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Development of consistent Thermomechanical ALE Formulation with Application to Simulation of Machining

Tadi Beni, Yaghob | 2009

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 39778 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Movahhedy, Mohammd Reza; Farrahi, Hossein
  7. Abstract:
  8. Accurate description of kinematics of continuum mechanics is essential in simulation of large deformation problems in solid mechanics. From the numerical viewpoint, two main approaches have been used for such description; the Lagrangian approach and the Eulerian approach. However, each of these approaches suffer from shortcomings which hinders their application in large deformation problems. A more general approach called the Arbitrary Lagrangian-Eulerian method (ALE) provides an opportunity to exploit the advantages of both Lagrangian and Eulerian approach, while avoiding their shortcoming. In an ALE analysis, the FE mesh is neither attached to the material nor fixed in space, necessarily. Rather, the mesh can in general have a motion independent of the material. In this way, the Eulerian or Lagrangian approaches can be considered as special cases of ALE. In this research, systematic derivation of the fully coupled thermomechanical ALE formulation is presented. Starting from the principle of virtual work and the law of conservation of energy, the implicit ALE equation of motion and thermal equation are derived and descretized into the finite element equations of motion and energy balance. The ALE formulation is fully coupled, i.e. the mesh and material motions occur simultaneously, as opposed to operator split approaches. Full expression of the resulting finite element matrices and vectors are given. This general ALE formulations is capable of handling large deformation thermomechanical problems involving dynamic, strain rate and thermal effects. For solving the Numerical algorithms for time dependent solution, viscous effects, mesh motion, and contact and friction are presented. The developed formulation is employed to solve several benchmark problems variably involving large deformation, dynamic, strain rate and thermal effects. The results of these simulations are compared with existing numerical and experimental results in the literature, which demonstrates good agreement between these results. Finally, the orthogonal metal cutting problem is simulated as a challenging problem involving various nonlinear effects in the small area at the root of chip is solved and its results are shown to be in agreement with existing experimental results.

  9. Keywords:
  10. Finite Element Method ; Large Deformation ; Viscoplasticity ; Arbitrary Lagrangian-Eulerian Method ; Thermal Effect ; Thermomechanical Processing

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