Multi-objective topology optimization of energy absorbing structures incorporating shape memory polymers: Design, behavior, and recoverability

A Hat-shaped Multi-cell Core (HMC) was developed, drawing inspiration from aperiodic monotile geometry, with geometric parameterization defined by characteristic angle [Formula: see text] (0[Formula: see text] to 90[Formula: see text]) and wall thickness [Formula: see text] (0.03–0.10 mm). The configuration was engineered to achieve superior multi-criteria crashworthiness performance compared to Conventional Honeycomb Core (CHC) through tunable morphological design. The energy absorption mechanism of HMCs was theoretically modeled through a discretization method employing Typical Angle Elements (TAEs), with theoretical predictions rigorously validated against Finite Element (FE) simulation results demonstrate predictive accuracy within 5% error tolerance, and the FE model was validated by quasi-static compression tests using a HMC specimen, demonstrating strong agreement between simulation and experiment. Comparative analysis at [Formula: see text] mm revealed that HMCs within [Formula: see text][Formula: see text] exhibited superior multi-criteria crashworthiness compared to CHC, demonstrating 7.7% to 16.3% Peak Crush Force (PCF) reduction with concomitant improvements of 6.8% to 8.2% in Specific Energy Absorption (SEA) and 13.2% to 15.1% in Crush Force Efficiency (CFE). The [Formula: see text] configuration was identified as a Pareto-optimal design with balanced crashworthiness criteria (PCF: 17.66 kN, SEA: 23.05 kJ/kg, CFE: 0.25), achieving a 197% higher comprehensive crashworthiness criterion [Formula: see text] than CHC. A multi-objective optimization framework integrating polynomial surrogate models (quadratic for PCF, cubic for SEA/CFE) and Multi-Objective Particle Swarm Optimization (MOPSO) identified optimal configurations across four optimization scenarios. Case-4 optimization yielded an optimal solution at [Formula: see text] and [Formula: see text] mm (PCF: 18.439 kN, SEA: 22.993 kJ/kg, CFE: 0.268). These findings substantiated the superior crashworthiness performance of HMCs over CHC in selective multi-criteria optimization, while establishing a theoretical framework to guide subsequent design iterations and parametric refinements of HMC configurations.

Multiobjective crashworthiness optimization of multi-cornered thin-walled sheet metal members

Crashworthiness performance and multiobjective optimization of a combined splitting circular tube energy absorber under eccentric impact for subway vehicles

Crashworthiness analysis and multiobjective optimization of bio-inspired sandwich structure under impact load

Two strategies are proposed to design new hierarchically reinforced double-square tubes (HRDST). Strategy A: adding triangles from inside to outside in one direction. Strategy B: adding triangles along both the outer and inner quadrilateral directions at the same time. Their crashworthiness analyses are carried out under the conditions of the same wall thickness and the same mass. The results show that the proposed double square tubes, combined with the gradient hierarchical design, can effectively improve the crashworthiness of the structure under both conditions. The improvement of strategy B is more significant than that of strategy A. The energy absorption (EA), specific energy absorption (SEA), and crushing force efficiency (CFE) and initial peak crush force (IPCF) of HRDSTB-3 are improved by 2343.87%, 493.17%, 573.74% and 262.73%, respectively, under the same wall thickness. The EA, SEA, CFE of HRDSTB-3 also increased by 111.23%, 111.23%, and 226.34%, respectively, for the same mass, while the IPCF decreased by 35.27%. The parametric study shows that the effect of wall thickness on structural crashworthiness is significant, but the rate of increase between two adjacent wall thicknesses decreases as the wall thickness increases. The inner and outer edge length ratios (k) also have a substantial effect on structural crashworthiness, with SEA and CFE being 24.42% and 23.47% higher for k = 5/12 compared to k = 8/12 for HRDSTA-3, and 29.24% and 27.55% higher for k = 4/12 compared to k = 8/12 for HRDSTB-3. Finally, comparing HRDSTA-3 and HRDSTB-3 with other square-layered multicellular designs, the results show that the two designs proposed in this paper, combining double square tubes with gradient hierarchies, exhibit better crashworthiness. Compared with MSTL2-2, the SEA of HRDSTA-3 and HRDSTB-3 are 27.98% and 33.01% higher, respectively, and the CFE is 27.86% and 32.96% higher, respectively.

