Energy Absorption Model Research Articles

Mechanical response characteristics and cushioning of sealed airbags under different length–diameter ratios

In the event of a mine fire, rapidly constructing blast-resistant seals is one of the most effective measures to contain the disaster. This study conducted blast cushioning experiments on sealed airbags and numerical simulations by analysis system/Livermore software-dynamics (ANSYS/LS-DYNA), an explicit simulation software, to analyze the mechanical response characteristics and cushioning effectiveness of sealed airbags under different length-to-diameter ratios. The research results indicate that airbags with different length-to-diameter ratios all exhibit cushioning effects, and the airbag can recover its deformation after pressure release. As airbag length increases, vertical deformation along the pipeline appears, forming a radial compression failure mode. Stress concentrations are mostly located at the edges of the airbag, while arched structures can reduce the concentrated stress. Excessively long or short airbags significantly increase localized stress concentrations. The total energy absorbed by the airbag during cushioning shows a linear relationship with its length, and an energy absorption model for single-chamber airbags with varying length-to-diameter ratios was established. Under full-scale simulation conditions, the optimal length-to-diameter ratio range is 0.75:1. The reflected energy of shockwave encountering airbag is independent of airbag length and remains a fixed value when inflation pressure remains constant. These findings provide theoretical support for the design and application of explosion-resistant airbag.

On the role of local reinforcement in an adhesively bonded AL/CFRP energy absorber under axial loading: A theoretical investigation and optimization

AbstractThis paper aims to develop a novel theoretical model that incorporates the effects of local composite reinforcement using adhesive bonding on the energy absorption of aluminum structures under axial loading. The goal is to optimize energy absorption prior to any connection failures and to prevent uneven structural deformation. Moreover, it strives to reduce the structure's weight and material usage, achieving superior results compared to traditional global reinforcement techniques. The theoretical model was validated through experimental testing and finite element analysis, demonstrating good agreement with the predicted results. The results reveal that increasing the CFRP fiber angle, layer thickness, and number of layers generally leads to improved energy absorption capacity. An optimization analysis was performed to determine the optimal design parameters, yielding a fiber angle of 80°–90°, composite thickness of 1.5 mm, and aluminum thickness of 2.5 is the best configuration, offering the highest specific energy absorption and adequate peak load capacity for maximized energy absorption. The proposed model offers significant improvements over existing approaches, enhancing the predictive capabilities and practical applicability of energy absorption predictions in engineering design.Highlights A novel theoretical model for energy absorption in locally reinforced hybrid AL/CFRP structures. The influence of design parameters, such as CFRP layer count, fiber orientation, and thickness ratio. Optimization to maximize the average crushing force while meeting weight and geometric constraints. Findings can inform the design of safer and more efficient energy‐absorbing structures in various applications.

Theoretical model of energy absorption for square tubes under transverse loading with variable axial constraint condition

Thin-walled tubes in the actual engineering structure (e.g., autobody) are usually connected to other structure, and the boundary constraint condition at both ends of tubes are usually very complex when bending deformation occurs under transverse loading. This paper aims at the effect and mechanism of axial constraint on the bending energy absorption effect of thin-walled tube under limited and variable axial constraint condition at both ends. A typical of thin-walled tube, square tube, is taken as an example. Firstly, we compare the experiment results of square tube under transverse loading with three-point-bending condition and fully clamped condition, revealing that the axial constraint force has a significant effect on the energy absorption effect. After that, a FE model of the square tube under variable axial constraint condition at both ends is established and validated based on experiment. Based on the validated FE model, the effect of different sizes of axial constraint stiffness on the bending energy absorption of square tube are investigated, and it is found that it has a significant effect on the deformation mode and bending energy absorption. With the increase of axial constraint stiffness, it will mainly affect the latter segment of the force–displacement curve in the bending process, which increases the bending energy absorption. Finally, theoretical models are developed to predict the force–displacement curves and bending energy absorption of the square tube under three different types of variable axial constraint properties: linear axial constraint, unequal linear axial constraint and nonlinear axial constraint.

