Mean Crush Force Research Articles

Identification of crashworthiness indicators of column energy absorbers with triggers in the form of cylindrical embossing on the lateral edges using artificial neural networks

The paper presents the possibility of neural network application in order to identify the most advantageous design variants of column energy absorbers in terms of the achieved energy absorption indicators. Design variants of the column energy absorber made of standard thin-walled square aluminium profile with triggers in the form of four identical cylindrical embossments on the lateral edges were considered. These variants differ in the diameter of the trigger, its depth and position. The geometrical parameters of the trigger are crucial for the energy absorption performance of the energy absorber. The following indicators are studied: PCF (Peak Crushing Force), MCF (Mean Crushing Force), CLE (Crash Load Efficiency), SE (Stroke Efficiency) and TE (Total Efficiency). On the basis of numerical studies validated by experimentation, a neural network has been created with the aim of predicting the above-mentioned indices with an acceptable error for an energy absorber with the trigger of specified geometrical parameters and position. The paper demonstrates that the use of an effective multilayer perceptron can successfully speed up the design process, saving time on multivariate time-consuming analyses.

Out-of-plane crushing performances of cell-based hierarchical honeycombs based on the evaluation criteria for ideal energy absorption

A cell-based hierarchical strategy was introduced in the preparation of traditional honeycombs to design a novel structure, known as cell-based quadrangular hierarchical honeycombs (CQHHs). The out-of-plane crashworthiness of CQHHs was investigated using experimental, numerical, and analytical methods. The criteria of ideal energy absorption were employed to evaluate the crushing performance. Then, the effects of a hierarchical strategy and geometric parameters, including the cell densities of macrocells and microcells, the relative density, and the thickness coefficient, on the crushing performance of the CQHHs were tested. Consequently, the optimal hierarchical strategy, namely, the completely ordered arrangement (COA) was identified, and a parameter analysis demonstrated that the cell density and thickness coefficient effectively improved the energy absorption efficiency of the CQHHs. Based on the combination of the COA strategy and optimal parameters, an improvement of 74.45% in energy absorption efficiency was observed, compared with a traditional honeycomb with 3 × 3 cells. The mean crushing force (MCF) reached 96.24% of the full plastic strength of the matrix, indicating that the ideal energy absorption could be closely approached by the cell-based hierarchical honeycomb. These achievements provide an effective way for developing lightweight energy absorbers and achieving ideal energy absorption.

The axial crushing performance of bio-inspired hierarchical multi-cell hexagonal tubes

Both the concepts of bio-inspiration and hierarchy are found to be effective in enhancing the crushing performance of tubes. In this paper, the bio-inspired hierarchical multi-cell hexagonal tubes (BHMH) were developed by combing the bio-mimicked and hierarchical configurations in tubular structures. The crushing behaviors of BHMH tubes with various hierarchical orders and wall thicknesses were firstly investigated numerically. The results show that the peak crushing force (PCF) of all BHMH tubes is less than that of hexagonal tubes in each group, which is beneficial in minimizing possible injury and damage when tubes are crushed. With the increase of hierarchical order and wall thickness, the mean crushing force (MCF), crushing force efficiency (CFE) and specific energy absorption (SEA) of BHMH tubes also increase. The SEA of the third order BHMH tubes is approximately 2.5 times that of the zeroth order BHMH tubes (multi-cell hexagonal tubes) in each of the four groups. Compared with conventional hexagonal tubes, a maximum increase of 146% in the SEA of BHMH tubes is obtained, which demonstrates that BHMH tubes are better energy absorbers than that of traditional single and multi-cell hexagonal tubes. Subsequently, theoretical analysis based on the Simplified Super Folding Element (SSFE) theory was carried out to determine the mean crushing force of BHMH tubes. The theoretical results agree well with the simulated results for all BHMH tubes.

