Model reduction in elastoplasticity: proper orthogonal decomposition combined with adaptive sub-structuring

Model reduction techniques such as the proper orthogonal decomposition (POD) method can be used to reduce the computational effort of simulations with a very large number of degrees-of-freedom. The reduction of finite element models including elastoplastic material behavior is still far from being trivial and inevitably leads to problems of efficiency and accuracy. One aim of the present paper is to combine the two methods-sub-structuring and POD-based model reduction-to overcome these difficulties. A typical field of application where plasticity dominates the material behavior are forming processes. The second aim of the paper is to investigate the applicability of the new approach in this context. The presented combined approach selective POD (SPOD) where the reduction is only applied in sub-domains with approximately elastic behavior shows higher accuracy than the general POD method. In this paper, the SPOD method is extended by an adaptive method of sub-structuring (A-SPOD) in which the sub-domain where model reduction is applied is determined automatically. While achieving errors of the same magnitude as by means of SPOD, the computational effort can be reduced significantly by using the A-SPOD approach.