Design and Performance of Layered Heterostructure Composite Material System for Protective Armors.

A new layered heterostructure composite material system (TC4 as front layer and 2024Al alloy as back layer) was developed and analyzed for its design and performance in terms of an enhanced absorption capability and anti-penetration behavior. The Florence model for energy absorption was modified, so that it can be utilized for the layered heterostructure composite material system with more efficacy. Numerical simulation through Ls-Dyna validated the analytical model findings regarding the energy absorption of the system and both were in good agreement. Results showed that two ductile materials with diverse properties, the hardness gradient and varied layer thickness joined together, specifically behaved like a unified structure and exhibited elastic collision after slight bending, which is possibly due to the decreased yield strength of the front layer and increased yield strength of the second layer. To validate the analytical and numerical findings, the samples of the layered heterostructure composite material system were subjected to a SHPB (Split Hopkinson pressure bar) compression test. The deformation behavior was analyzed in the context of the strain energy density and stain rate sensitivity parameter at different strain rates. The encouraging results proposed that two ductile materials with a hardness gradient can be used as an alternate structure instead of a brittle-ductile combination in a layered structure.

Experimental Characterization and Numerical Modelling of the Impact Behavior of PVC Foams

BackgroundPolyvinyl chloride (PVC) foams are widely used in crashworthiness and energy absorption applications due to their low density and the capability of crushing up to large deformations with limited loads. This property is due to their particular constitutive behavior: the stress-strain curve is characterized, after an initial yield or peak stress, by a relevant plateau region followed by a steep increase due to foam densification. Furthermore, the mechanical response of PVC foam is strongly strain rate dependent.ObjectiveThis work aims to characterize the mechanical behavior of PVC foams and to develop a complete constitutive model for impact and energy absorption applications.MethodsCompressive tests are carried out at different speeds on PVC foam samples having different relative densities. Quasi-static and intermediate strain rate tests are performed by a pneumatic machine, while high strain rate tests are conducted by means of a Split Hopkinson Pressure Bar. The uniaxial stress-strain curves are used to calibrate the visco-elastic and visco-plastic constitutive model. In particular, the material behavior is divided into two parallel branches: the former describes the elasto-plastic behavior, while the latter accounts for the visco-elastic one; the plastic branch also includes a multiplicative term accounting for the strain rate sensitivity of the base material.ResultsThe tests highlight a strong compressibility of the foam with negligible lateral expansion. The energy absorption efficiency, as well as the densification strain, is evaluated. The material model is also implemented in Finite Element (FE) simulations of puncture impact tests, validating the results of the calibration procedure.ConclusionsThe calibration of the visco-elasto-plastic material model offers a physically consistent identification of the constitutive response of the PVC foams, showing an effective characterization of the impact behavior of the material.

Annular laser cladding of CuPb10Sn10 copper alloy for high-quality anti-friction coating on 42CrMo steel surface

Reducing the damage caused by friction and wear to components such as Al alloy parts could extend the service lives of parts in automobile and other industrial fields. An effective approach to this is improving the anti-friction properties of key surfaces. In this study, an annular laser cladding (ALC) method was designed, an energy absorption model of the ALC process was established, and the cladding of a CuPb10Sn10 copper alloy coating on a 42CrMo steel surface was studied experimentally. The effects of the ALC process parameters on the laser absorptivity, porosity, and microstructure of the ALC sample were analyzed, and the coating properties (e.g., microhardness and anti-friction properties) were evaluated. The results showed that laser cladding of a CuPb10Sn10 copper alloy coating or other coating materials with low absorptivity could be realized on the surface of 42CrMo steel using the ALC process. The ALC process increased the laser absorptivity to 58 %, and the porosity of the ALC sample was reduced to 0.39 %. The coating microstructure was divided into three layers, in which the top layer of the Cu-rich phase had a uniform structure and no macroscopic crack defects. The main anti-friction component Pb phase and other Cu, Pb, and Sn elements were uniformly distributed. The microhardness of the coating fluctuated, and the value of the top-layer Cu-rich phase was approximately 120 HV0.3. The shear strength of the coating was 194 MPa, and the friction coefficient of the coating decreased by approximately 50 % to 0.19. The ALC method effectively improved the laser absorptivity during the laser cladding of copper alloys on iron substrates, providing theoretical guidance for designing and manufacturing anti-friction functional components in the automotive industry and other fields.

