Foam-filled Columns Research Articles

Low-velocity impact of density-graded foam-filled square columns

In this paper, low-velocity impact of square columns filled with density-graded foam (DGF) is investigated experimentally, numerically and analytically. The low-velocity impact experiments are carried out to study the effect of density gradient on the deformation patterns and energy absorption of the DGF-filled columns. Numerical calculations are performed to study the effects of density distribution mode, density difference, average density of DGF and wall thickness of square column on the energy absorption. According to the energy method and basic folding element theory, the instantaneous dynamic crushing force is predicted analytically. The analytical predications are in good agreement with experimental results. It is found that the DGF-filled columns have excellent energy absorption capacity and low initial peak force compared to the uniform-filled columns with the same weight.

Optimization of Foam-Filled Square Thin-Walled Aluminium Structures

Crash box are the structural part designed to absorb energy during crash and minimize the injury to passengers. Various design of energy absorbers has been introduced to unleash design with the best crashworthiness behavior. Foam-filled structures are one of the promising designs. In this study, foam-filled structure was investigated to increase the energy absorption capability and reduce the initial peak force simultaneously. Since most foam-filled structures tend to absorb more energy with high peak force, optimization of the energy absorbers is significant in obtaining the optimum design. Response surface methodology (RSM) has been dominant technique in crashworthiness optimization mainly because of it provides efficient and accurate solution. This paper focused on the optimization foam-filled columns with respect to thickness of the tube and length of foam to enhance energy absorptions and reduce initial peak force. The optimization results suggested by Design Expert software for impact test is 515.9 J for EA and 134.94kN for IPF value with the column thickness of 2.0mm and foam length of 185mm. For quasi-static test, the optimum solution value for EA and IPF are 864.5J and 88.33kN respectively with column thickness of 1.87mm and foam length of 200mm.

Foam filling options for crashworthiness optimization of thin-walled multi-tubular circular columns

There is an increasing trend in using aluminum foam-filled columns in crash management systems due to their light weight in automotive industry. The main goal of this study is to optimize the crashworthiness of aluminum foam-filled thin-walled multi-tubular circular columns under quasi-static loading. The existing studies in the literature considered only lateral foam filling (the foam lateral dimension is variable and the foam height is equal to the column height). In the present study, we considered both lateral and axial foam filling and compared the performances of these two options. In optimization, the column thicknesses, taper angle, foam density, and foam height/diameter are considered as design variables. The quasi-static responses of the columns are determined through explicit dynamic Finite Element Analysis (FEA) using LS-DYNA software, and validated with quasi-static tests conducted in our facilities. Response surface based crashworthiness optimization of the columns for maximum Crush Force Efficiency (CFE) and maximum Specific Energy Absorption (SEA) is performed. It is found that lateral foam filling is superior to axial foam filling in terms of both CFE and SEA maximization. The maximum CFE obtained through lateral foam filling is 19% larger than the maximum CFE obtained through axial foam filling. Similarly, the maximum SEA obtained through lateral foam filling is 6% larger than the maximum SEA obtained through axial foam filling. For both CFE and SEA maximization, the columns should be tri-tubular type and have a large thickness and a taper angle. To attain the maximum CFE, foam should be designed with large density and medium foam diameter. However, foam plays an adverse role in maximization of SEA because of its weight. The increase in energy absorption obtained by using foam does not compensate the additional weight introduced by the foam.

Optimization analysis of novel foam-filled elliptical columns under multiple oblique impact loading

Thin-walled columns have been widely employed as energy absorbers for vehicle structures due to their dramatic merits of high energy absorption to weight ratios. Meanwhile, columns filled with low-density metal foams have demonstrated notable improvement on energy absorption capabilities compared with their empty counterparts. Accordingly, the present study aims to investigate and optimize the crashworthiness characteristics of novel foam–filled elliptical column (F-EC) under multiple oblique impact loading. More specifically, the finite element (FE) models of hollow and foam-filled elliptical columns (H-EC, F-EC) are first built and validated against theoretical and experimental outcomes. On this basis, a detailed crashworthiness comparison between the elliptical columns (ECs) and the circular columns (CCs), including hollow and foam-filled columns (H-CC, H-EC, F-CC, F-EC), reveals the superiority of F-EC relative to others on overall crashworthiness characteristics under multiple oblique impact loading. Next, a Taguchi-based design of experiment (DoE) is implemented to investigate the impact of column parameters of F-EC, including the sectional ellipticity e, the column thickness t and the foam density ρf, on the column peak crushing force under axial impact loading (PCF0) and overall specific energy absorption under multiple oblique impact loading (SEAθ). Subsequently, the Taguchi method coupled with grey relational analysis (GRA) is utilized to explore the optimal design of F-EC for maximizing SEAθ and minimizing PCF0 simultaneously, which is then verified through a detailed crashworthiness comparison between the optimized design and the original design. The optimal F-EC reveals more superior crashworthiness characteristics relative to the original design and thus demonstrates enormous potential as a candidate energy absorber particularly under multiple oblique impact loading.