Application of a weighted graph representation method to the crashworthiness optimization of subway collision frame structures

The collision frame structure is the most important subway structure for energy absorption and impact load transfer during foreign object collision. To improve the crashworthiness of the collision frame structure, a parameter optimization method based on a weighted graph representation method was proposed. Based on weighted graph theory, an equivalent mathematical model of the collision frame structure was established. Combined with the Belytschko beam element method, which is a large deformation calculation technique, a parametric finite element model (FEM) considering plastic mechanical properties was constructed, which was validated by a detailed finite element model and a quasi-static crush test. Based on the practical requirements, the crush displacement, the intrusion space and the mean crush force (MCF) were determined as constraints. The structural total mass was considered as the objective. The optimized structural parameters and key performance indicators were obtained and compared by the genetic algorithm (GA), Colliding bodies optimization (CBO), Enhanced colliding bodies optimization (ECBO). The results showed that the GA algorithm had the best optimization objective. The comparison results showed that the optimized collision frame structure could meet the crashworthiness requirements, while the structural mass was reduced from the initial 168.92 kg to 97.33 kg, thus giving a reduction rate of 42.38 %.

Mechanical analysis characteristics of bionic structure based on NiTi alloy additive manufacturing

In recent years, the demand for protective structures in aerospace, transportation and other fields has become increasingly intense. In this paper, multi-rotation structure(MRS) and single rotation structure (SRS) are designed based on the microstructure of grass stem cross-section. Selective laser melting (SLM) is used to fabricate the structural model. The mechanical properties of two structures are investigated by numerical simulations and experiments. Results show that the specific absorption energy (SEA) of MRS is 33% higher than SRS. In addition, MRS is tested with cyclic compression and shape recovery experiments, which show the deformation recovery rate of MRS is 96%. Based on the superiority of MRS in mechanical and recovery performance, this paper also analyzes the influence of cell thickness t and cell angleθ on the performance. It is found that the sample with t = 0.45 mm, θ = 60° has the best comprehensive performance. Compared to SRS and initial design structure of MRS, its SEA is improved by 129% and 72.2%, and mean crushing force (MCF) is increased by 330% and 74%. This provides a theoretical basis for the development of new bionic protective structures.

Research on out-of-plane impact characteristics of self-similar gradient hierarchical quasi-honeycomb structure

From the perspective of bionics, this paper proposes a new self-similar hierarchical quasi-honeycomb (SHQ) structure. It specifically analyzes the hierarchy and gradient distribution’s influence on the impact characteristics under different impact loads by using a combination of numerical simulation, theoretical analysis and experimental validation. Research found that the hierarchical design can improve the out-of-plane impact performance of the honeycomb, and a reasonable out-of-plane gradient distribution can greatly reduce the peak crushing force (PCF) of the out-of-plane impact. In addition, based on the simplified super folding element theory, an out-of-plane impact theoretical model of the SHQ was established, which can better predict the mean crushing force (MCF) and energy absorption (EA).

High-velocity impact response of cylindrical tubes with linear gradient grooves: A comparative study

Grooved tubes benefit from optimized energy absorption characteristics compared to regular tubes. This paper investigated the crashworthiness characteristics of cylindrical tubes with various types of grooves under high-speed impact loads. Furthermore, the dynamic load response of tubes with external grooves having linear thickness distribution was studied experimentally and numerically for the first time. To assess the performance of gradient grooved tubes (GGTs), the crashworthiness of typical cylindrical specimens and tubes having internal or external grooves with uniform thickness distributions was compared. The results showed that the dynamic crush mode of GGTs was axisymmetric, progressive, and sequential. Furthermore, the mean crushing force (MCF) in GGT tubes was considerably less compared to other tubes (e.g., 89% difference between GGT and non-gradient tube). Moreover, the initial peak forces of all types of tubes having the same number of grooved sections were almost in the same range. However, the crushing force efficiency of GGTs was remarkably lower than other tubes due to their non-uniform load response. The numerical results showed that by increasing the number of grooves in GGTs, peak force, energy efficiency, and axial shortening decreased, but mean crushing and overall crushing forces increased. Altogether, the highest energy efficiency belonged to the GGT specimens, in which 17%, 4.2%, and 96% increases were observed compared to external and internal groove tubes and typical cylindrical tubes, respectively. Also, the energy efficiency increased with the number of grooves.

