Space–time model order reduction for nonlinear viscoelastic systems subjected to long-term loading
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The solution of nonlinear structural problems by means of a space–time model order reduction approach is investigated. The main target is the prediction of the long-term response while reducing both the computation time and the storage requirements considerably. A nonstandard discretization approach is used which treats the internal degrees of freedom as additional unknowns. The resulting nonlinear problem is formulated in a variational setting. The proposed reduced basis represents the behavior of the structure in a complete time interval, e.g. during one load cycle (for cyclic processes). The reduced variables are obtained by a projection of the time-local stationary conditions onto appropriate test functions defined in space–time. This leads to a low-dimensional nonlinear system of equations. Details regarding the theoretical derivation, the discretization and the numerical treatment of the nonlinearity are presented. In the numerical examples the reduced model is compared to FEM reference solutions. Different choices for the test functions are discussed and the postprocessing abilities offered by the reduced model are illustrated.
KeywordsModel order reduction Space–time compression Nonlinear viscoelasticity Cyclic processes
This work was effected by the Emmy-Noether-Group EMMA supported through Grant DFG-FR2702/6 within the Emmy-Noether program of the Deutsche Forschungsgemeinschaft (DFG). The authors gratefully acknowledge the financial and personal support of the DFG. The authors acknowledge the input of the anonymous reviewers that helped in the completion of the manuscript.
This study was funded by Deutsche Forschungsgemeinschaft (DFG) (Grant DFG-FR2702/6)
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Conflict of interest
The authors declare that they have no conflict of interest.
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