Oblique Impact Loading Research Articles

Energy Absorption of a Novel Lattice Structure‐Filled Multicell Thin‐Walled Tubes Under Axial and Oblique Loadings

Multicell design and lattice structure as filling material are two effective methods for enhancing the energy absorption performance of thin‐walled tubes. This study combines these two approaches to present a multicell tube with a novel lattice structure and investigates the energy absorption performances of these hybrid multicell tubes under axial (0°) and oblique (10°, 20°, and 30°) impact loading conditions. As filling structure, β‐Ti3Au lattice geometry with varying lattice strut diameters and the number of lattice unit cells are used, while the single and multicell thin‐walled tubes with different tube thicknesses are employed as main absorbing element. In this context, the effects of numbers of lattice unit cells, lattice strut diameter, cell numbers of the tube, and tube thickness on energy absorption performance of hybrid tubes are examined using validated nonlinear finite element models. This investigation unveils that the synergistic interplay between the multicell tubes and lattice structure during deformation significantly elevates the energy absorption performance of the hybrid structure. Notably, the findings demonstrate that multicell hybrid tubes exhibit a remarkable capacity to absorb up to 30.36% more impact energy compared to the aggregate absorption of individual components in hybrid tubes.

Quantitative analysis of the protective performance of bicycle helmet with multi-direction impact protection system in oblique impact tests

PurposeThe current study aimed to assess the protective performance of helmets equipped with multi-directional impact protection system (MIPS) under various oblique impact loads. MethodsInitially, a finite element model of a bicycle helmet with MIPS was developed based on the scanned geometric parameters of an actual bicycle helmet. Subsequently, the validity of model was confirmed using the KASK WG11 oblique impact test method. Three different impact angles (30°, 45°, and 60°) and 2 varying impact speeds (5 m/s and 8 m/s) were employed in oblique tests to evaluate protective performance of MIPS in helmets, focusing on injury assessment parameters such as peak linear acceleration (PLA) and peak angular acceleration (PAA) of the head. ResultsThe results demonstrated that in all impact simulations, both assessment parameters were lower during impact for helmets equipped with MIPS compared to those without. The PAA was consistently lower in the MIPS helmet group, whereas the difference in PLA was not significant in the no-MIPS helmet group. For instance, at an impact velocity of 8 m/s and a 30° inclined anvil, the MIPS helmet group exhibited a PAA of 3225 rad/s2 and a PLA of 281 g. In contrast, the no-MIPS helmet group displayed a PAA of 8243 rad/s2 and a PLA of 292 g. Generally, both PAA and PLA parameters decreased with the increase of anvil angles. At a 60° anvil angles, PAA and PLA values were 664 rad/s2 and 20.7 g, respectively, reaching their minimum. ConclusionThe findings indicated that helmets incorporating MIPS offer enhanced protection against various oblique impact loads. When assessing helmets for oblique impacts, the utilization of larger angle anvils and rear impacts might not adequately evaluate protective performance during an impact event. These findings will guide advancements in helmet design and the refinement of oblique impact test protocols.

Dynamic Responses of Single-Layer Reticulated Shells under Oblique Impact Loading

This paper focuses on the response of reticulated shell structures under oblique impact loads, with a departure from the traditional emphasis on vertical impact loads. These structures are typically utilised in large-span spaces such as iconic buildings and large venues. The study begins by establishing a numerical simulation method for reticulated shell structures subjected to oblique impact loads, which is then validated against existing experimental results. Building on this verified method, the research delves into the effects of varying impactor mass, velocity, and initial kinetic energy on the reticulated shell structure under oblique impacts, as well as the influence of different oblique impact angles. The study extensively examines the failure modes of the structure, node displacements in the structure, and variations in member stress under different impactor parameters. It further investigates how these parameters influence the maximum impact bearing capacity, impact duration, energy dissipation capability, and response forms of the structures, analyzing the reasons behind these effects. The findings offer valuable insights for further research and practical engineering design of reticulated shell structures.

