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Experimental and numerical investigation on the crashworthiness optimization of thin-walled aluminum tubes considering damage criteria

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Abstract

This paper aims to investigate the crashworthiness performance of thin-walled tubes under quasi-static conditions both experimentally and numerically. Single-cell and multi-cell tubes made of aluminum were tested under quasi-static compressive loading. A three-dimensional finite element (FE) model accounting for the damage in the constitutive equations was developed. It was validated through experiments based on the force–displacement behavior and the deformation views of the tubes. The sensitivity of the initial peak force, total energy absorption, specific energy absorption, and crush force efficiency to different model parameters such as the tube height and thickness, velocity of the rigid upper plate, and the type of the constitutive equations used were investigated in detail. It was observed that the element type used (shell/solid) in the FE model and the element size in the thickness direction played an important role in simulating the tests accurately. In addition, surrogate-based optimization of the single-cell tubes (T0) and two different types of multi-cell tubes (T4E, T8E) is performed to maximize crush force efficiency (CFE) and specific energy absorption (SEA). It is found that CFE of the optimum T4E design is 8.5% greater than CFE of the optimum T8E design and 30% greater than CFE of the optimum T0 design. It is also found that SEA of the optimum T4E design is 9.8% greater than SEA of the optimum T8E design and 213% greater than SEA of the optimum T0 design.

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Acknowledgements

The experimental results obtained in this paper is from the research project which was supported by TUBITAK (the Scientific and Technological Research Council of Turkey) under the ARDEB-1002 Program (Project Number 115M025).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Ankara Yildirim Beyazit University, Ankara, 06010, Turkey

    Sinem K. Mert

  2. College of Engineering and Technology, American University of the Middle East, Egaila, 54200, Kuwait

    Murat Demiral & Mehmet A. Güler

  3. Department of Mechanical Engineering, University of Turkish Aeronautical Association, Ankara, Turkey

    Murat Demiral

  4. Department of Automotive Engineering, Gazi University, Ankara, Turkey

    Murat Altin

  5. Department of Mechanical Engineering, TOBB University of Economics and Technology, Ankara, 06560, Turkey

    Erdem Acar & Mehmet A. Güler

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  1. Sinem K. Mert
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Correspondence to Mehmet A. Güler.

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The original online version of this article was revised: Following publication of the original article, we were notified that Figures 4 to 7 were misplaced: Fig. 4 in the online version should have been Fig. 5, Fig. 5 in the online version should have been Fig. 6, Fig. 6 in the online version should have been Fig. 7, and Fig. 7 in the online version should have been Fig. 4. Figure citations and figure legends were published in the correct order.

Appendix: Details on optimization results

Appendix: Details on optimization results

This section provides some details on optimization results for design problem stated in Eq. (8). Note that graphical optimization method can also be used to find the optimum values of the tube thickness (t) and tube length (L) instead of using genetic algorithm, because Eq. (8) is a design optimization problem with two design variables. In graphical optimization method, the optimum solution is obtained by drawing contours of the objective function. For illustration, optimization of T0 design for maximum CFE is shown in Fig. 23a, and optimization of T0 design for maximum SEA is shown in Fig. 23b. Note that the contour data of Fig. 23a are generated by using KR1 model, and that of Fig. 23a is generated by using QRS model. Notice that by using graphical optimization method, it was possible to confirm the optimum solutions found through genetic algorithm.

Tables 10 and 11 show the optimum results obtained by using QRS and KR1 models, respectively. We notice that even though KR1 models are globally more accurate than QRS models for CFE and SEA prediction of the T4E design, optimum tube designs obtained by using QRS models have better CFE and SEA values than optimum tube designs obtained by using KR1 models. Similarly, optimum T8E design obtained by using KR1 model has larger CFE value than the optimum design obtained by using QRS model, even though PRS model is globally more accurate than KR1 model for CFE prediction of the T8E design. The underlying reason for these findings is that the globally most accurate model does not necessarily display the best performance locally (e.g., near the optimum).

Fig. 23
figure 23

Optimum tube thickness (t) and tube length (L) for T0 design obtained by using graphical optimization method, where the contour data are generated using KR1 model for CFE prediction, and using QRS model for SEA prediction

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Table 10 Optimization results for T0, T4E, and T8E designs obtained by using QRS
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Table 11 Optimization results for T0, T4E, and T8E designs obtained by using KR1
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Mert, S.K., Demiral, M., Altin, M. et al. Experimental and numerical investigation on the crashworthiness optimization of thin-walled aluminum tubes considering damage criteria. J Braz. Soc. Mech. Sci. Eng. 43, 113 (2021). https://doi.org/10.1007/s40430-020-02793-6

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