Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/153678
Title: APPLICATION OF DISCONTINUOUS GALERKIN METHODS IN HYPERELASTICITY PROBLEMS
Authors: GOH CHUN FAN
Keywords: discontinuous Galerkin
fluid structure interaction
hyperelasticity
conservation laws
Lagrangian
Neo-Hookean
hyperbolic system
constitutive equation
Issue Date: 2008
Citation: GOH CHUN FAN (2008). APPLICATION OF DISCONTINUOUS GALERKIN METHODS IN HYPERELASTICITY PROBLEMS. ScholarBank@NUS Repository.
Abstract: In fluid structure interaction (FSI) problems, the transfer of the information between the coupled system: fluid models and structure models is important. In exploring the application of discontinuous Galerkin (DG) methods in FSI problems, we want to set up the DG solver for the general structure model using the conservation laws formulation. By casting the structure model into a system of conservation laws, the fluid loading (including pressure and shear stress) can be transferred naturally from fluid models to the structure models as boundary conditions in the context of the DG methods. In this work, the general hyperelasticity model cast in a first order hyperbolic system using the conservation laws and constitutive equations in Lagrangian frame of reference has been developed. The hyperelastic model is used because it is for large and nonlinear deformation and it is the basis for more complex material models. Using the compressible Neo-Hookean material description, two test cases in 1-dimensional and 2-dimensional are successfully implemented using the DG method. For both cases, the numerical solutions for small deformation correlate well with the linear analytical solutions. The numerical solutions deviate from the linear solutions when the deformation is large. From the simulation, we conclude that hyperelastic material deforms linearly at small deformation, but non-linearly when the deformation is large. From the convergence analysis, the DG method applied in this nonlinear hyperbolic system shows a convergence rate of O(N + 1) for an order of accuracy N, which is the optimal convergence rate for the DG method.
URI: https://scholarbank.nus.edu.sg/handle/10635/153678
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