Numerical model reduction for FEanalysis of the viscoplasticity problem
Examensarbete för masterexamen
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|Type: ||Examensarbete för masterexamen|
|Title: ||Numerical model reduction for FEanalysis of the viscoplasticity problem|
|Authors: ||Hård, Daniel|
|Abstract: ||Some numerical problems require, despite modern computational power, a lot of
time to solve. The nonlinear viscoplasticity model is one such problem, where the
plasticity in a material depends on the rate at which the load is applied. A method
for reducing the system and decreasing the simulation time would therefore be an
This thesis aims to adopt one such method to reduce the computational cost for
the viscoplasticity problem and evaluate it for some test cases. A mixed weak form
together with the Finite Element Method (FEM) on monolithic form is established.
Thereby, displacements and viscoplastic strains are solved for simultaneously rather
than in the standard nested fashion. Proper Orthogonal Decomposition (POD) is
performed on snapshots of the viscoplastic strains from a set of finite element training
simulations carried out in an offline phase. The Nonuniform Transformation
Field Analysis (NTFA) approach expresses the displacements in a corresponding
reduced basis. The numerical computations have been implemented in Julia and
tested in 2D for varying load combinations.
It was shown that it was possible to reduce the solve time and still obtain good
approximations of the solution. However, there is a crucial dependency on the
training, with higher accuracy for targeted simulations similar to the training. Still,
the robustness of the procedure was illustrated by near monotonic error convergence.
Although more research would be needed, the results show promise for the
development of highly efficient approximations of the viscoplasticity problem.|
|Keywords: ||viscoplasticity;finite element method;numerical model reduction;proper orthogonal decomposition|
|Issue Date: ||2021|
|Publisher: ||Chalmers tekniska högskola / Institutionen för industri- och materialvetenskap|
|Collection:||Examensarbeten för masterexamen // Master Theses (IMS)|
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