Dynamic enhancement mechanism of energy absorption of multi-cell thin-walled tube

In order to study dynamic response of multi-cell thin-wall tubes with small aspect ratio and diameter thickness ratio under high velocity impacts of lightweight devices, the mass block impact tests were performed on three types of thin-walled tubes including circular tube (CirT), multi-cell tube (MT) and polyurethane foam (PUR) filled multi-cell tube (FMT). The dynamic enhancement mechanism of collapse force of MTs was discussed based on numerical simulation and deformation pattern analysis of MTs and FMTs. The results indicated that the dynamic enhancement coefficient of mean crushing force (MCF) was 1.0–1.17 and 1.12–1.3 for MTs and FMTs, respectively. The dynamic enhancement of EA was 24–29.2% for CirTs, 0–14.7% for MTs and 9.42–21.16% for FMTs, compared to the quasi-static compression. The multi-cellularization tended to degenerate the sensitivity of collapse force of MTs to the loading rate, while the foam filling increased the rate sensitivity. With the impact velocity increasing from 30 to 70 m/s, the folding half-wavelength of MTs and FMTs decreased about 2–5 mm. Also, the effective stress level of the MTs increased with the impact velocity and the material strain hardening mechanism. The folding pattern of MTs could be improved by foam filling and enhancing the impact velocity.

A reinforced energy-absorbing structure formed by combining multiple aluminum foam-filled open-hole tubes

In order to improve the energy absorption (EA) performance of thin-walled structures and overcome defects of a large peak impact force and large load fluctuation of multi-tube combined structures, the crashworthiness of aluminum foam-filled open-hole tubes (AFOTs) and their combined energy-absorbing structure was studied. Their EA performance was evaluated and effects of open-hole parameters including size, number and spacing of holes on axial compression characteristics were investigated through experiments and finite element analysis. The results indicate that the initiator of square holes can effectively reduce the initial peak crushing force (IPCF), but the reduced IPCF does not decrease exponentially with the increase of the number of holes, and the number and spacing of holes affect phases of wave crests and troughs on force–displacement curves. When at unequal spacings, the deformation mode of AFOTs changes in a sequence of extensional, mixed, and symmetric deformations with the increase in the spacing of the first hole. In view of wave crests and troughs with significant phase differences on force–displacement curves, a collaborative innovation combination mode based on AFOTs with different numbers and spacings of holes was proposed. A new, steady energy-absorbing structure, namely a structure combining four AFOTs, was developed by the combination of different numbers of tubes. In comparison with similar combined structures, the mean crushing force (MCF) is increased by 28.11% and the fluctuation in undulation of load-carrying capacity (ULC) is reduced by 66.09%.

Crashworthiness analysis of gradient hierarchical multicellular columns evolved from the spatial folding

Based on the gradient hierarchical distribution of vascular bundles of bamboo, a gradient hierarchical multicellular column (GHMC) evolved from the spatial folding was proposed. Crashworthiness analysis of GHMC was carried via Abaqus/Explicit. Results show that the proposed GHMC has better energy absorption ability compared with the square tube under the same thickness or the same mass. The folding wavelength of GHMC is significantly decreased and it can produce more number of folds compared with the square tube. Under the condition of the same mass, the peak crushing force of GHMC decreases meanwhile its energy absorption increase by 10.1% to 72.44% compared with the square tube. Effect of hierarchical level and cell wall thickness on the energy absorption and their deformation mode under different height-length ratio (H/L) and cell wall thickness have been analyzed. Simplified super folding element theory was used to predict the mean crush force of GHMC, and the results were in good agreement with the simulations.

