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Multiscale Modeling of Cohesive Crack and Bulk for Softening Materials

Saadat, Mohammad Ali | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 50390 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Khoei, Amir Reza
  7. Abstract:
  8. Multiscale modeling is performed within the framework of homogenization methods for problems in which the scales are separated. The existence of representative volume element (RVE) is one of the main ingredients of homogenization methods. Due to non-existence of RVE and macroscale mesh sensitivity, the continuous homogenization method is not applicable for softening materials. Despite the non-existence of RVE for softening materials, it has been demonstrated that by performing the average over the active damage zone rather than the entire domain, objective responses with respect to RVE size could be obtained. That is why discontinuous homogenization is used instead of continuous homogenization for softening materials, in which the homogenization is performed only for crack segments and the macroscopic cohesive law is obtained from the microscopic sample that exhibits diffusive damage. In the present thesis, RVE size dependency and macro scale mesh sensitivity of continuous homogenization method are circumvented by introducing macroscopic length scale parameter. In order to capture nonlocality at both scales, two RVEs are introduced for every macro scale’s gauss point; one to compute the tangent moduli and one to compute the macroscopic stress. Moreover, nonlocal strain is scaled down instead of nonlocal equivalent strain. The proposed method is verified by comparing the results against the results obtained with the direct numerical simulation (DNS)
  9. Keywords:
  10. Multiscale Method ; Representative Volume Element ; Direct Numerical Simulation (DNS) ; Homogenization ; Softening Material ; Macroscopic Length Scale Parameter

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