POD-DEIM model order reduction for strain softening viscoplasticity

POD-DEIM model order reduction for strain softening viscoplasticity

Ghavamian, F. (TU Delft Applied Mechanics)
Tiso, P. (ETH Zürich)
Simone, A. (TU Delft Applied Mechanics)

2017

We demonstrate a Model Order Reduction technique for a system of nonlinear equations arising from the Finite Element Method (FEM) discretization of the three-dimensional quasistatic equilibrium equation equipped with a Perzyna viscoplasticity constitutive model. The procedure employs the Proper Orthogonal Decomposition-Galerkin (POD-G) in conjunction with the Discrete Empirical Interpolation Method (DEIM). For this purpose, we collect samples from a standard full order FEM analysis in the offline phase and cluster them using a novel kk-means clustering algorithm. The POD and the DEIM algorithms are then employed to construct a corresponding reduced order model. In the online phase, a sample from the current state of the system is passed, at each time step, to a nearest neighbor classifier in which the cluster that best describes it is identified. The force vector and its derivative with respect to the displacement vector are approximated using DEIM, and the system of nonlinear equations is projected onto a lower dimensional subspace using the POD-G. The constructed reduced order model is applied to two typical solid mechanics problems showing strain-localization (a tensile bar and a wall under compression) and a three-dimensional square-footing problem.

Model order reduction
Proper orthogonal decomposition
Discrete empirical interpolation method
Perzyna viscoplasticity
Strain-softening
Machine learning
k-means clustering algorithm

http://resolver.tudelft.nl/uuid:b0a01fa0-2226-4e91-ab23-3cddc78c2c4b

0045-7825

Computer Methods in Applied Mechanics and Engineering, 317, 458-479

Institutional Repository

journal article

© 2017 F. Ghavamian, P. Tiso, A. Simone