Numerical simulation of crashworthiness parameters for design optimization of an automotive crash-box

Automotive manufacturers rely on rigorous testing and simulations to construct their vehicles durable and safe in all aspects. One such vital factor is crash safety, otherwise known as crashworthiness. Crash tests are conventional forms of non-destructive methods to validate the vehicle for its crashworthiness and compatibility based on different operating conditions. The frontal impact test is the most primary form of crash test, which focuses on improving passenger's safety and comfort. According to NHTSA, a vehicle is rated based on these safety criteria, for which automobile manufacturers conduct a plethora of crash-related studies. Numerical simulation aids them in cutting down testing time and overall cost endured by providing a reliable amount of insights into the process. The current study is aimed at improving the crashworthiness of a crash box in a lightweight passenger car, such that it becomes more energy absorbent in terms of frontal impacts. All necessary parameters such as energy absorption, mean crush force, specific energy absorption, crush force efficiencies are evaluated based on analytical and finite element methods. There was a decent agreement between the analytical and simulation results, with an accuracy of 97%. The crashworthiness of the crash box was improved with the help of DOE-based response surface methodology (RSM). The RSM approach helped in improving the design of the crash box with enhanced EA & CFE by 30% and 8.8% respectively. The investigation of design variables on the energy absorption capacity of the thin-walled structure was also done. For the axial impact simulations, finite element solver Virtual Performance Solution − Pam Crash from the ESI group is used.

Crushing behaviors of buckling-oriented hexagonal lattice structures

Lattice structures have been widely applied as energy absorbers in engineering. In this paper, buckling-oriented hexagonal lattice structures (BOHLSs) made of AISI 316 L were designed and printed by SLM (selective laser melting) technique. Quasi-static in-plane and out-of-plane compression experiments were carried out to investigate the crushing behavior and energy absorption and the effect of the structure. Numerical investigations were further performed to reveal the effects of different parameters on the crushing behavior and energy absorption of the BOHLS. It is shown that the buckling pattern can effectively improve the specific energy absorption (SEA) and the mean crushing force (MCF) of the hexagonal lattice structure (HLS) under quasi-static in-plane compression. On the contrary, under quasi-static out-of-plane compression, the SEA and MCF of the BOHLS were mostly smaller than the HLS. However, the initial peak force (IPF) of the BOHLS can be greatly reduced and the crushing efficiency is improved.

Crashworthiness analysis of bio-inspired fractal tree-like multi-cell circular tubes under axial crushing

This study proposes novel bio-inspired fractal multi-cell circular (BFMC) tubes for energy absorption. The inner structures of the proposed BFMC tubes were constructed based on the fractal tree-like forms found in many biological structures such as giant water lily and dragon blood tree. The crashworthiness performances of the proposed structures with different fractal orders and mass were numerically investigated. The numerical results indicated that the specific energy absorption (SEA) increased with the fractal order and the SEA of the 2nd-order BFMC tube was 35.43% higher than that of the conventional multi-cell circular tube. Furthermore, the complex proportional assessment (COPRAS) method was adopted to optimize the performance of the BFMC. The results demonstrated that the proposed structure with four number of tree-like branches and 2nd-order fractal provided the best performance. Finally, a theoretical derivation of the mean crushing force (MCF) was developed for the proposed tubes based on the simplified super folding element theory. The theoretical results of MCF agreed well with the numerical results. The findings of this study provide an effective guide for using the biomimetic approach with the fractal tree-like forms for the design of a multi-cell energy absorber with high energy absorption efficiency.

