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IGA-SPH: coupling isogeometric analysis with smoothed particle hydrodynamics for air-blast–structure interaction

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Abstract

We introduce a novel immersed-like numerical framework that combines isogeometric analysis with smoothed particle hydrodynamics for simulating air-blast–structure interaction. The solid domain is represented by a Lagrangian point cloud, which is immersed into a background Eulerian fluid domain. The smoothed particle hydrodynamics framework is employed to solve the equations of motion of the solid point cloud, whereas isogeometric analysis is used for the fluid mechanics equations on the background domain. The coupling strategy relies on a penalty-based volumetric coupling scheme that penalizes the velocity difference between the two domains, and involves a minimal amount of modification to existing codes, resulting in a straightforward implementation. The immersed nature of the proposed approach, combined with volumetric coupling, eliminates the need for explicit tracking of fluid–structure interfaces and imposes no limitations on solid domain motion and topology. Ample mathematical details are provided, and the proposed method is verified and validated against established numerical tools and experimental studies. The results affirm the method’s accuracy, robustness, and ease with which it seamlessly integrates two distinct computational techniques.

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Acknowledgements

The authors would like to thank Stony Brook Research Computing and Cyberinfrastructure, and the Institute for Advanced Computational Science at Stony Brook University for access to the high-performance SeaWulf computing system, which was made possible by a $1.4M National Science Foundation grant (#1531492).

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Authors and Affiliations

  1. Department of Civil Engineering, Stony Brook University, Stony Brook, NY, 11794, USA

    Mohammad Naqib Rahimi & Georgios Moutsanidis

  2. Institute for Advanced Computational Science, Stony Brook, NY, 11794, USA

    Georgios Moutsanidis

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  1. Mohammad Naqib Rahimi
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Contributions

MN.R. developed the code, ran the analyses, visualized the results, and wrote the initial draft of the manuscript. G.M. conceptualized the work, developed the mathematical formulation, reviewed the initial draft, and edited and final version of the manuscript.

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Correspondence to Georgios Moutsanidis.

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Appendix: Omega correction for improved fracture surface in particle methods

Appendix: Omega correction for improved fracture surface in particle methods

In this appendix, we investigate the application and efficacy of the proposed omega correction [Eq. (45)] in refining fracture surface predictions within particle methods. The focus is on two pivotal experiments: dynamic crack branching and the Kalthoff–Winkler experiment. The case setups are adopted from [16, 83, 84]. For the dynamic crack branching scenario, a plate with a pre-existing crack is subjected to surface tension from the top and bottom, leading to crack propagation and subsequent branching, as illustrated in Fig. 18. The conventional TLSPH approach exhibits minor non-physical fracture irregularities and particle disturbance, as depicted in Fig. 19. The incorporation of the omega correction markedly enhances the fracture surface, yielding a cleaner and more accurate representation, especially when using an omega value of \(\omega _s > 10^{-3}\). In Fig. 20, the influence of the omega correction on strain and dissipated fracture energy over time is observed. The impact is found to be quite negligible, indicating the effectiveness of the omega correction in enhancing the fracture surface without imposing significant effects on the physics of the system. This holds particularly true for values of \(10^{-3}< \omega _s < 10^{-2}\). In the Kalthoff–Winkler experiment, a plate with a pre-existing crack is exposed to pure shear loading from the left lower part, inducing a mixed mode I–II fracture in a diagonal direction. Figure 21 compares the predicted fracture surfaces with and without the omega correction. In Fig. 22 we compare the predicted energies of the system to the ones found in literature [83]. The results underscore the efficiency of the omega correction in predicting a clean and realistic fracture surface without imposing significant changes on the physics of the problem.

Fig. 18
figure 18

Dynamic crack branching. Crack propagation

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Fig. 19
figure 19

Dynamic crack branching. Effects of correction factor, \(\omega _s\), on the fracture surface. The deformation is magnified by a factor of 200 to show the crack opening

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Fig. 20
figure 20

Dynamic crack branching. Time evolution of the strain (a) and dissipated fracture energy (b) of the system for different \(\omega _s\) values compared with literature [83]

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Fig. 21
figure 21

Kalthoff–Winkler experiment. Effects of correction factor, \(\omega _s\), on the fracture surface. The deformation is magnified by a factor of 5 to show the crack opening

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Fig. 22
figure 22

Kalthoff–Winkler experiment. Time evolution of the strain (a) and dissipated fracture energy (b) of the system for different \(\omega _s\) values compared with literature [83]

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Rahimi, M.N., Moutsanidis, G. IGA-SPH: coupling isogeometric analysis with smoothed particle hydrodynamics for air-blast–structure interaction. Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-01978-0

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