Dynamic crushing behavior of a novel bi-directional gradient lattice structure under axial and oblique impact loadings

To meet the crashworthiness requirement of lightweight structures under different impact directions, a series of novel bi-directional gradient lattice structures (BD-GLSs) are proposed to improve their oblique impact resistance performance. In this paper, four types of BD-GLSs with both symmetric and asymmetric gradient topology configurations are constructed by varying the side lengths of lattice unit cells in xy-plane, and their crushing behavior under axial and oblique impact loadings are numerically investigated. The dynamic crushing behaviors are highlighted by comparing with the traditional uniform and uni-directional gradient lattice structures, which is validated via experiment studies. It is demonstrated that the specific energy absorption of the BD-GLSs with symmetric gradient topology configuration can achieve an increment of 42.26 % as compared to the uniform lattice structure. Moreover, the specific energy absorption of BD-GLSs with symmetric gradient topology configuration is 47.63 % higher than that of the uni-directional gradient lattice structure under oblique impact, which suggests that the bi-directional gradient topology can provide better crashworthiness performance under the oblique impact conditions. The symmetrical gradient topology configuration has greater bearing capacity and better crashworthiness under both axial and oblique impact loadings by comparing with other gradient topology configurations. The proposed bi-directional gradient topology configuration provides an optimal design strategy for the crashworthiness design of lightweight structures, especially in the case of unknown impact load directions, which has a great competitive advantage in crashworthiness applications.

Optimizing functionally graded hexagonal crash boxes with honeycomb filler for enhanced crashworthiness

A crash box is typically designed to enhance crashworthiness by absorbing impact energy and reducing the crushing force that can cause injury or fatality to passengers. However, the structural integrity of conventional crash boxes is often compromised due to buckling deformations during collisions. This study introduces a novel approach utilizing functionally graded thickness (FGT) in hexagonal crash box design with honeycomb fillers to improve crashworthiness through multi-objective optimization. Finite element analysis using LS-DYNA was performed for axial and oblique impacts. Mesh sensitivity study indicated that constructing the FGT crash box with 41 layers yielded favourable outcomes, with simulation results differing by a mere 2.5% compared to experimental data. A surrogate model based on response surface methodology was employed to mathematically formulate the objective functions, which aimed to maximize specific energy absorption (SEA) and minimize initial peak crash force (IPF). Subsequently, a multi-objective particle swarm optimization was used to determine the optimal grading exponent of both outer and filler structures. The optimized FGT crash box demonstrated superior control over progressive deformation, exhibiting high SEA and reducing IPF compared to the uniform thickness crash box. Particularly, under oblique impact loads, using two grading exponents in optimizing the FGT crash box potentially achieved significant improvements in crashworthiness within the design procedure.

Analytical modeling and analysis of the low-velocity penetration and non-penetration behaviors of fiber-reinforced composite cylindrical shells based on critical impact velocity criterion

An analytical model is developed to predict the impact characteristic parameters of composite cylindrical shells when low-velocity penetration and non-penetration damage are considered. The critical impact velocity criterion for judging the penetrating failure of such structures is also proposed. The impact contact force, displacement, and load-displacement curve of the structure subjected to oblique non-penetrating impact loading are solved using the improved Hertz contact theory, cumulative damage theory, stiffness degradation method, etc. Based on the formula derivation of critical impact velocity, the key impact parameters are solved, such as the residual velocity of the projectile and damage area of the structure with penetrating impact, which takes into account three energy absorption mechanisms, such as delamination, laminating crushing and linear momentum transfer. A series of non-penetrating and penetrating impact tests are conducted using a low-velocity drop hammer rig and a light gas gun. The prediction results of the proposed model are compared to both experimental and literature results. One can find out that the largest prediction errors of the peaks of impact contact force and displacement deformation are 12.3 and 9.2 %, respectively, and the counterparts of residual velocity and damage area are 12.0 and 6.2 %, respectively. Hence, the present model is trustworthy for predicting these impact parameters. Moreover, it is advised to adopt an appropriate stacking sequence, a high ratio of structural thickness to radius, a large oblique impact angle of the projectile, and a small mass ratio of the projectile to such a structure to enhance its impact resistance or reduce impact response. In addition, it is worth noting that the current model probably has a big prediction error of the high-velocity impact behaviors involving the material heating and soft effects caused by penetration damage since high strain rate and temperature effects are not considered.