Ballistic response of ultra-high molecular weight polyethylene laminate impacted by mild steel core projectiles

This paper presents the effect of interlaminar shear property on the ballistic response of ultra-high molecular weight polyethylene (UHMWPE) fiber composite laminate and discusses the detailed progressive ballistic damage process. Specifically, two kinds of UHMWPE fiber composite laminates with different interlaminar shear strength (ILSS) are impacted by a standard projectile (7.62 mm × 39 mm), and their multi-scale internal damage morphologies are characterized. Based on damage patterns, an evaluation model of laminate energy absorption is established to analyze the dissipation mechanism of the kinetic energy of the projectile. Results of ballistic tests indicate that the reduction of ILSS may result in the degradation of anti-penetration performance and in more serious internal damage. Internal damage morphologies show that shear fracture and delamination fracture are the primary failure modes during ballistic impact. The energy absorption by the laminate via tensile deformation, delamination failure and shear failure may account for 56.21%, 17.45%, and 16.49% of the projectile kinetic energy, respectively. Hence, tensile deformation may be the primary energy dissipation mechanism of projectile kinetic energy.

Modeling of the quantitative effect of temperature on key mechanical properties of metal foams

In this study, the effect of temperature and external force on the plastic collapse of metal foams was briefly analyzed firstly. Subsequently, the maximum energy density for the plastic collapse of the material at different temperatures was put forward. Finally, a temperature-dependent energy absorption model, a temperature-dependent plastic collapse strength model, and a temperature-dependent plateau stress model were developed. The proposed models have no fitting parameters and simple structure. The accuracy and practicality of the models are well verified by comparison with the available 12 sets of experimental data over a wide temperature range (the highest temperature reached 0.83Tm). The temperature-dependent energy absorption model and the temperature-dependent plastic collapse strength only need data at room temperature to quickly predict their energy absorption and plastic collapse strength at different temperatures. These two models can be used as an optional method for rapidly assessing the high-temperature mechanical properties of metal foams. This work has important implications for the further development of metal foams applications in high-temperature service environments such as aerospace.

Dynamic Model of Impact Energy Absorption by a Conveyor Belt in Interaction with the Support System

Measurements of the dynamic load of conveyor belts of identical strengths were used to evaluate and compare the data for belts with and without a support system. The goal was to identify the effects of the support system in terms of a relative amount of impact energy absorbed by a conveyor belt. A dynamic model was designed based on selected parameters of the impact process. Damage to conveyor belts, caused by the absorption of impact energy, was evaluated using the applied methods of mathematical statistics.

A new method for design and calculating the mechanical properties and energy absorption behavior of cellular structures using foam microstructure modeling based on Laguerre tessellation

In this paper, the elastic modulus and energy absorption behavior of cellular structures such as aluminum foams have been investigated. The main purpose of this study is to develop microstructure modeling of cellular structures and to study their elastic–plastic behavior through finite element method. In this research, first a unit cell is prepared to reduce numerical calculations, which has the characteristics of the main foam. The behavior of the unit cell under impact is then simulated and analyzed by the finite element method. Using simulated experiments, a model using the response surface method to obtain the densification strain, elastic modulus, mean plastic stress, yield stress as well as foam compaction behavior will be presented. Finally, the results of finite element and response surface methods for cellular structures with experimental results is validated. The results of this study showed that the possibility of modeling and analysis of energy absorption (impact) of foams is possible using the response surface model presented in this study and finally a suitable model can be achieved to analyze the microstructure of different foams. As a consequence, the hybrid cellular structures are simulated in view of applications of foams as filler in the thin-walled structures about energy absorption subject.