Crushing and energy absorption of density-graded foam-filled square columns: Experimental and theoretical investigations

The static axial crushing and energy absorption of density-graded aluminum foam-filled square metal columns are experimentally and theoretically investigated. Typical deformation modes are observed in experiments, such as symmetric, asymmetric, extension and rupture modes. Theoretical analysis is carried out and the predictions are in good agreement with the experimental results. The effects of gradient pattern, density difference, average density of foam, and wall thickness on the crushing of foam-filled columns are discussed. It is shown that the density-graded aluminum foam-filled square metal column is a novel topological structure with higher energy absorption, higher load-carrying capacity and much higher crushing force efficiency.

Foam-Filled Columns with Rectangular Cross-Section During the Flattening Process: Theory and Experiment

In this paper, flattening process of polyurethane foam-filled aluminum columns with rectangular and square cross-sections subjected to lateral compression load is investigated, theoretically and experimentally. For this purpose, some flattening tests were performed on the foam-filled rectangular columns using a DMG machine, model 7166. Based on a new theoretical plastic deformation model, a relation is derived in order to predict instantaneous lateral load of the foam-filled rectangular columns during flattening process. Theoretical instantaneous lateral load versus lateral displacement diagrams of the specimens are compared with the experimental measurements, which shows a good agreement between them. Also, based on the experimental results, effects of different parameters such as load application directions, injection of polyurethane foam into columns, foam density and presence of the adhesion between the foam and the column inner wall are investigated on the flattening behavior of the structure. Furthermore, deformation modes of the specimens with different cross-sections are studied.

Crashworthiness analysis of foam–filled square column considering strain rate effect of the foam

This paper presents results on the crushing behavior of aluminum foam–filled columns with square cross section. Here, the effect of inserting an aluminum foam to single–walled and double–walled columns were studied. Parametric study for both types of columns compared with single–walled and double–walled columns were also carried out. In this work, the effect of strain rate of the aluminum foam was considered in the material model. The numerical results were compared with the available experimental data and shown to be in a very good agreement. The models that considered the strain rate effect of foam core gave better predictions compared to the ones without considering the strain rate effect. It will result in higher energy absorption and bigger local deformation on corners resulting a slightly increase of the overall crushing force. It can be said that the strain rate of the foam core plays a quite significant role in crushing behavior of the foam-filled columns, and should be taken into account. The results also showed that the interaction between the foam core and the column wall will change the deformation mode from one localized fold to multiple propagating folds and lead to the increase of total mean crushing force of the column. Similar effect of foam filling was also found in double–walled foam–filled columns. Further investigation has been conducted on the effect of core thickness to the mean crushing force response of the columns. It is also found that increasing the core thickness in double–walled foam–filled column will improve the crushing behavior up to a point where there is still interaction between the walls. After that, the further increase of the core thickness will make the column response approaching the crushing force of single–walled foam–filled.

A constitutive model of aluminum foam for crash simulations

A new constitutive model for metallic foams is developed to overcome the deficiency of existing models in commercial finite element codes. The proposed constitutive model accounts for volume changes under hydrostatic compression and combines the hydrostatic pressure and von Mises stress into one yield function. The change of the compressibility of the metallic foam is handled in the constitutive model by allowing for shape changes of the yield surface in the hydrostatic pressure-von Mises stress space. The backward Euler method is adopted to integrate the constitutive equations to achieve numerical accuracy and stability. The model is implemented into LS-DYNA as a user-defined subroutine, verified with existing solutions, and validated with foam testing data. The verified and validated model is then utilized in the crushing simulations of foam-filled columns with square and hexagonal cross-sections. Two constitutive models are studied: the first using an exponential function to describe the relationship of plastic Poisson's ratio with respect to true strain and the second using linear interpolation function as an alternative approximation. The new foam model provides satisfactory prediction of crushing forces and deformed shapes compared to experimental results. Additionally, the new foam model was shown to have better numerical stability and accuracy than existing LS-DYNA built-in material models.