Crashworthiness analysis and optimization of a novel “cake-cutting” multi-cell tube

Increasing the number of corners can effectively increase the energy absorption of thin-walled tubes. To obtain a thin-walled tube with better energy absorption performance, a novel type of multi-cell thin-walled tube is formed by adding three rib plates, imitating the way of cutting a cake. The rib plates can divide the circular tube into multi-cell tubes with different numbers of multi-cells, and numerical simulations are conducted for the crashworthiness analysis under the axial and oblique impact loadings. The results show that the deformation mode under axial impact is more stable when the number of "cakes" is maximum, and the specific energy absorption is increased by 46% compared with the traditional circular thin-walled tube. Then, a multi-objective optimization framework is employed to find the cutting configuration for better crashworthiness performance. It is found that the optimal multi-cell tube inspired by the “cake-cutting” method can increase energy absorption by 17.4% compared with the original tube. This cake-cutting method provides an innovative designing idea of a thin-walled structure for energy absorption.

Forward and inverse analysis of transient responses for a cantilevered rectangular plate under normal and oblique impact loadings

This study investigates the transient responses of a cantilevered rectangular aluminum plate under normal and oblique impact loadings. The transient displacement and strain histories of the aluminum plate are forward calculated as a superposition of the normal modes using first-order shear deformation plate theory and the spectral collocation method considering both in-plane and out-of-plane dominant vibrations. A laser displacement meter and strain gauges are used to measure the displacement and strain histories of the same aluminum plate when subjected to normal and oblique loadings. Subsequently, frequency-dependent damping ratios are obtained from the associated wavelet spectrograms. The measured histories correlate well with those estimated using the theoretical analysis considering the damping ratios. Additionally, the inverse problem of determining the impact force history from the transient response is investigated. First, the transfer function between the impact force and measured response is derived using a theoretical analysis developed in the time domain. Subsequently, a wavelet deconvolution method is applied to reconstruct the impact force using a discrete wavelet transform with different scale and shift components. Thus, the impact force is obtained by reconstructing the wavelet expansion coefficients using these components, thereby demonstrating the validity of the wavelet deconvolution technique utilizing the theoretical transfer function.

Crashworthiness Analysis of Square Aluminum Tubes Subjected to Oblique Impact: Experimental and Numerical Study on the Initial Contact Effect

This study investigates the crashworthiness behavior of square aluminum thin-walled tubes subjected to both axial and oblique impact loading, emphasizing the effects of crushing angle and initial contact between impactor and tube on the plastic collapse initiation and energy absorption capacity. A parametric study in crushing angle is conducted until 15°, while the two examined types of initial contact between impactor and tube consist of a contact-in-edge case and a contact-in-corner one, aiming to capture the effect of initial contact on both plastic collapse and energy absorption. Both experimental quasi-static tests and numerical simulation via finite element modeling in LS-DYNA software are carried out for the evaluation of the crushing response of the tested tubes. The 5° oblique cornered crushing revealed the greatest energy absorption, reflecting the most efficient loading case as significant tearing failure occurred around the tube corners in axial crushing due to a higher peak crushing force, while the increase in crushing angle caused a drop in energy absorption and peak force regarding the oblique loading. Finally, an initial contact-in-corner case revealed higher energy absorption compared to both axial and edged oblique loading, while peak force showed a slight decrease with crushing angle in that case.

