Crushing behavior on the cylindrical tube based on lotus leaf vein branched structure
基于荷叶脉分枝结构的圆柱形管上的破碎行为

Thin-walled structures are of great importance to the fields of aviation, vehicles and industry due to its extraordinary mechanical behavior. In the past decades, the static and dynamic mechanical properties of conventional single-walled structures have been extensively studied, including circular (Karagiozova and Jones, 2001), square (Jensen et al., 2004; Zhang et al., 2009) and triangular tubes (Krolak et al., 2007; Wu and JinZhou, 2013). The results show that the mechanical properties of thin-walled tubes are closely related to their cross-section characteristics.
薄壁结构由于其非凡的机械性能，对航空、车辆和工业领域非常重要。在过去的几十年里，传统单壁结构的静态和动态机械性能得到了广泛的研究，包括圆形（Karagiozova 和 Jones，2001 年）、方形（Jensen 等人，2004 年;Zhang等人，2009 年）和三角管（Krolak等人，2007 年;Wu 和 JinZhou，2013 年）。结果表明，薄壁管的力学性能与其截面特性密切相关。

In recent years, thin-walled tubes have been widely used in many fields, and scholars have carried out extensive research on their mechanical properties. Yamashita et al. (2003) pointed out that the increase of the number of corner elements can enhance the energy absorption capacity of tubes. Zhang et al. (Zhang and Zhang, 2013) and Wu et al. (2016) further confirmed that multi-cell tubes have superior energy absorption ability through experimental and simulation research. Nia (Nia and Parsapour, 2014) found that the multi-cell thin-walled tubes with hexagonal and octagonal sections have the best energy absorption characteristics. After studying the dynamic response of multi-cell tubes under impact loads in different directions, Fang et al. (2015) carried out optimization design in crashworthiness. Tran et al., 2014a, 2014b, 2015 theoretically deduced the axial impact force of several multi-cell tubes based on the analysis of the deformation mechanism. Xiang et al. (2016) introduced the key performance indicators to analyze and evaluate the mechanical behavior of polygonal tubes, multi-cell tubes and honeycombs. Mahmoodi et al. (2016) studied the energy-absorption properties of tapered multi-cell tubes by means of theory and simulation. Tabacu et al. (Tabacu, 2015) numerically simulated and analyzed the mechanical behavior of circular tubes with rectangular multi-cell insert.
近年来，薄壁管已广泛应用于许多领域，学者们对其机械性能进行了广泛的研究。Yamashita et al. （2003） 指出，角元件数量的增加可以提高管材的能量吸收能力。Zhang et al. （Zhang and Zhang， 2013） 和 Wu et al. （2016） 通过实验和模拟研究进一步证实了多细胞管具有优越的能量吸收能力。Nia （Nia and Parsapour， 2014） 发现具有六边形和八边形截面的多孔薄壁管具有最佳的能量吸收特性。在研究了多单元管在不同方向冲击载荷下的动态响应后，Fang et al. （2015） 进行了耐撞性的优化设计。Tran et al.， 2014a， 2014b， 2015 基于变形机理的分析，理论推导出了几种多胞管的轴向冲击力。Xiang et al. （2016） 介绍了分析和评估多边形管、多单元管和蜂窝的机械行为的关键性能指标。Mahmoodi 等人（2016 年）通过理论和模拟研究了锥形多细胞管的能量吸收特性。Tabacu 等人 （Tabacu， 2015） 对带有矩形多孔嵌件的圆管的机械行为进行了数值模拟和分析。