Relationships between distribution characteristics of ceramic fragments and anti-penetration performance of ceramic composite bulletproof insert plates

Through quantitative statistics and morphological characterization of ceramic fragments for ceramic composite bulletproof insert plates (CCBIPs), distribution characteristics of ceramic fragments within a specific size range were analyzed for different Armor Piercing Incendiary (API) and shot times. To quantitatively evaluate the effect of energy absorption for ceramic plates, a model of energy absorption during penetration for CCBIPs was established based on statistics of the size distribution of ceramic fragments (SDCF). Variation in the SDCF and its influence on energy absorption for CCBIPs were investigated. The results indicate that the distribution feature of ceramic fragments in the range of 0.25–2.25 mm is Gaussian distribution. Compared with Type 56 of API (56-API), ceramic fragments formed by 53-API with higher kinetic energy possess more quantity and more concentrated distribution, whose average equivalence size decreases by 6.5%, corresponding to increasing by 83.9% of estimated energy absorption. Besides, the ability of CCBIPs to resist the third shot is significantly weakened, whose estimated energy absorption decreases by 58.8% compared with the first shot. More concentrated distribution and fewer fragments are formed after the third shot, the average equivalence size of ceramic fragments increases by 6.9%, which may attribute to the micro-cracks induced by the previous two shots.

Study on laser welding of copper material by hybrid light source of blue diode laser and fiber laser

Focusing on the problem of high-power laser welding of high reflectivity of copper, in this article, a physical model of energy absorption for the temperature field of hybrid laser deep penetration welding of copper materials is established by using a Gaussian rotating body heat source of 450 nm blue diode laser and 1060 nm fiber laser. The main factors are analyzed such as welding joint design, laser energy density, focal position, and shielding gas. When the 1000 W fiber laser is combined with a 300, 500, and 700 W blue diode laser to weld copper material, the relationship between the welding temperature field and the light source absorption rate is analyzed on the condition of a hybrid heat source distance of 2.2–6.2 mm and a welding speed of 10–30 mm/s. The results show that the absorption rate of a fiber laser welded by double-beam hybrid welding can be increased by 20% compared with that of a single light source; that is, 300, 500, and 700 W blue diode laser together with 1000 W fiber laser combines to weld copper materials, and the absorption rate of the light source reaches the highest when the hybrid heat source distance and the welding speed are 3.0 mm and 20 mm/s, respectively.

Interpenetrating Lattices with Tailorable Energy Absorption in Tension

This paper introduces the chain lattice, a hierarchical porous structure comprising two interpenetrating cellular solids. One constituent toughens the material and prevents catastrophic localized failure while the other serves as a porous matrix which densifies to absorb energy during tensile loading. Through tension testing, we demonstrate 3D-printed plastic chain lattices that exhibit delocalized damage and an order of magnitude increment in strain-to-failure over the fully dense base material. These experiments validate a micromechanics-based model of tensile specific energy absorption, which we then use in a parametric study on the effects of chain geometry and matrix properties on tensile behavior. We find that ceramic chain lattices can achieve an order of magnitude improvement in tensile specific energy absorption over the fully dense material, in line with the improvement seen when forming monolithic ceramics into fiber-reinforced ceramic matrix composites. The experiments and analysis highlight the ability of the chain lattice to impart damage-tolerance to 3D-printable materials that are normally brittle and flaw-sensitive.

