reza
  7. Abstract:
  8. The use of conventional multi-scale models for materials that exhibit softening behavior is not possible due to the phenomenon of localization, because the fundamental assumptions of homogenization are no longer satisfying around the localization region, and therefore the macro-scale results depend on the size of the representative volume element and the macro-scale mesh discretization. Also, if the finite elements mesh be fine enough, the solution does not converge to acceptable physical values. This research concerns the multi-scale study of failure and proposes an appropriate method for computational homogenization of that. The main idea is to apply the enhanced homogenization method to the nonlocal theory of continuum mechanics, which makes the development of failure in microstructures more compatible with its actual behavior. Moreover, the concepts of the nonlocal continuum theory and its related mathematical model have been discussed in order to provide a more clear modeling base as a practical solution for regularization of the softening problems. Determining the intrinsic length of material, solving the problem of intense localization, providing an optimal computational formulation denote other issues discussed in this thesis. The examples solved in this study include two verification problems for the damage model and two verification problems for multi-scale modeling to verify the validity of implementation algorithms. Also, a homogenization problem has been investigated to compare the results of direct analysis of microstructures and first-order homogenization and enhanced homogenization. This example shows how the implementation of enhanced homogenization on non-local homogenization improves the computational results
  9. Keywords:
  10. Multiscale Modeling ; Damage ; Softening ; Representative Volume Element ; Nonlocal Continuum Theory ; Localization ; Enhanced Homogenization ; Internal Intrinsic Length

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