In recent years, many researchers further sought inspiration from nature and proposed thin-walled tubes with self-similar hierarchical characteristics to improve its mechanical performances (Gibson et al., 2010; Zhang et al., 2015). Sun et al., 2016a, 2016b analyzed the energy absorbing ability of self-similar triangular lattice tubes and found that the incorporation of hierarchy greatly improved its energy absorption capacity. Luo et al. (Luo and Fan, 2018; Fan et al., 2018) investigated the dynamic behavior of rectangular self-similar multi-cell structures and theoretically calculated its mean crushing force. He et al. (2021) proposed Sierpinski hierarchical triangular (SHT) tube and studied its mechanical properties.
近年来，许多研究人员进一步从大自然中寻求灵感，并提出了具有自相似分层特征的薄壁管，以改善其机械性能（Gibson et al.， 2010;Zhang et al.， 2015）。Sun et al.， 2016a， 2016b 分析了自相似三角晶格管的能量吸收能力，发现层次结构的加入大大提高了其能量吸收能力。Luo 等人（Luo 和 Fan，2018 年;Fan et al.， 2018）研究了矩形自相似多细胞结构的动力学行为，并从理论上计算了其平均破碎力。他等人（2021 年）提出了 Sierpinski 分层三角形 （SHT） 管并研究了其机械性能。

Some experts also proposed to introduce mathematical functions or curves into the section design of thin-walled structures. Wu (Wu et al., 2017) studied the deformation mechanism of the Fourier-varying sectional tubes and carried out the optimization of crashworthiness. Liu et al. (LiuWenqian et al., 2015) introduced the sinusoidal patterns into the corrugated tubes and investigated its dynamic response under axial impact. Sun (Sun et al., 2017) parametrically modeled a wide range of criss-cross sections with spline curves and studied the influence of structural parameters on its mechanical properties. Deng et al. (2018) put forward a new type of lateral corrugated tube (LCTs) with a sinusoidal cross-section and the crashworthiness was studied systematically. Wang et al. (2018) focused on the Koch fractal structure and found that the 2nd order hybrid Koch structure had better energy absorption performance. Li et al. (2019) numerically analyzed the mechanical performance of a new corrugated square tube controlled by a cosine expression.

The inspiration from bionics has opened up a new idea for the design of thin-walled structure to improve their mechanical properties (San HaLu, 2020). Chen et al. (Chen et al., 2018; Song et al., 2018; Liu et al., 2017; Fu et al., 2019) proposed some new thin-walled structures inspired by bamboo and found that the bionic-bamboo tubes exhibit superior crashworthiness characteristics. The crashworthiness of a group of bionic multi-cell tubes based on the microstructure of beetle forewings had also been widely studied (Hao and Du, 2018; Chen et al., 2012, 2014; Xiang and Du, 2017). Ding et al. (2018) designed new square multi-cell tubes with lateral variable thickness based on the stem of a plant and bones structure of animals. Mousanezhad et al. (2015) proposed the spider-web hierarchical structure which displayed high stiffness and toughness. Zhang et al. (2018) and He et al. (2020) further analyzed the effect of hierarchical structural parameters on the crashworthiness of this structure. It is widely known that the leaf vein veins not only carry nutrients, but also support the weight and external load of the whole blade in structure to ensure the overall stiffness and plane ductility of the blade. Therefore, the rationality and size of the vein distribution play a decisive role in the blade bearing capacity and maintaining the shape of the blade. However, up to now, there is still no relevant research introducing such structural features into thin-walled energy absorbing structures.

In order to further improve the energy absorption characteristics of thin-walled tube, a new excellent energy absorption structure named as the leaf vein branched circular tubes (LVBCT) is proposed. The crushing behavior of LVBCT subjected to axial impact load is studied systematically by numerical simulation method. Section 2 describes the configurations of the LVBCT. In Section 3, the computational models are established and further verified by comparing with the experimental results. Finally, systematic parametric study on the influences of geometric parameters (the number of main veins N, the structural parameter $\gamma$, which is defined as the ratio of radius of inner circle $R_{inner}$ to radius of outer circle $R_{outer}\gamma$ and thickness of all the cell-walls t) on the crushing behavior of LVBCTs is carried out to enhance the understanding of the clear correlation of vein branching characteristics and energy absorption performance in Section 4.