Experimental Investigations on the Folding Process of Polyurethane Foam-Filled Aluminium Columns with Circular Discontinuities

This article performs an experimental study on empty and polyurethane foam-filled thin-walled aluminium columns with quadrangular cross section in two different conditions: with or without centrally circular discontinuities on the longitudinal or latitudinal sides of column cross section during the folding process (local buckling). In each sample, two circular cut-outs were perforated into the opposite sides of specimens and the samples were axially compressed between two rigid platens under the quasi-static loading. The samples were prepared with different initial lengths, filling conditions and cut-out diameters. Effects of mentioned characteristics are investigated on total absorbed energy, specific absorbed energy, crush force efficiency, peak load and folding wavelength. Experimental observations show that by increasing the cut-out diameter and also by filling the column with the foam, folding wavelength decreases. Also, experiments show that there is an optimum diameter for the longitudinal side cut-outs which total absorbed energy by the filled rectangular specimen with the optimum cut-out is the highest. Furthermore, results illustrate that total absorbed energy increases due to increment of column length, but specific absorbed energy and crush force efficiency are independent of column length.

Multiobjective optimization for empty and foam-filled square columns under oblique impact loading

This paper aims at optimizing the crashworthiness of empty and foam-filled thin-walled square columns under oblique impact loading, for variations in the load angle, geometry and material parameters of the column. Another focus is to reveal the relative merits of the optimized configurations for both types of columns under such loads. Dynamic finite element analysis (FEA) techniques validated by theoretical solutions and experimental data in the literature are used to simulate the crash responses of such devices subjected to different impact angles. Based on the FEA results, the Kriging metamodels are constructed for the two columns to predict the crashworthiness criteria of specific energy absorption (SEA) and peak crushing force (PCF) under oblique impact loading, which are set as design objectives in the following multiobjective optimization design (MOD) process. The Pareto fronts are identified for the MOD problems of the two types of columns under both single angle impact and the cases involving multiple impact angles, using the multiobjective particle swarm optimization (MOPSO) algorithm. It is found that the optimal designs are generally different under different load angles for either empty or foam-filled column. Results also indicate that more robust designs against oblique impact could be achieved by including multiple load angles in the MOD process. Compared to the empty column, the optimal foam-filled column may have better crashworthiness under pure axial loading, but the optimal empty column has more room to enhance the crashworthiness under oblique impact.

Theoretical and experimental study on empty and foam-filled columns with square and rectangular cross section under axial compression

This article derives some theoretical relations to predict diagrams of absorbed energy and axial force versus axial displacement during the folding process in square and rectangular columns. By considering the folding wavelength as a constant parameter during the folds creation and using balance of internal and external energy and minimum principle in plasticity, final relations are calculated. Also, two different relations are introduced to predict the maximum folding force of the empty and polyurethane foam-filled columns with square and rectangular cross sections, by considering the interaction effects between column wall and foam-filler. Furthermore, some experiments were carried out on the empty and foam-filled metal columns and the experimental measurements were compared with predictions of the theoretical formulas that showed good correlation.

Nonlinear finite element analysis of the crush behaviour of functionally graded foam-filled columns

The use of metallic foams as a filler in thin-walled structures can significantly enhance their crashworthiness characteristics. It is further believed that tailoring the properties of the foam filler would enhance the energy absorption characteristics of the foam-filled structure. It is the objective of this study to examine the crush behaviour of density-graded foam-filled columns and evaluate the effect of the density distribution upon both total and specific energy levels. The effect of density grading, number of grading layers, and thickness of the interactive layer upon the resulting specific energy absorption was investigated. To this end, nonlinear parametric finite element simulations were developed and performed to achieve this objective. The results show relative improvement of 12% in specific energy absorption levels of density-graded foam-filled structures over their uniform density counterparts with the same mass.