A machine learning approach to estimate the strain energy absorption in expanded polystyrene foams

Traditional modeling of mechanical energy absorption due to compressive loadings in expanded polystyrene foams involves mathematical descriptions that are derived from stress/strain continuum mechanics models. Nevertheless, most of those models are either constrained using the strain as the only variable to work at large deformation regimes and usually neglect important parameters for energy absorption properties such as the material density or the rate of the applying load. This work presents a neural-network-based approach that produces models that are capable to map the compressive stress response and energy absorption parameters of an expanded polystyrene foam by considering its deformation, compressive loading rates, and different densities. The models are trained with ground-truth data obtained in compressive tests. Two methods to select neural network architectures are also presented, one of which is based on a Design of Experiments strategy. The results show that it is possible to obtain a single artificial neural networks model that can abstract stress and energy absorption solution spaces for the conditions studied in the material. Additionally, such a model is compared with a phenomenological model, and the results show than the neural network model outperforms it in terms of prediction capabilities, since errors around 2% of experimental data were obtained. In this sense, it is demonstrated that by following the presented approach is possible to obtain a model capable to reproduce compressive polystyrene foam stress/strain data, and consequently, to simulate its energy absorption parameters.

Identification of the LLDPE Constitutive Material Model for Energy Absorption in Impact Applications.

Current industrial trends bring new challenges in energy absorbing systems. Polymer materials as the traditional packaging materials seem to be promising due to their low weight, structure, and production price. Based on the review, the linear low-density polyethylene (LLDPE) material was identified as the most promising material for absorbing impact energy. The current paper addresses the identification of the material parameters and the development of a constitutive material model to be used in future designs by virtual prototyping. The paper deals with the experimental measurement of the stress-strain relations of linear low-density polyethylene under static and dynamic loading. The quasi-static measurement was realized in two perpendicular principal directions and was supplemented by a test measurement in the 45° direction, i.e., exactly between the principal directions. The quasi-static stress-strain curves were analyzed as an initial step for dynamic strain rate-dependent material behavior. The dynamic response was tested in a drop tower using a spherical impactor hitting a flat material multi-layered specimen at two different energy levels. The strain rate-dependent material model was identified by optimizing the static material response obtained in the dynamic experiments. The material model was validated by the virtual reconstruction of the experiments and by comparing the numerical results to the experimental ones.

Experimental study and numerical simulation for the interaction between laser and PEEK with different crystallinity

Polyetheretherketone (PEEK) sheets with the thickness of 0.5 mm were prepared by compression molding process using Victrex PEEK-450PF, and then PEEK sheets with different crystallinities were obtained by controlling the cooling rate. The optical characteristics of the samples were respectively measured by laser power meter, UV-VIS-IR spectrophotometer. And with the process parameters of laser power density of 245 W/cm2 and moving speed of 5 mm/s, the effect of crystallinity on the laser energy absorption of PEEK and the influence of laser irradiation on the crystallization properties of PEEK sheets were systematically studied. Finally, numerical model of laser energy absorption by PEEK was constructed with COMSOL software. The results show that the reflectivity of PEEK will increase with the increase of crystallinity, while the transmittance decreases. The pure PEEK sheets do not strongly absorb the laser at the wavelength of 1070 nm and the amorphous PEEK is more likely to be ablated. Carbonized samples during the laser irradiation was taken for XRD test and found to be amorphous. After laser irradiation, the crystallinity of the semi-crystalline PEEK material will decrease, but the originally amorphous peek crystallinity will increase slightly. Besides, the numerical simulation results are in good agreement with the experimental results.

Carbon Fibers Embedded with Aligned Magnetic Particles for Efficient Electromagnetic Energy Absorption and Conversion.

