TY - CHAP

T1 - A Semi-incremental Scheme for Cyclic Damage Computations

AU - Alameddin, Shadi

AU - Fau, Amélie

AU - Néron, David

AU - Ladevèze, Pierre

AU - Nackenhorst, Udo

N1 - Funding information: This research was funded by the German Research Foundation/Deutsche Forschungsgemeinschaft (DFG) through the International Research Training Group (IRTG) 1627.

PY - 2020/3/4

Y1 - 2020/3/4

N2 - 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 [1] 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.

AB - 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 [1] 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.

UR - http://www.scopus.com/inward/record.url?scp=85081558017&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-38156-1_12

DO - 10.1007/978-3-030-38156-1_12

M3 - Contribution to book/anthology

AN - SCOPUS:85081558017

SN - 978-3-030-38155-4

T3 - Lecture Notes in Applied and Computational Mechanics

SP - 229

EP - 247

BT - Lecture Notes in Applied and Computational Mechanics

CY - Cham

ER -