A Semi-incremental Scheme for Cyclic Damage Computations
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High fidelity structural problems that involve nonlinear material behaviour, when subjected to cyclic loading, usually demand infeasible computational resources; this demonstrates the need for efficient model order reduction (MOR) techniques in order to shrink these demands to fit into the available means. The solution of cyclic damage problems in a model order reduction framework is investigated in this chapter. A semi-incremental framework based on a large time increment (LATIN) approach is proposed to tackle cyclic damage computations under variable amplitude and frequency loadings. The involved MOR approach provides a low-rank approximation in terms of proper generalised decomposition (PGD) of the solution. The generated PGD basis can be interpreted as a set of linear subspaces altered on the fly to the current problem settings. The adaptation of PGD to new settings is based on a greedy algorithm that may lead to a large-sized reduced order basis (ROB). Thus, different orthonormalisation and compression techniques were evaluated to ensure the optimality of the generated ROB in  and will be overviewed here. The proposed implementation and a displacement formulated finite element (FE) incremental framework are compared to illustrate their differences in terms of memory footprint and computational time. Numerical examples with variable loadings are discussed, and a typical implementation is provided as open-source code, available at https://gitlab.com/shadialameddin/romfem.
This research was funded by the German Research Foundation/Deutsche Forschungsgemeinschaft (DFG) through the International Research Training Group (IRTG) 1627.
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