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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 39619 (08)
- University: Sharif University of Technology
- Department: Mechanical Engineering
- Advisor(s): Zohoor, Hassan; Sohrabpoor, Saeeid
- Abstract:
- Two methods for simulating material behavior of heart mitral valve leaflet tissue are developed in this thesis, in the finite element setting. First, a mixed pressure-displacement formulation is used to implement the constitutive material behavior with general 3D elements. Second, a shell is formulated that incorporates the 3D material behavior by use of a local plane stress iteration method. Both of these works are based on an existing invariant-based strain energy function that has been experimentally determined for the mitral valve leaflet tissue. Since this material is considered to be nearly incompressible, a mixed pressure-displacement (u/p) formulation is needed to apply the material model in 3D elements. The standard (u/p) formulation is employed with a modification to ensure positive definiteness of the constitutive tensor at low strains. The shell formulation is introduced as a computationally less expensive alternative to the use of 3D elements. A 4-node shell element with mixed interpolation of transverse shears is implemented. To incorporate the 3D material model into this shell, a local plane stress iteration is used to enforce the shell stress assumption at each integration point. Comparisons of numerical results to analytical predictions verify the accuracy of both the (u/p) formulation and the shell formulation
- Keywords:
- Finite Element Method ; Strain Energy Function ; Soft Tissues ; Shell Element Method
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