Nowadays usage of vehicles tremendously increased throughout the world. The crashworthiness of vehicle structures plays a crucial role in ensuring passenger safety during collisions; in order to improve the energy absorption behaviors, this research aims to introduce the new arrangements of truncated single, double and tri tubes. Both experimental and numerical axial compression loading is done on 6 different orientations in normal and reversed taper tubes and made to analyze various crashworthiness indicators such as peak crushing force (Fpeak), mean crushing force (Fmean), total energy absorption (TEA), specific energy absorption (SEA) and crush force efficiency (CFE). The deviations between experimental and numerical results are very close to each other. Further, a multi-objective optimization of factors affecting crashworthiness indicators was given utilizing the Taguchi technique and Grey relational analysis (GRA). The findings indicate that, in comparison to an inline order configuration, the TEA increases when the tubes are arranged in triangle order with SEA and CFE also increase in reasonable manner. It is observed that the reversed taper orientation withstands for the maximum crash loads in all the orientations.

Inspired by the hierarchical distribution of canine osseous structures and the inherent stability of triangular configurations, this article introduces a novel bio-inspired bidirectional gradient hierarchical triangular honeycomb (HTH) structure. This design integrates hierarchical strategies within triangular structures, founded upon a hexagonal framework. By manipulating the dimensions of the inner hexagon, two distinct configurations are developed: the hierarchical equilateral triangular honeycomb (HETH) and the HTH. Experimental methodologies are employed to validate the established finite element model. Subsequently, this verified model is utilized to systematically investigate the effects of parameters such as hierarchy and triangular geometry on structural performance. The findings reveal that, under equivalent wall thickness conditions, structures with higher hierarchical configurations exhibit superior crashworthiness. Specifically, HETH-3 demonstrates enhancements of 1326% in energy absorption (EA), 300% in specific energy absorption (SEA), 256% in initial peak crushing force (IPCF), and 301% in crushing force efficiency (CFE), when compared to HETH-0. Similarly, HTH-3 displays improvements of 1181% in EA, 254% in SEA, 261% in IPCF, and 255% in CFE relative to HTH-0. Under equivalent mass conditions, higher hierarchical structures also significantly outperform their lower counterparts. Furthermore, when compared to other conventional hierarchical honeycombs of the same mass, the SEA and CFE values of the vertex-based HTH (VBT) were only 79% of those of HETH-3, while the SEA and CFE of HTH-3 were 95% of HETH-3. The proposed bio-inspired bidirectional gradient HTH structure, informed by natural bone architecture, demonstrates enhanced crashworthiness, offering valuable insights for the design of lightweight 3D-printed honeycombs with exceptional mechanical properties.

In this study, the crush behaviour of thin-walled straight and conical shell structures was systematically determined for various absorber designs and investigated comparatively under axial impact loading. The main parameters in the design of these structures are cross-section geometry, wall thickness and semi-apical angle. Several cross sections have been studied: circular, square and hexagonal. In the finite element simulations, these designs were fixed at one end and impacted by a rigid wall from the other with specified mass and velocity giving the required impact energy according to the European regulation ECE R29 by using explicit finite element code LS-Dyna. After crash simulations, energy absorption characteristics and crush forces were obtained for each crush element having different cross sections, wall thicknesses and semi-apical angles. Peak crush force, mean crush force, crush force efficiency and specific energy absorption (SEA) were calculated for a deformation length of 100 mm. In all cases it was found that tubes were crushed progressively. The results of the simulations showed that the square cross-sectioned energy absorber has the lowest crush force efficiency among three cross-section geometries. The crush force efficiency was found to be the highest for the circular absorber which has a semi-apical angle of 12.5° and a wall thickness of 2 mm. Finally, the peak crush forces were lowered by creating blanks and corrugations.