Harvesting electromagnetic (EM) energy from the environment and converting it into useful micropower is a new and ideal way to eliminate EM radiation and while providing power for microelectronic devices. The key material of this technology is broadband, ultralight, and ultrathin EM-wave-absorbing materials, whose preparation remains challenging. Herein, a high magnetic field (HMF) strategy is proposed to prepare a biomass-derived CoFe/carbon fiber (CoFe/CF) composite, in which CoFe magnetic particles are aligned in CFs, creating magnetic coupling and fast electron transmission channels. The graphitization degree of CFs is improved via the "migration catalysis" of CoFe particles under HMF. The HMF-derived CoFe/CF shows a largely broadened EM wave absorption bandwidth under ultralight and ultrathin conditions (1.5 mm). Its absorption bandwidth increases 5-10 times compared with conventional CoFe/CF that has randomly distributed CoFe particles and surpasses the reported analogues. A device model for EM energy absorption and reuse is designed based on the HMF-derived CoFe/CF membrane, which exhibits a 300% higher capability than conventional CoFe/CF membrane in converting EM energy to thermal energy. This work offers a new strategy for the design and fabrication of broadband, ultrathin, and ultralight EM wave absorption materials and demonstrates a potential conversion approach of the waste EM energy.

Statistical Model for Impact and Energy Absorption of 3D Printed Coconut Wood-PLA

Fused deposition modeling (FDM)-3D printing has been the favored technology to build functional components in various industries. The present study investigates infill percentage and infill pattern effects on the printed parts’ impact properties through the 3D printing technique using coconut wood-filled PLA composites. Mathematical models are also proposed in the present study with the aim for future property prediction. According to the ASTM standard, fifteen specimens with different parameter combinations were printed using a low-cost FDM 3D printer to evaluate their impact properties. Statistical analysis was performed using MINITAB to validate the experimental data and model development. The experimental outcomes reveal the honeycomb pattern with 75% infill density achieves the highest energy absorption (0.837 J) and impact energy (5.1894 kJ/m2). The p-value from statistical analysis clearly shows that all the impact properties are less than the alpha value of 0.05, suggesting all the properties are vital to determine the impact properties. The validation process affirms that the generated mathematical model for the energy absorbed and the impact energy is reliable at an acceptable level to predict their respective properties. The errors between the experimental value and the predicted value are 3.98% for the energy absorbed and 4.06% for impact energy. The findings are expected to provide insights on the impact behavior of the coconut wood-filled PLA composites prepared by FDM-3D printing and a mathematical model to predict the impact properties.

Crashworthiness Characteristic of Dynamically Expanded Circular Tubes Made of Light Alloys: Experimental and Theoretical Investigation.

The paper presents the process of dynamic expansion of thin-walled pipes made of T6 temper 7075 aluminum alloy. The obtained results were related to the mass of tested elements, which allowed for calculating the specific energy absorption. The registered crushing force was in the range of 600–800 kN/kg. The obtained values were much greater than the crushing force of traditional crash boxes made of steel (80–120 kN/kg) or AZ31 magnesium alloy sheets (150 kN/kg). The analytical model for predicting crushing force depending on the thickness of the pipe wall was developed and proven to be correct by conducting real experiments and FEM simulation. The mathematical model for energy absorption named further as ETMEA (expanding tubes model for energy absorption) was developed based on calculated energy-deflection curves. It was proven that the energy absorption could be easily scaled. In cases where high energy absorption is needed, it can be easily achieved by increasing the thickness, while for lower energy absorption application, the thickness may be reduced and the goal may be achieved by selecting the appropriate length of the profile.

Structure design of LFT passenger car seat structure based on topology optimisation

The newly revised GB 13057-2014 ‘The strength of the seats and their anchorages of passenger vehicles’ replaces the static test with a dynamic test, which puts forward higher requirements on seat safety. Considering safety and lightweight design, the LFT (Long glass Fiber reinforced Thermoplastic) is used to replace the original steel seat back frame. Combined with energy absorption model and topology optimisation, the force transmission path and detail structure design under both the forward loading and rearward loading conditions are carried out. In order to analyse the occupant protection performance, numerical models of composite seat and HybridIII dummy are established, and the safety and lightweight effect of LFT seat back frame are optimised and verified.