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An improved 3D multi-sphere DE-FE contact algorithm for interactions between an off-road pneumatic tire and irregular gravel terrain

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Abstract

The traveling analysis of an off-road tire on granular terrain is a typical application of contact interaction problems between structures and granular particles. In previous studies, extensive efforts normally idealized irregular gravel materials using spherical discrete elements (DEs), and the influence of irregular shapes was ignored. In our recent works, a coupling algorithm that used a multi-sphere model to accurately represent irregular gravel particles in the context of tire-terrain interactions was proposed. However, this algorithm suffers from low computational efficiency for contact interactions. To address this issue, this work develops a robust and efficient contact algorithm to handle the complex interactions between multi-sphere DEs and finite element segments for tire traveling analysis. The advantages of the presented algorithm are three-folded. Firstly, a rectangular dynamic contact domain is reconstructed to reduce the computational cost in the global searching phase with the use of an efficient multi-grid algorithm. Secondly, we use virtual bounding spheres instead of virtual bounding boxes for hexahedral FE segments to reduce memory storage. Thirdly, a numerical treatment is developed to deal with multi-point contact problems between multi-sphere DEs and FE segments using an inside-outside algorithm in the local searching phase. Finally, the traveling behavior of two off-road tires on multi-sphere gravel terrain using our proposed algorithm is simulated, and the robustness, accuracy and efficiency of the presented algorithm is demonstrated via an indoor soil-bin data.

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Acknowledgements

This work was supported by the Science and Technology Planning Project of Guangzhou (No. 201804020065), the International Cooperation Project of the Ministry of Science and Technology of China (No. 2017YFE0117300), the National Natural Science Foundation of China (No. 11672344), and the Innovation Group Project of Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai) (No.311021013).

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Authors and Affiliations

  1. School of Mechanical and Automotive Engineering, South China University of Technology, 381 Wushan RD., Tianhe District, Guangzhou, 510641, People’s Republic of China

    Xiaobing Guo & Mengyan Zang

  2. School of Mechanical Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan, 250353, China

    Zumei Zheng

  3. School of Marine Engineering and Technology, Sun Yat-Sen University, Zhuhai, 519082, China

    Shunhua Chen

  4. Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai, 519082, China

    Shunhua Chen

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  1. Xiaobing Guo
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Appendix A: Data structure

Appendix A: Data structure

In the global search algorithm, two 1D arrays MSDE_ID (k1) and FES1_ID (k2) are needed to store the ID information of the multi-sphere DE IDs and the hexahedral FE segments IDs, where k1 and k2 are the maximum numbers of the multi-sphere DEs and the FE segments in the rectangular dynamic contact region, respectively. For establishing the first layer grid, two 3D arrays are used to store the cell numbers of the bounding spheres of the multi-sphere DEs and FE segments, i.e., MSDE_CN (\(n_{{{\text{fir}},x}}\), \(n_{{{\text{fir}},y}}\), \(n_{{{\text{fir}},z}}\)) and FES_CN(\(n_{{{\text{fir}},x}}\), \(n_{{{\text{fir}},y}}\), \(n_{{{\text{fir}},z}}\)), where \(n_{{{\text{fir}},x}}\), \(n_{{{\text{fir}},y}}\) and \(n_{{{\text{fir}},z}}\) are the numbers of the cells in the x, y and z directions. In order to record the potential contact pairs between the bounding spheres of multi-sphere DEs or between the bounding spheres of multi-sphere DEs and the bounding spheres of FE segments, two 2D arrays (i.e., MSDE_PCP (K1, K3) and MSFE_PCP (K2, K4)) and two 1D arrays (TNM_MSDEPCP (K5) and TNM_MSFEPCP (K6)) are introduced, where K3 denotes the number of the potential contact pairs for the target bounding spheres of the multi-sphere DE K1, and K4 is the number for the target bounding sphere of the FE segment K2, respectively; K5 and K6 are, respectively, the total numbers of the potential contact pairs between multi-sphere DEs or between multi-sphere DEs and FE segments in the first layer grid.

Furthermore, two 2D arrays are also need to record ID information of the elemental spheres and the FE segments in the second layer grid, i.e., ES_ID (K1, K7) and FES2_ID (K2, K8), where K7 and K8 are the thresholds which are the maximum numbers of elemental spheres and FE segments in the local search domain. Since there is only one FE segment in the local coordinate system, the threshold of K8 in the array FES2_ID (K2, K8) is 1. For the contact detection between the elemental spheres of two multi-sphere DEs in the second layer grid, one 3D arrays ES_CN(\(n_{\sec ,x}\), \(n_{\sec ,y}\), \(n_{\sec ,z}\)) is extra required to store the cell numbers of the elemental spheres, where \(n_{\sec ,x}\), \(n_{\sec ,y}\) and \(n_{\sec ,z}\) are the numbers of the cells in the \(\alpha\), \(\beta\) and \(\chi\) directions, respectively. Finally, one 3D array ES_PCP (K1, K7, K9) is used to store the potential contact pairs between the elemental spheres of two multi-sphere DEs, where K9 is the total number of potential contact pairs in the second layer grid.

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Guo, X., Zheng, Z., Chen, S. et al. An improved 3D multi-sphere DE-FE contact algorithm for interactions between an off-road pneumatic tire and irregular gravel terrain. Comp. Part. Mech. 10, 97–120 (2023). https://doi.org/10.1007/s40571-022-00479-5

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