Comparisons of honeycomb sandwich and foam-filled cylindrical columns under axial crushing loads

For the conventional thin-walled energy absorber, the energy dissipation during a collision is concentrated in relatively narrow zones. This means that a great deal of material does not participate in the plastic deformation or enter the large plastic deformation stage. To expand the plastic deformation zones and improve the energy absorption efficiency, the authors presented a new type of honeycomb sandwich circular column. This innovative energy absorber is a composite structure composed of two circular aluminum tubes filled with core shaped as a large-cell honeycomb lattice. In this paper, six different honeycomb sandwich circular columns were investigated numerically. Comparisons of the interaction effect between tubes and filler, the deformation modes and the energy absorption abilities of these columns were conducted. The results were as following. The kagome sandwich column had the best energy absorption capability, followed by the columns sandwiched with triangle, hexagon lattices. In addition, foam-filled columns with different adhesive conditions were also simulated and compared with the honeycomb sandwich columns. It was found that increasing the adhesive strength improved the energy absorption and changed the deformation mode of the foam-filled columns. Furthermore, comparison showed that the honeycomb sandwich columns had higher specific energy absorption capability than the foam-filled tubes except for the strong bonded case. The kagome sandwich column performed best in crashworthiness, followed by triangle sandwich column.

Optimization of foam filled spot-welded column for the crashworthiness design

To improve crashworthiness efficiency, aluminum foam has been adopted as one of new filler materials in engineering. Introduction of the foam material changes the crash behavior of structural component and make neces-sary exploration of more sophisticated design optimization methodology. This paper presents a crashworthiness design of foam-filled columns made from mild steels and joined by spot-weld. During the design optimizations, maximum crushing force (Pm) is set as the design objective, wall thickness , foam density and side length (continuous vari-ables) and also the number of spot-weld (discrete variable) are selected as design variables, and specific energy ab-sorption (SEA) is set as the design constraint. To formu-late the complex crashworthiness design problem, the re-sponse surface method (RSM), is used.

The role of plastic deformation on the impact behaviour of high aspect ratio aluminium foam-filled sections

The main objective of this work is to investigate the role of the plastic deformation of metal foams on the dynamic behaviour of aluminium foam-filled columns with respect to their energy absorbing capabilities. The influence of the cross-section shape as well as other parameters is thoroughly studied. A comparison with correspondent hollow-sections is performed concerning the dissipation of kinetic energy and the obtained deformed profiles. For this particular purpose, three-dimensional finite element modelling dynamic analyses are carried out using ABAQUS/Explicit in order to achieve an in-depth study of the structural crash behaviour, during which energy needs to be absorbed in a controlled manner. A comprehensive numerical study of the crush behaviour of aluminium foam-filled sections undergoing axial compressive loading is performed. The results obtained are also analysed with respect to the reduction in the length of the structural element and impact time, the effect of friction between the foam and the outer skin, the energy decomposition, the role of plastic deformation, the influence of the skin material and impact velocity, and the influence of the shape of the cross-section on the impact behaviour. A comparison with existing analytical expressions is made in order to corroborate the numerical results.

Crashworthiness investigation of kagome honeycomb sandwich cylindrical column under axial crushing loads

For the classic thin-walled energy absorber, the energy dissipation during a collision is concentrated over relatively narrow zones. This means that a great deal of materials of the columns do not participate in the plastic deformation or not enter into the large plastic deformation stage. To expand the plastic deformation zones and improve the energy absorption efficiency, a new type of kagome honeycomb sandwich bitubal circular column is presented in this paper. This innovative impact energy absorber is made of two circular aluminum tubes filled with core shaped as a large-cell kagome lattice. The interaction effect, deformation mode and energy absorption characteristics of the composite structure are investigated numerically. Observing the collapsing process, it is found that the kagome lattices buckle first, which triggers the outer and inner skin tubes to fold locally. This behavior increases the plastic deformation areas. Moreover, the presence of the outer and inner tubes strengthens the buckling capacity of kagome cell. Furthermore, the folded tube walls intrude into the gap of the honeycomb cell, which further retards the collapse of the honeycomb cell. So the interaction effects between the honeycomb and column walls greatly improve the energy absorption efficiency. In addition, the effects of geometrical parameters of the kagome honeycomb on the structural crashworthiness are studied. It is found that the cell wall thickness and cell distribution (cell number in the circumferential direction) have distinct effects on the specific energy absorption. Besides, we also studied the foam-filled column with the same foam density as the kagome honeycomb and compared it with the kagome sandwich structure. It is found that the kagome sandwich column has higher mean crash force and better energy absorption characteristics.