Modelling of woven CFRP plates subjected to oblique high-velocity impact and membrane loads

In this work, an analytical model was employed to model the perforation of woven plates made of AS4/8552 (carbon/epoxy) laminates exposed to oblique impact and preload in plane. The model assumed six mechanisms for the absorption of the kinetic energy of projectile: the laminate acceleration, elastic deformation of fibres, fibres failure, shear plugging, delamination and matrix cracking. The model was validated with numerical and experimental data from previous works and, was used to determine the influence of an oblique and perpendicular impacts on laminates with and without the in-plane preload.

Crashworthiness of lantern-like lattice structures with a bidirectional gradient distribution

Oblique impact loading conditions strongly influence the crashworthiness of energy-absorbing structures. In the present work, inspired by the distribution characteristics of spider webs, a bidirectional gradient configuration of cell wall thickness was introduced to enhance the crashworthiness of lattice structures based on the functional similarity of longitudinal gradient distribution and lateral gradient distribution. A comparative study of different gradient configurations was carried out using the finite element (FE) simulations. It was found that the longitudinal gradient distribution was beneficial to improve the comprehensive energy absorption capacity of the lattice structure, especially under small-angle impact conditions. With the increase of impact angle, the effect of the lateral gradient distribution on the stability of energy absorption became more prominent. In comparison to the uniform structure and the single gradient structure, the lattice structure with the positive longitudinal gradient and the negative lateral gradient distribution exhibited great potential in enhancing the energy absorption capacity and reducing the peak crushing force. A detailed parametric study was executed to explore the effects of the gradient layer number and the gradient thickness increment of the bidirectional gradient distribution on the comprehensive energy absorption capacity and energy absorption stability of the structure under multi-angle impact conditions. The findings of this research provide valuable guidelines to design bio-inspired lattice structures subjected to complex loading conditions.

Design Loads and Pier Responses for Oblique Side Barge Impacts on Bridges

For bridges susceptible to barge collision, design provisions are typically utilized in determining collision scenarios and impact loading. Provisions in the United States require that bridges be designed to withstand two distinct collision events: direct (head-on) and glancing (e.g., oblique side). Head-on impact scenarios are represented using empirically determined static loads, and perpendicular impact loads are applied with magnitudes assumed equal to 50% of head-on impact loads. Subsequent to the formation of these provisions, numerous studies have identified the need to account for dynamic phenomena when designing bridges to resist vessel collision loads. Further, design-oriented computational techniques have been developed to characterize representative vessel–bridge collision scenarios, quantify dynamic barge impact loads, and compute time-varying bridge responses. While previous studies focused on head-on barge–bridge collision, the current study characterizes oblique side barge impact loading and resulting bridge response. Parameters such as barge flotilla configuration, impact angle, and location of impact initiation are investigated across a range of bridge models, leading to the identification of design-relevant oblique side impact scenarios. An alternative to the 50% design approach for oblique side impact scenarios involving the corners of barge bows is then proposed for assessing overall stability. The proposed approach incorporates dynamic phenomena and maintains agreement relative to more detailed analyses.

On novel foam-filled double-hexagonal tube for multiple load cases

In this article, novel foam-filled double-hexagonal tubes (F-DHTs) are proposed and investigated for multiple load cases. First, the finite element (FE) models of DHTs with four different foam filler modes under axial and multiangle oblique impact loading are built and verified by experiment. The four foam filler modes are, respectively, Hollow-Hollow-DHT, Filled-Hollow-DHT, Hollow-Filled-DHT and Filled-Filled-DHT (FF-DHT). Second, a comprehensive crashworthiness comparison is conducted among the above DHTs, which discloses the relative advantage of novel F-DHTs. On this basis, taking the FF-DHT as research object, a systematic parameter influence study is implemented. Subsequently, the FF-DHT is multiobjective crashworthiness optimized by using a hybrid method. According to the optimization result, the FF-DHT obtains 16.69% higher overall specific energy absorption () yet 1.11% higher initial peak crushing force compared with the baseline design. Hence, the novel F-DHTs could be superior potential thin-walled energy-absorbers.