Mechanical reinforcement mechanism of a hierarchical Kagome honeycomb

A hierarchical Kagome honeycomb with triangular sub-structures (KHT) is proposed in this study. KHT is constructed by introducing hierarchical configurations to conventional Kagome honeycomb. The theoretical model is established to analyze the compressive behaviors in terms of plateau stress and specific energy absorption (SEA) based on two-scale analysis method. Compared to the conventional Kagome honeycomb (KH), subjected to y-direction loading, the improvement of mean crushing force (MCF) and SEA of KHT is up to 104% and 83%, respectively. The remarkable enhancement on crashworthiness induced by the hierarchical configuration is demonstrated by the theoretical spectrum. The predicted plateau stress and SEA show high agreement with the simulated results. The mechanical reinforcement can be further realized by tailoring the topology and the number of sub-structures and the structure relative density. Subjected to the increasing impact speed, the reinforcement generated by the hierarchical design is gradually eclipsed by the inertial effect. The reinforcement mechanism is explicitly revealed from the aspects of macroscopic wall interactions and microscopic sub-structures collapse patterns. This study provides insight and opportunities into the role of structural hierarchy in designing hierarchical honeycombs equipped with extraordinary energy absorption properties.

Crushing behaviors of buckling-induced metallic meta-lattice structures

Thin-walled lattice materials can be applied as energy absorbers in protective structures of civil defense. In this paper, quasi-static in-plane crushing tests were carried out to investigate the crushing behavior and energy absorption of buckling induced meta-lattice structures (BIMSs) with different central angles made of plastic iron material DT3 and formed by wire cutting technique. Three crushing patterns were revealed and analyzed. The test results clearly show that the initial peak force (IPF), the crushing force efficiency (CFE), the specific energy absorption (SEA) and the mean crushing force (MCF) can be substantially improved by introducing buckling pattern into the straight-walled lattice structure. The MCF of the BIMS was consistently predicted based on the simplified super folding element (SSFE) and the flattening element.

Foam-filled lightweight braided-textile reinforced and nested tubular structures for energy absorption applications

Composite tubular structures have excellent energy absorption (EA) and can be widely applied in lightweight energy absorbers. Made up of thin-walled braided-textile tubes and polyurethane (PU) foams, a hybrid carbon fiber-reinforced composite (CFRC) tubular structure with a simple making process and low cost was designed, made, and tested in this research. Through axial compression tests, the crushing mode, the EA, the specific energy absorption (SEA), the mean crushing force (MCF), the peak force (PF), and the peak force loss rate (PFLR) of the tubes were revealed. The experimental results indicate that filling PU foam can effectively improve the EA of thin-walled braided-textile reinforced tubes. The crushing mode changes from local buckling and diamond crushing mode to progressive annular crushing mode. The nesting of braided-textile tubes with different inner diameters can effectively increase the EA, the MCF, and the PF, but the SEA of some samples will decrease. Filling PU foam can effectively reduce the PFLR. The PLFR of the nested composite structure is negative, indicating that the MCF is greater than the PF within the effective crushing distance (ECD).

Low-velocity impact performance of composite-aluminum tubes prepared by mesoscopic hybridization

Novel circular hybrid structures with overlapped carbon-fiber-reinforced plastic (CFRP), glass-fiber-reinforced plastic (GFRP) and/or aluminum layers were fabricated. Such structures were hybridized at the mesoscopic scale, generating multiple CFRP-GFRP or composite-aluminum interfaces. Also, aluminum foam was utilized as inner filler to further enhance the energy absorption of the thin-walled structures. The interactive effects on crashworthiness among different materials were explored by axial drop-weight impact testing. The experimental results showed a progressive failure process of all CFRP/GFRP and composite/aluminum hybrid tubes. The mean crushing force (MCF) of empty CFRP/GFRP hybrid structures were significantly improved by more than 20% when compared to pristine CFRP tube. On the other hand, the composite/aluminum hybrid design effectively reduced the peak crushing force (PCF) and improved the crushing force efficiency (CFE). However, the specific energy absorption (SEA) was decreased by about 10% owing to the moderate strength-to-weight ratio of inserted aluminum sheet. Compared to empty tubes, the filling of aluminum foam significantly enhanced MCF by more than 10%, while declining SEA due to the low weight efficiency of aluminum foam. In sum, the proposed hybrid design maximized some aspects of crashworthy performance at a low cost, thereby promising for the future design of practical light-weight energy absorbers.

