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Modeling of Cohesive Crack Propagation with Energy Method using XFEM

Asadi, Mansure | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48537 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Khoei, Amir Reza
  7. Abstract:
  8. Crack propagation in materials is an attractive problem in engineering because of the impact on the safety as well as economic issues. Much research studies have been done on the crack initiation, crack propagation criteria and path in the materials with different characteristics and conditions. Crack modeling depending on the material properties in brittle and quasi-brittle materials is done as Linear Elastic Fracture Mechanics (LEFM) and cohesive crack, respectively. The aim of this thesis is the modeling of crack propagation using energy method and comparing it with the cohesive crack. In order to model this problem, it is necessary to solve the governing equilibrium equation of the cracked body considering existing discontinuities. Energy can be earned and used in order to apply energy criterion, by calculating the displacement and stress field. Because of the complexity of the problem, its modeling requires the use of numerical methods. In this thesis, the eXtended Finite Element Method (XFEM), as an efficient numerical method, is used. In XFEM, unlike the limitations of classical finite element method, meshing of the body can be done independent of the position of the discontinuities. For this, there is no need to remesh and using fine mesh in crack tip. In this approach, by selecting appropriate enrichment functions analytically obtained and increasing the degrees of freedom at nodes which are affected by the discontinuity, the problem will be solved. Cohesive crack model is used for fracture modeling. In this model, the cohesive traction distribution is considered as a function of crack separation, and unlike the linear elastic fracture model, the stress in this region is not singular which is closer to reality. The base of energy method has been formed according to the principle that the total energy of system is minimum on stable condition. Using this method, the path of the crack propagation can be determined. The total energy consists of the internal energy, energy of external and body forces and also the surface energy of the crack. The crack will growth in a path that the total energy is minimized between all possible paths. In this case, the surface energy of the crack reaches at the maximum level. Finally, using this method, the direction of crack growth will be determined in various examples
  9. Keywords:
  10. Cohesive Crack ; Extended Finite Element Method ; Crack Growth ; Energy Method ; Energy Growth Criterion

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