Numerical crushing analysis on energy absorption capability of a tapered corrugated composite tube under axial and oblique impact loading

Compared with metals, composites have unique advantages, such as lightweight, high specific strength and suitable stiffness, high energy absorption, and ease of design,making them worthy of special consideration. Corrugating the surface of energy absorbers makes it possible to control and optimize the crashworthy properties of the composite structure. In this study, the effect of corrugation geometric parameters on the tube surface of the glass-epoxy, under oblique and axial impact, was numerically investigated using the ABAQUS software by considering cohesive layers. There was an excellent agreement between the simulation results and the validated experimental ones. The effect of amplitude and wavelength of the corrugated wall of the composite tapered tube, the angles of the cone tip and oblique impact, the orientation of the composite fibers, and composite layer on the absorption energy, the peak force, and crushing force efficiency related to the composite tube were examined. The results indicated that the energy absorption capacity of the tapered composite tube reduces by decreasing the angles of the cone tip and increasing oblique impact. Moreover, one can control the crashworthy properties of the composite tube by modifying the amplitude and wavelength of the corrugated surface, and the angles of fiber and layering.

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.

Numerical and experimental investigation on the oblique successive impact behavior and accumulated damage characteristics of fiber metal laminates

This paper mainly investigates the dynamic response and accumulated damage characteristics of fiber metal laminate (FML) under successive impact loads through numerical and experimental methods. Firstly, the experimental tests are conducted to measure the successive impact response and explore the damage morphologies of FML under four times impacts of 10 J. Then, an integrated successive numerical model is developed to predict the impact behavior and characterize the failure mechanisms of FML, whose accuracy and reliability are well demonstrated. Subsequently, in virtue of the developed numerical model, different oblique successive impact loads are implemented on FMLs to characterize the interface delamination evolution and energy absorption. And the damage tolerances of FMLs under different impact angles are further simulated and compared. The conclusions indicate that the stiffness of FML and impact force experiences an evident enhancement after the first impact because of the strain hardening phenomenon of metal material. In addition, according to the number of impacts, the damage tolerance of FML can be improved at the greater impact angle. And for the last impact event, the metal crack propagation, the further fiber/matrix damage and even the penetration of metal layer will dissipate more successive impact energy.

Crashworthiness analysis and multi-objective optimization for honeycomb structures under oblique impact loading

Oblique impact loading conditions are unavoidable in practical applications, which strongly influence the performance response of energy-absorbing structures. In this paper, the finite element models of four typical cellular structures (hexagon honeycomb, re-entrant hexagon honeycomb, star-shape honeycomb, double arrow honeycomb) are established and experimentally validated. The dynamic responses of four structures under different impact angles (from 0 to 30°) and impact velocities (from 5 to 50 m/s) are investigated. On this basis, the influences of impact angle and impact velocity on the specific energy absorption (SEA) and peak crushing force (PCF) of four structures are discussed. The results reveal that the negative Poisson’s ratio structure has the advantage of energy absorption under axial impact due to the characteristics of compression and contraction at the low impact velocity. The hexagonal honeycomb structure has great advantages in terms of comprehensive energy absorption capacity and better stability at varying inclination angles. The Non-dominated Sorting Genetic Algorithm (NSGA-II) coupled with the ideal point method (IPM) is utilised to explore the optimal design of hexagon honeycomb structure, which is then verified by a detailed crashworthiness comparison with the original design. The optimal honeycomb structure shows excellent crashworthiness characteristics and demonstrates great potential for applications in impact engineering, especially the oblique impact loading situations.

