Explicit asynchronous time scheme with local push-forward stepping for discontinuous elastic wave propagation: One-dimensional heterogeneous cases and Hopkinson bar experiment

0573529 - ÚT 2024 RIV NL eng J - Journal Article
Dvořák, Radim - Kolman, Radek - Fíla, T. - Falta, J. - Park, K.C.
Explicit asynchronous time scheme with local push-forward stepping for discontinuous elastic wave propagation: One-dimensional heterogeneous cases and Hopkinson bar experiment.
Wave Motion. Roč. 121, August (2023), č. článku 103169. ISSN 0165-2125. E-ISSN 1878-433X
R&D Projects: GA ČR(CZ) GF22-00863K
Grant - others:AV ČR(CZ) EstAV-21-02
Program: Bilaterální spolupráce
Institutional support: RVO:61388998
Keywords : elastic wave propagation * finite element method * localized Lagrange multipliers method * local pushforward-pullback method * asynchronous integration * Split Hopkinson pressure bar
OECD category: Applied mechanics
Impact factor: 2.4, year: 2022
Method of publishing: Limited access
https://www.sciencedirect.com/science/article/pii/S0165212523000550?via%3Dihub

This is a presentation of robust and accurate explicit time-stepping strategy for finite element modeling of elastic discontinuous wave propagation in strongly heterogeneous, multi-material and graded one-dimensional media. One of the major issues in FEM modeling is the existence of spurious numerical stress oscillations close to theoretical wave fronts due to temporal-spatial dispersion behavior of FE discretization. The numerical strategy presented for modeling of 1D discontinuous elastic waves is based on (a) pushforward-pullback local stepping — ensuring the elimination of dispersion due to different critical time step sizes of finite elements, (b) domain decomposition via localized Lagrange multipliers — to satisfy coupling kinematics and dynamic equations , (c) asynchronous time scheme — ensuring the correct information transfer of quantities for the case of integer ratios of time step size for all domain pairs. Dispersion behaviors, existence of spurious stress oscillations, and sensitivity of the dispersion to time step size are then suppressed. The proposed method is numerically tested with regard to the rectangular step pulse elastic propagation problem considering in-space varying Young’s modulus. To prove robustness and accuracy, a comparison with results from commercial software, an analytical solution, and experimental data from partial assembly of a split Hopkinson pressure bar (SHPB) setup is provided.
Permanent Link: https://hdl.handle.net/11104/0344123