Modeling of Incompressible Materials Using the Extended Finite Element Method (XFEM)<br/>

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Modeling of Incompressible Materials Using the Extended Finite Element Method (XFEM)

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 39585 (09)
University: Sharif University of Technology
Department: Civil Engineering
Advisor(s): Khoei, Amir Reza
Abstract:
In the limit case of incompressibility, the displacement-based finite element methods are not capable of finding the solutions with adequate accuracy. Moreover, discontinuities in displacement field or strain field which exist in the interior of the elements should be dealt with appropriately. The u/p mixed formulation provides a suitable context for modeling the incompressible problems. It is capable of solving general problems in which there exist geometrical or material nonlinearities. In the case of employing the eXtended Finite Element Method (XFEM), uniform meshes can be used for problems with discontinuities and in fact the discontinuities can be decoupled from the mesh. In this thesis, a combination of these two methods is implemented so that we can take advantage from both. Two major applications are simulation of rubber-like materials and metal forming processes. Here the first application is thoroughly discussed and also the necessary preliminaries for investigating on the second application are introduced.
Keywords:
Finite Strains ; Extended Finite Element Method ; Compressibility ; Hyperelasticity ; Mixed Formulation ; Stress Integration ; U/P Formulation

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