Effects of cutout and impact loading condition on crashworthiness characteristics of conical frusta

This study focuses on the axial and oblique low-velocity impact response of thin-walled aluminium conical frusta with circular cutouts at two different locations through experimental and finite element procedures. In this regard, a circular cutout was laterally introduced on 15°, 25°, and 35° semi-apical angled conical frusta at mid-height (0.5 H c) and three-fourth (0.75 H c) of axis height. The low-velocity axial and oblique impact loading was performed with the perfect and imperfect (i.e. hole) conical frusta by varying the impact angle from 0° to 20° to the frustum axis and impact velocity from 4 m/s to 8 m/s. The changes in energy absorption (E abs) and specific energy absorption (SEA) characteristics of perfect and imperfect conical frusta were analysed with the change of semi-apical angle of the frusta, location of the cutout, impact angle and direction of impact. The results show that the crush performance of 35° semi-apical angled perfect conical frustum is found to be better than 15° and 25° semi-apical angled specimens. Further, the SEA capacity of 25° semi-apical angled conical frusta having cutout at 0.75 H c is found to be better than the SEA capacity of conical frusta having cutout at 0.5 H c.

Multi-objective optimization of crash box filled with three-dimensional cellular structure under multi-angle impact loading

Oblique impact loading conditions are common in automobile collision accidents, which strongly influence the energy absorption performance of thin-walled structures. In this paper, a novel three-dimensional (3-D) hexagonal structure-filled crash box with better comprehensive crashworthiness under multiple working conditions is proposed. First, the finite element models of four 3-D typical cellular structures (hexagon structure, re-entrant hexagon structure, star-shape structure, double arrow structure) are established. The dynamic responses of four structures under different impact angles (from 0° to 30°) and impact velocities (from 5 to 15 m/s) are discussed. The results reveal that the 3-D hexagonal structure has great advantages in terms of the energy absorption at varying inclination angles. Second, the 3-D hexagonal structure is filled in the crash box in the form of gradient distribution. The multi-island genetic algorithm (MIGA) based on the response surface model (RSM) is utilized to explore the optimal design of crash box. Compared with the traditional crash box, the optimal 3-D hexagonal structure-filled crash box increases 18.9% in specific energy absorption and decreases 21.7% in maximum peak force, which demonstrates great potential for applications in impact engineering.

Development of a detailed human neck finite element model and injury risk curves under lateral impact

Advanced neck finite element modeling and development of neck injury criteria are important for the design of optimal neck protection systems in automotive and other environments. They are also important in virtual tests. The objectives of the present study were to develop a detailed finite element model (FEM) of the human neck and couple it to the existing head model, validate the model with kinematic data from legacy human volunteer and human cadaver impact datasets, and derive lateral impact neck injury risk curves using survival analysis from the upper and lower neck forces and moments. The detailed model represented the anatomy of a young adult mid-size male. It included all the cervical and first thoracic vertebrae, intervening discs, upper and lower spinal ligaments, bilateral facet joints, and passive musculature. Material properties were obtained from literature. Frontal, oblique, and lateral impacts to the distal end of the model was applied based on human volunteer and human cadaver experimental data. Corridor and cross-correlation methods were used for validation. The CORrelation and Analysis (CORA) score was used for objective assessments. Forces and moments were obtained at the occipital condyles (OC) and T1, and parametric survival analysis was used to derive injury risk curves to define human neck injury tolerance to lateral impact. The Brier Score Metric (BSM) was used to determine the hierarchical sequence among the injury metrics. The CORA scores for the lateral, frontal, and oblique impact loading conditions were 0.80, 0.91, and 0.87, respectively, for human volunteer data, and the mean score was 0.7 for human cadaver lateral impacts. Injury risk curves along with ±95% confidence intervals are given for all the four biomechanical metrics. The OC shear force was the optimal metric based on the BSM. A force of 1.5 kN was associated with the 50% probability level of AIS3+ neck injury. As a first step, the presented risk curves serve as human tolerance criteria under lateral impact, hitherto not available in published literatures, and they can be used in virtual testing and advancing restraint systems for improving human safety.