By means of the local surface nanocrystallization that enables to change the material on local positions, an innovative embedded multi-cell (EMC) thin-walled energy absorption structures with local surface nanocrystallization is proposed in this paper. The local surface nanacrystallization stripes are regarded as the moving morphable components in the domain for optimal design. Results reveal that after optimizing the local surface nanocrystallization layout, the specific energy absorption (SEA) is increased by 50.78% compared with the untreated counterpart. Besides, in contrast with the optimized 4-cell structure, the SEA of the nanocrystallized embedded 9-cell structure is further enhanced by 27.68%, in contrast with the 9-cell structure, the SEA of the nanocrystallized embedded clapboard type 9-cell structure is enhanced by 3.61%. This method provides a guidance for the design of new energy absorption devices.

At present, transport vehicles are developing towards high speed, with a lot of energy in the process of high-speed operation. Therefore, in the accidental collision, the problem of energy dissipation gradually attracts people’s attention. As a good energy absorption device, metal thin-walled structure is widely used in energy absorption devices such as spacecraft landing device, subway front end underframe, aircraft bird impact protection device and automobile bumper system. It has the advantages of high energy absorption performance, light weight and easy manufacturing. Due to the popularity of the concept of lightweight, a new standard is proposed for the protection of key structural components such as aviation, automobile and subway, which has important practical value by further optimizing the design of energy absorbing devices.

The research on thin-walled energy absorbing structures by researchers is not limited to single material or cross section. To improve the energy absorption performance of thin-walled structure, the composite tubes and metal tubes (aluminum alloy, low carbon steel, low carbon steel) have been studied according to the different material compositions and sectional types. In industrial manufacturing, polymer composites have high energy absorption capacity, specific strength and stiffness. Chouw et al. [

By changing the shape of the thin-walled tube structure, the designs of grooves (groove, half groove), holes (round hole, square hole, etc.), stiffeners, functionally graded tubes, multi cell tubes, nanocrystallized tubes [

The above-mentioned methods energy absorption mainly focused on the structural design, variable cross-section, introducing defects, composition of materials, etc. The energy absorption of thin-walled structure can be further improved by optimization methods. Liu et al. [

In most cases, fatigue damage, fracture, wear and other failure forms of the structure occur on the surface of the material due to stress concentration or inclusions on the surface of the structure [

Surface nanocrystallization is usually used for single thin-walled tube, which is relatively easier in processing, while it is difficult in manufacturing for multi-cell structures. In this paper, a emdedded multi-cell thin-walled structure with local surface nanocrystallization is studied. With the maturity of finite element software and the updating of computer, on one hand, it is possible to simulate the impact of thin-walled tube by computer, on the other hand, the optimization of improving the energy absorption is gradually developed. In 2014, Guo et al. [

Energy absorption studies focus on the absorption of energy in the process of plastic buckling deformation of thin-walled structures, which effectively dissipates and transforms collision energy into other forms. When impacted by external load, the active protection device is required to buffer the collision energy and absorb as much energy as possible to avoid passing the collision energy to any object after its collapse. The optimization design is introduced to improve the energy absorption effect of the nanocrystallized square tube, which can meet the requirements of the practical working conditions for the thin-walled tubes, so as to minimize the resource consumption and achieve the optimal energy absorption performance.

In numerical calculation, when the central difference method is used to solve collision problems, it is neither necessary to decompose the stiffness matrix, nor to assemble the overall stiffness matrix of the system, which reduces the storage amount and improves the efficiency of the operation. The format is as follows:

Among them,

In this paper, based on moving morphable components, the local nanocrystrallization stripes are regarded as components that move and shrink in the feasible region, and the design of a new thin-walled embedded multi-cell energy absorbing structure with nanocrystallization surface is optimized. The basic idea of MMC optimization method is to place a certain number of components represented by the display topology description function in the design domain, so that the components can move, rotate, shrink and overlap in the design domain. Explicit geometric information is used to express the structure in the optimization process. The relationship between models is independent to each other, which improves the iterative efficiency, reduces the variables in the design process, and overcomes the problems of checkerboard patterns, mesh dependency and sawtooth boundary in traditional topology optimization [

In order to improve the deformation condition of the component in the design process, hyperelliptic equation is used to describe the component and its topological description function can be expressed by explicit geometric information (length, thickness and center coordinates of the component). Take the description of the k-th structural component as an example [

Here,

where

In the MMC optimization framework, the optimization formula can be written as follows:

In the MMC optimization framework, the energy absorption is taken as the optimization objective function, and the component width, the length from the component centerline to the upper surface, the distance between two adjacent components and the proportion of nanocrystallization area on the model surface are taken as the design variables. The optimization formulation of the thin-walled embedded tubes can be expressed as:

where

By solving the optimization problem in

It is of great significance to characterize the energy absorbed by structure and how to establish a complete evaluation system is also the goal of scientific researchers [

The EMC structures is consist of a group of single tubes confined under an outer thin-walled envelope. The outer tube can be made of folded plate welding or relatively large tube to accommodate the inner single tubes. The crystal microstructure of the surface layer is changed after SSNC, which is conducive to the buckling of the energy absorbing structure in the region with weak yield limit and resulting in layered compression mode. Xu et al. [

The EMC structure is made of 304 stainless steel, the constitutive relations of the untreated and nanocrystallized materials are approximately bilinear. Chen et al. [^{3}, the yield stress of untreated 304 stainless steel is 260