A double-tapered rectangular tube with diaphragms (DTRTD) for energy absorbance in railway vehicles is proposed. The mean crushing force (MCF) of DTRTD was derived. The code LS-DYNA3D (971) was used to build a finite element model, validated using a quasi-static test. The experiment results and numerical simulation indicate the accuracy of the theoretical prediction for the MCF of DTRTD and the regularity and stability of the collapse pattern of this energy-absorbing structure (EAS). To explore the effects of the thickness of different EAS parts on the crashworthiness indexes and obtain the optimal designs, the design of experiment (DOE) and a surrogate model were employed for a parameter study and multi-objective optimisation (MOO). The specific energy absorption (SEA) and crush force efficiency (CFE) cannot reach the optimal values concurrently. Nonetheless, all designs from the Pareto front of MOO significantly improve the crashworthiness of EAS because of the larger SEA and CFE.

In the automotive industry, sustainable materials, such as bio-composites, are progressively being adopted due to their lightweight feature, which reduces vehicle weight, fuel consumption and pollutants emissions. Bio-composites are renewable and biodegradable, making them more environmental-friendly. However, limited investigations into the use of bio-composites in crash box applications have indicated that they lack the impact strength to fully absorb collision energy. This study aims to compare the crashworthiness performance of crash boxes made from OPEFB fiber/epoxy and kenaf fiber/epoxy composites, with conventional steel and carbon fiber/epoxy using LS-DYNA quasi-static simulations. Six different crash box designs are proposed: square, hexagonal, decagonal, hexagonal 3-cell, hexagonal 6-cell, and decagonal 10-cell structure, to evaluate the effect of these designs on crash box performance. The results show that bio-composite crash boxes are inferior to traditional materials in terms of energy absorption and specific energy absorption, but they yield better performance in crush force efficiency. In terms of design, decagonal 10-cell structure produces the highest specific energy absorption and energy absorption for bio-composites. Hence, optimization is performed on the OPEFB fibre/epoxy decagonal 10-cell crash box, aiming to increase energy absorption capability by varying the thickness, perimeter, and length of the crash box. The design is optimized by increasing thickness and maintaining length and perimeter. Compared to the original design, the optimized design improves energy absorption by 59% and specific energy absorption by 19%. The optimized design is then subjected to both quasi-static and impact loading tests, revealing that the optimized OPEFB fibre/epoxy crash box design exhibits 44% lower energy absorption than steel under quasi-static load, but it demonstrates a 56% increase in crush force efficiency and a 6 % increase in specific energy absorption. Under impact load, it shows a 91% increase in specific energy absorption compared to the traditional square steel crash box.

Crashworthiness is vital for vehicle safety. It ensures structures absorb impact efficiently, reduces occupant injuries, and enhances survival rates. This increases the demand for researchers to design and optimise the crash box with better crashworthiness parameters. The research aims to evaluate the effects of horizontal grooves inspired by bamboo nodes on the crashworthiness of square tubular structures in crash boxes, optimising their design for improved safety. AL6063 square tubes (50 × 50 mm cross-section, 3 mm thickness, 140 mm height) with 0, 2, 4, 6, and 8 horizontal square grooves (1 mm size) were modelled with a CAD programme. Finite Element Analysis (FEA) was performed using the FEA programme to assess crashworthiness parameters, including Energy Absorption (EA), Specific Energy Absorption (SEA), Initial Peak Crushing Force (IPCF), Mean Crushing Force (MCF), and Crush Force Efficiency (CFE). The four-grooved tube reduced IPCF by 16.81%, increased EA by 4.85%, SEA by 5.9%, MCF by 6.4%, and CFE by 27.91% compared to the plain tube. Incorporating four horizontal grooves optimises crashworthiness, with performance declining beyond this number. Thus, four grooves provide the best enhancement for crash boxes.

