- Journal Article
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 -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. Show more
Journal / seriesComputer Methods in Applied Mechanics and Engineering
Pages / Article No.
SubjectModel order reduction; Proper orthogonal decomposition; Discrete empirical interpolation method; Perzyna viscoplasticity; Strain-softening; Machine learning; k-means clustering algorithm
Organisational unit03973 - Haller, George / Haller, George
02618 - Institut für Mechanische Systeme / Institute of Mechanical Systems
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