COMPLAS 2023

Adaptive techniques for MOR of unitcells in non-linear FE simulations

  • Özmen, Yasemin (University of Duisburg-Essen)
  • Niekamp, Rainer (University of Duisburg-Essen)
  • Nigro, Paulo Salvador Britto (Akselos S.A.)
  • Schröder, Jörg (University of Duisburg-Essen)

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In recent years, model order reduction techniques have undergone substantial development and use in the field of mechanical simulations. Various techniques exist, which are also used in numerical simulations that incorporate non-linearities. For example, applying a Proper Orthogonal Decomposition (POD) technique to subdomains with approximate linear behavior is advised in [1]. Additionally, reduced order methods are applied in the context of multiscale finite element simulations. For instance, to regulate the decreasing dimension, local reduced bases for the dynamically updated microproblems in each Gauss point could be employed in conjunction with Hyper-Reduction (HR), as suggested in [2]. The work that is being presented illustrates an adaptive POD technique for small strain elasto-plastic material behavior. One of the main aspects in this work is choosing an appropriate reduced basis to capture the overall non-linearities of the problem’s response without the requirement for costly pre-computations. This is achieved by using an adap- tive selection technique, which provides the algorithm with the flexibility to adjust the reduced basis as necessary. Within this, the reduced basis is updated during the Newton Raphson scheme, in order to ensure convergence. Additionally, the relevance of the solu- tion vector in each load step is checked via a relative POD. This approach of performing a relative POD is also used for reducing the dimensions of the reduced basis, therefore dropping basis vectors which have lost relevance with respect to the basis. This gives an optimal choice of the projection vectors. It can be observed, that the computational cost of the simulation is decreased due to the loss of dimensionality while controlling the error of the result. Numerical simulations with illustrations from multiscale analysis are included in the presentation. REFERENCES [1] Robens-Radermacher A., Reese S. Model reduction in elastoplasticity: proper orthogonal decomposition combined with adaptive sub-structuring. Int. J. Comp. Mech., Vol. 54, pp. 677-687, 2014. [2] He W., Avery P., Farhat C. MIn situ adaptive reduction of nonlinear multiscale structural dynamics models. Int. J. Numer. Methods Eng., Vol. 121, pp. 4971-4988, 2022.