## 1 Introduction  
Collisions are common mechanical phenomena, and include car collisions, ship collisions, plane collisions, etc. The accidents cause a lot of personal and property losses [1]. Therefore, improving the crashworthiness of vehicles has become an attractive object of research, and various energy-absorbing structures have thus emerged [2]. Passive safety relies mainly on the energy-absorbing material at the front end of the frame to absorb external loads. Energy-absorbing devices based on the principles of composite material crushing and polymer material friction have emerged in recent years [3], metal deformation energy-absorbing structures have the advantages of high efficiency, good manufacturability and low price [4]. Therefore, metals are still the first choice in various collision situations. Scholars have conducted a large number of impact tests and simulation analyses on energy-absorbing structures [5; 6; 7], analysing the crashworthiness of the energy-absorbing structures and summarizing their design methods. Common metal deformation energy-absorbing structures include metal thin-wall crushing, metal tube expansion and metal cutting, etc. [8; 9; 10]. Among these, the thin-walled metal crush structure is the most widely used because of its economy and simplicity, leading this type of structure to be the object of most research. [PERSON] et al. [11] have summarized the influencing factors of thin-walled energy-absorbing elements and their design and optimization methods. A large number of articles [12; 13; 14; 15] have summarized the influencing factors of thin-walled energy-absorbing elements under axial compression, have analysed the deformation patterns of thin-walled tubes under different loading conditions, and have proposed an average crushing force for square and round tubes. Although the specific energy absorption of the lateral crushing and bending deformation of thin-walled components is small. In actual collisions, energy absorption caused by lateral loads is inevitable. The crashworthiness of thin-walled components has been analysed [16; 17; 18]. Metal tube expansion structures are widely used in rail vehicles, and the research on such energy-absorbing structures is similarly in-depth. [PERSON] has stated that an expanded tube structure could still maintain good crashworthiness and energy absorption efficiency under different external force loading conditions, and they analysed the geometric dimensions, material strength, diameter expansion of the expanded tube in detail through experiments, simulations and theoretical derivation. Energy absorption of the expander energy absorber have also been researched [16; 17; 18]. [PERSON] et al. [19] propose a new hybrid absorber with an external die added to the outside of the expanding-splitting tube. Experimental results show that the hybrid tube deforms in a controlled manner and has a high energy absorption. [PERSON] et al. [20] proposes a novel design of regenerative shock absorber for the in-wheel motor. Their results show that the shock absorber is effective and feasible for renewable energy applications in electric vehicles. Research on the energy absorption mechanism and structural design of metal expansion tubes is also now relatively mature. The energy-absorbing structure based on the principle of metal cutting has the advantages of compact structure and high volume-specific energy-absorbing efficiency [21], and its application in the engineering field has gradually increased in recent years [22]. [PERSON] et al. [23] endeavoured to accentuate the material response at high strain rates as well as the structural response, with their results showing a good absorption of energy. [PERSON] et al. [24] derived an analytical modelling procedure to predict the complete force-displacement response. The mean load and total energy absorption were predicted to within 5% of experimental values.