For tubes with the same structural mass, numerical simulations of untreated thin-walled single tube, embedded tube and embedded four-cell tube are carried out under axial impact loading. Deformation modes on four moments (0.003, 0.006, 0.009, 0.012 s) are extracted for comparison to demonstrate the compression deformations for the three kinds of structures. Numerical results are displayed in

By comparing the area enclosed by the displacement load curves of the three types of tubes in

The optimal design of energy absorbing structure is to find the optimal parameters for energy absorbing performance with the aid of computer under the premise of setting constraints. The MMC method is used to optimize the number of nanocrystallized stripes on the surface of thin-walled structures, so as to improve the ability of absorbing impact kinetic energy in the impact process. The number of components (nanocrystallized stripes) affects collapse mode in the buckling process, and then makes an effort on the structural energy absorption. Consistent nanocrystallization components (CNC) are selected as the constraint functions, and the number of components is limited between 2 and 10. According to the nanocrystallization distributions of Type A and Type B, optimization results for the two different types are obtained and the displacement-load curves of models with different stripe numbers are displayed in

3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
---|---|---|---|---|---|---|---|---|

Type A (J) | 8662.34 | 8508.65 | 8697.79 | 9290.22 | 9559.44 | 9032.51 | 9078.76 | 9030.13 |

Type B (J) | 8342.00 | 8802.98 | 9023.85 | 8750.13 | 8630.68 | 8795.22 | 8612.11 | 8959.71 |

7 stripes of Type A | 202.89 | 132.77 | 65.44 | 9559.44 | 14983.45 |

5 stripes of Type B | 220.02 | 125.33 | 56.96 | 9023.85 | 14143.97 |

As long as the component width is consistent, the optimal number of components (nanocrystallization stripe number) and the proportion of nanocrystallization areas with two different design types are determined. Release the component width constraint and select the disordered nanocrystallization components (DNC) as the optimization component, the above mentioned embedded four-cell structures with 7 equally distributed nanocrystallization layouts is further optimized, the local optimal solution is obtained in the geometric parameter design, and the energy absorption performance is further improved. By comparing the results with that of the CNC design, the accuracy of the design is further verified. In order to clearly observe the buckling path and evolution process of the structure, the buckling characteristics of the internal variation of the structure is shown in

From the

Single tube untreated | 81.28 | 29.12 | 35.83 | 2096.56 | 3286.14 |

Embedded tubes | 130.01 | 46.95 | 36.11 | 3380.70 | 5289.90 |

Embedded four-cell tubes | 191.38 | 90.52 | 47.30 | 6517.25 | 10215.13 |

CNC embedded four-cell tubes | 217.50 | 132.77 | 61.40 | 9559.44 | 14936.63 |

DNC embedded four-cell tubes | 215.39 | 137.61 | 63.89 | 9908.14 | 15530.00 |

DNC embedded nine-cell tubes | 288.21 | 223.07 | 77.40 | 16061.11 | 19828.53 |

Based on the optimization results of nanocrystallization area ratio and nanocrystallization components of the thin-walled EMC energy absorption structures, the DNC embedded 9-cell structure is further investigated numerically. For the embedded 9-cell tube, there is a distribution state that provides more energy absorption than that of 7 stripe DNC distribution. When the 5 stripe DNC is distributed, when the nanocrystallization area at the top of the impacted end accounts for a large proportion, the specific energy absorption is 385.66 J/kg higher than that of the 7 stripe, but it is unstable in the process of impact and the impact load efficiency decreases. When the nanocrystallization components are inconsistent, the energy absorption changes with the number of iterations, as shown in _{max} of the 9-cell structure is increased and the impact process is stable, besides, the SEA is also increased by 27.68%. From the results, it is concluded that the SEA is significantly enhanced by optimizing the structural and nanocrystallization design.

Due to the multi-layer problem in the multi-cell structures, a novel DNC clapboard type energy absorbing structure is proposed by selecting the DNC nanocrystallization layout and optimizing the number of nanocrystallization components.

In virtue of local surface nanocrystallization, the distribution of material properties and load-carrying capacity of the structure are changed, and the buckling deformation of the structure can be induced. Compared with the multi-cell thin-walled structure, the EMC thin-walled structure is more suitable for local surface nanocrystallization treatment and the processing is simple. Thus, method of MMC is used directly to optimize and design the nanocrystallization layouts on the local surface. In the design of EMC thin-walled structure, the local surface nanocrystallization distributions of the outer tube and the embedded inner tube can be diversified. The results show that the design scheme of the nanocrystallized area for the inner tube corresponding to the untreated part for the outer tube can coordinate the overall deformation, and this layout can be used as the basic design mode. The optimized numerical results proved that the SEA and CFE of the embedded 4-cell thin-walled structure with local surface nanocrystallization are 50.78% and 35.07% higher than those of the same structure without nanocrystallization. Moreover, compared with the optimized 4-cell structure, the SEA of the nanocrystallized embedded 9-cell tube structure under the same distribution is further increased by 27.68% and the CFE is enhanced by 21.15%. On account of the multi-layer problem in the multi-cell structure, a novel DNC clapboard type energy absorption structure is proposed. The specific energy absorption of this structure is 3.61% higher than that of DNC embedded 9-cell tube. The design method of EMC thin-walled structure with local surface nanocrystallization provides a guidance for the design of new energy absorption devices.