The potential of 3D-printed AlSi10Mg auxetic structures for diverse mechanical and energy-absorbing needs remains untapped. This article reveals a multi-criteria framework for the laser powder bed fused (L-PBF) −υ architecture considering elastic modulus (E), yield strength (σy), specific energy absorption (SEA), peak crush force (PCF) and crush force efficiency (CFE). The framework seamlessly combines trial data, multi-criteria decision-making, and performance indicators. Five auxetic structures were 3D-printed, characterised for mechanical and energy absorption traits within a 0.17–0.26 relative density range. The outcomes revealed a range of values for various parameters, including the Poisson’s ratio (−0.03 to −0.22), porosity (80.87–87.60 %), CFE (33–83 %), elastic modulus (100–632 MPa), yield strength (1.8–10 MPa), and SEA (0.5–6.8 kJ/kg). The reliability of these structures was ensured through a meticulous selection process based on an extensive literature review and empirical validation. To address the limitations of theoretical models, our work goes beyond theoretical predictions by experimentally validating these properties and integrating advanced methodologies such as the ‘analytic hierarchy process’ (AHP) and the ‘technique for order of preference by similarity to ideal solution’ (TOPSIS). This allows us to determine the best-performing auxetic architecture. The decision-making process was informed by five user-defined parameters prioritised in the order of CFE>−υ> E>σy> SEA based on their relative closeness identifying AUX5 as the best performing auxetic architecture. This study introduces an innovative method for crafting scenario-based auxetic architectures with varying performance levels based on their relative importance.

Investigation of the effect of friction force on the energy absorption characteristics of thin-walled structures loaded with axial impact force

This work investigates the crash response of conical tubes made from different steel grades ranging from low to high strength steels using finite element (FE) simulations. The FE model was first validated against experimental results before being applied for the numerical analysis using LS DYNA software. Peak crushing load, mean load, energy absorption, crush force efficiency (CFE) and specific energy absorption (SEA) were evaluated from the cones of different steel grades and of various thicknesses. It was found that high strength steel exhibit high SEA and low CFE values. Both SEA and CFE were found to increase with increase in tube wall thickness for the five steel compared. For improved safety of the occupant, steel-CA5 is best because of higher CFE values for 1.5 mm, 2.0 mm and 2.5mm thicknesses. For better weight reduction, steel-DP600 with SEA of 10.6 kJ/kg is the best. Steel-HA3 and steel-SAP H440 with 2.5 mm thickness offer moderate CFE and SEA values. The findings of this study are useful in designing high safety performance vehicle front energy absorption components. Keywords : Conical tube; Crashworthiness; Crush force efficiency; Specific energy absorption

The paper corrugation tube is an innovative kind of energy absorbing structure and shock absorber which can play an important role on the cushioning energy absorption for airdrop equipments and transportation packaging. The deformation characteristics and failure modes of the regular triangle, quadrangle, pentagon and hexagon paper corrugation tubes were comparatively studied by a series of axial static compression experiments, the cushioning energy absorption was evaluated by the seven characteristic parameters ( e.g. initial peak force, mean crush force, total energy absorption, specific energy absorption, crush force efficiency, unit area energy absorption and stroke efficiency), and the influences of tube direction, cross-sectional shape, tube length and compression rate on failure modes and cushioning energy absorption were analyzed and compared. These researches showed that the tubes along X direction only have the accordion deformation mode, yet the tubes along Y direction have four deformation modes including steady state progressive buckling, Euler buckling, angular tear and transverse shear. For the paper corrugation tubes along Y direction, the cross-sectional shape has obvious influence on the cushioning energy absorption of structures, and the specific energy absorption and unit area energy absorption of regular triangle and pentagon tubes are better than those of the tubes with regular quadrilateral and hexagonal cross-section at compression rates of 12 and 48mm/min. The tube length of 150 mm or compression rate of 72 mm/min would cause the increase of contribution proportion of non-ideal deformation mode and the decrease of cushioning properties. The paper corrugation tubes along X direction have more stable and controllable deformation mode, yet the paper corrugation tubes along Y direction have better cushioning energy absorption.