On the crashworthiness performance of novel hierarchical multi-cell tubes under axial loading

In recent years, the concept of hierarchy has been introduced into crashworthy design to explore an ultralight energy-absorbing structure with outstanding mechanical properties. In this study, a group of novel hierarchical multi-cell tubes (NHMTs) are proposed by replacing every sides of traditional multi-cell tubes with smaller square cells. The finite element model of NHMTs is first established and validated by experimental test. Then, the crashworthiness performance of NHMTs is analyzed and compared with taditional multi-cell tubes (TMTs). The results indicate that NHMTs exhibit superior crashworthiness behavior than TMTs and the hierarchical level has significant effect on the crashworthiness of NHMTs. Furthermore, in order to analyze energy absorption mechanism of NHMTs, the theoretical models of specific energy absorption (SEA) and mean crushing force (MCF) are established and validated. The result shows that the theoretical model of SEA and MCF can accurately predict the energy absorption behavior of NHMTs. This investigation offers a novel technique to design multi-cell tubes with excellent energy absorption capacity.

Multi-objective optimization of a multi-cellular aluminum extruded crush rail subjected to dynamic axial and oblique impact loading conditions

This work presents a multi-objective shape optimization study of a multi-cellular aluminum extrusion subjected to dynamic axial and oblique (20° angled) impact loading conditions. Finite element models are developed, validated with experimental data, parameterized, and used to exhaust the design space using a full factorial design of experiments. An analysis of different energy absorption characteristics, such as axial and oblique mean crush force, crush efficiency, and oblique impact coefficient, are presented. A multi-objective optimization problem is defined to generate new solutions that dominate a baseline profile in all aspects of performance, which produced a geometry with up to 16% improvements in energy absorption. The parametric study is used to define the “true” Pareto front, which is the set of non-dominated designs and the solution to the optimization problem. The response surface methodology (RSM) is used to perform the multi-objective optimization analysis. The traditional RSM approach is compared to an adaptive surrogate-assisted response surface method (ASA-RSM) in their speed and ability to identify the true Pareto front correctly. Using the traditional metamodel constraint, the traditional RSM approach could only identify 18% of the true Pareto front using up to 8% of the design domain. After relaxing the constraint, the traditional RSM approach still required approximately 63% of the entire domain to identify 67% of the true Pareto front accurately. In comparison, the ASA-RSM approach was able to identify 84.5% of the true Pareto front using 42% of the entire domain. In some instances, the ASA-RSM approach correctly identified 100% of the true Pareto front by using as little as 18% of the domain. However, the ASA-RSM approach’s peak performance is dependent on the initial sampling and resulting metamodel. This study provides a comprehensive understanding of the performance gains of multi-objective optimization in the application of structural crashworthiness considering various loading conditions.

Energy absorption characteristics of bio-inspired hierarchical multi-cell square tubes under axial crushing

In this study, the dynamic crushing behaviour and energy absorption characteristics of a novel bio-inspired hierarchical multi-cell square (BHMS) tubes were numerically and theoretically investigated. The proposed structures were constructed mimicking the gradient distribution of cell sizes in the biological structures such as bone and bamboo. A series of compression tests were numerically carried out for the BHMS structures with different hierarchical orders and mass of the structures. The results indicated that the specific energy absorption (SEA) of the 3rd order BHMS tube is 178.4% higher than that of the 0th order BHMS tube. Comparing with the conventional square and multi-cell square tube, the maximum increment of the SEA of the BHMS tube reaches up to 173.7% and 128.1%, respectively. Moreover, the undulation of the load-carrying capacity (ULC) used for evaluating the stability of the BHMS tubes under dynamic crushing was also considered. The ULC of the 3rd order BHMS tube reduces up to 88.8% and 85.7% compared to the square and multi-cell tubes. It indicates that the BHMS tube has a larger potential to improve energy absorption than the square tube and conventional multi-cell square tube. Finally, a theoretical study for the mean crushing force (MCF) was developed for the proposed tubes, which was in good agreement with the numerical results. This study provides an effective guide for the design of a multi-cell energy absorber with excellent energy absorption efficiency.