A comparative study of energy absorption characteristics of foam-filled and multi-cell square columns

A comparative study of energy absorption characteristics between foam-filled square columns and multi-cell square columns was conducted by using nonlinear finite element codes LS-DYNA. The columns and the foam were made of the same material aluminum and the thickness of all sidewalls of columns was kept 1.5 mm. Numerical results compared well with theoretical predictions and showed that the energy absorption efficiency of multi-cell columns was about 50–100% higher than that of foam-filled columns. It means that multi-cell columns were more attractive than foam-filled columns and the reason for this was analyzed by a comparison of the collapse modes. Furthermore, a type of pre-crushed trigger was introduced and modeled for multi-cell columns. This type of trigger was found to be effective to eliminate the initial peak force and improve the efficiency of a multi-cell column as an energy absorber.

Experimental and numerical analyses of the axial crushing behaviour of hat sections partially filled with aluminium foam

The axial crushing behaviour of hat sections partially filled with different lengths of aluminium foam was studied experimentally and numerically. Various foam filling lengths were used to identify structures that would minimize the initial peak force due to the aluminium foam filling, while still maintaining relatively high energy absorption capabilities. The superfolding element height of every non-filled hat section was measured first. Then the crushing pattern and forces of partially foamfilled hat sections were measured with different filling lengths. The test results and numerical simulations with the explicit finite element software LS-DYNA showed that appropriate partial aluminium foam filling could give a higher mean crushing force and mass specific energy absorption (SEA), in addition to a lower initial peak force than the fully foam-filled columns.

Aluminum foam-filled extrusions subjected to oblique loading: experimental and numerical study

The behavior of empty and foam-filled square thin-walled aluminum columns in alloy AA6060 subjected to quasi-static oblique loading was examined. Previous studies have shown that by introducing a load angle, the energy absorption decreases drastically compared to axial loading. One of the main objectives of the present investigation was to study the effect of introducing aluminum foam filler on the energy absorption. The square columns were clamped at one end and oblique load conditions were realized at the other end by applying a force with different angles to the centerline of the column. An experimental program was carried out where the main parameters were load angle, foam density and heat treatment of the extrusion material. Additionally, numerical analyses of the experiments were performed, mainly to verify a numerical model of the obliquely loaded foam-filled columns. The foam was modeled with the foam model of Deshpande and Fleck, together with a simple fracture criterion, which previously has been implemented as a user subroutine in LS-DYNA. The study shows that high-density aluminum foam filler increases the energy absorption considerably, but the specific energy absorption is lowered compared to the empty cross sections. Furthermore, the numerical analyses were able to predict the experimental results with reasonable accuracy.

On the layered micromechanical three-dimensional finite element modelling of foam-filled columns

In this article, a new micromechanical layered model is proposed for the finite element analysis of the quasi-static collapse of foam-filled ultralight aluminium box sections. The foam was modelled using a novel micromechanical approach in which the localised deformation of the foam was simulated using a discrete number of layers joined together at coincident nodes. The coincident nodes were subject to a tie-break criterion to allow the proper deformation of the foam. The newly proposed layered approach allows for the local penetration of the folds and shearing of the foam, as observed in testing, thus avoiding the commonly adopted approximations in which the foam must undergo global deformation to accommodate the externally applied loads. In this three-dimensional non-linear finite element model, the aluminium box 6061-T4 was assumed to be a Mises-type material that follows the isotropic hardening criterion. A specially developed constitutive law was used for the foam material to account for the hydrostatic component as well as the independence of the strain tensor components. Three types of contact were used in the model. An automatic surface to surface contact algorithm between the foam layers and the column wall. A single surface contact algorithm is used for the column so as to avoid interpenetration of the column walls. A node to surface contact is used between the rigid massless striker and the top of the column. Comparison with the experimental results of a number of foam-filled aluminium 6061-T4 box structures shows excellent agreement with the finite element predictions in terms of the number of folds developed, the instantaneous load–displacement relationship and the average collapse load versus displacement.