The introduction of Finite Element (FE) packages to the world of structural and mechanical calculations has been an invaluable tool in studying the characteristics of energy absorbers. In general, these structures tend to display complex deformation behaviours which, in practice, cannot be accurately modelled using the traditional analytical methods. With the use of the correct FE software, designers can simulate accurate models representing the static or dynamic crushing of certain energy absorbers under different loads (Farley, 1986). This technique becomes extremely valuable in the initial design of energy absorbing structures such as vehicles body parts. Finite element analysis can be accurate, time–saving and inexpensively repeatable.
Many structures of various geometries and materials have been modelled by researchers as parts of their investigation on the energy absorption characteristic of the structures. The outcomes of the models can help validate the analytical or experimental results.
Researchers use different packages for the purpose of the structural analysis of the deformation of energy absorbers. Abramowicz (2003) used CRASH CAD® to study the bending and axial collapse of thin–walled energy absorbing tubes in vehicles. Through definition of the desired cross–section for the tube, their detailed analysis of the dynamic crash behaviour of the vehicle produced satisfactory outcomes which were in agreement with the experimental results. In their study of 1999, Langseth et al. modelled the axial impact of square aluminium tubes using the explicit finite element code LS–DYNA®. They studied the effect of impact mass and velocity on the deformation mechanism of the tube. In line with the time–saving benefits of using FE packages, Langseth et al. (1999) took advantage of the symmetrical geometry of a square tube and by applying the appropriate boundary conditions, modelled one quarter of the entire aluminium tube, thus reducing the time of analysis. The results obtained in their experimental programme were agreeably comparable to the predictions of their dynamic simulations. Their FE simulation gave good evaluation of the final profile shape in addition to a force-displacement curve with a ratio of 0.87–1.0 between FE and experiment.
The selection of the FE package is based on the material and geometrical attributes of the structure as well as the details required from the output data. Researchers such as Karagiozova et al., (2000 and 2004) used the explicit code of ABAQUS® for their simulation purposes. More simplified models can be solved using the implicit package such as ABAQUS/Standard V.5.8 used by Karagiozova et al. (2001).
Depending on the complexity of a structure and the conditions for which it is being tested, an FE replica can be produced by 2D axisymmetric modelling or 3D , ’ . A j (2000) employed the 2D axisymmetric modelling technique to simulate the inversion of plastic tubes using ABAQUS® 5.7-3. Good agreement was obtained between the experimental results and their FE predictions. This 2D method can help save computation time by reducing the number of components.
Other studies on this subject area include the research of Santosa et al. (1998, 2000) on foam material and foam filling of EA structures. Chen et al. (2001) and Reyes et al. (2004) also studied the bending collapse and torsion deformation of these structures. Mamalis et al. (2001) carried out an FE simulation of the axial compression of metallic thin–walled square frusta. The FE code LS–DYNA® has largely been used by designers and engineers. Many researchers in the energy absorption area have used LS–DYNA® to simulate models and verify results against experimental and theoretical approaches. The investigation on the vehicular impact on a portable concrete barrier done by Ulker et al. in 2008 is one such example where LS–DYNA® pre and post–processor are used to model in details an available crash test in order to develop a set of charts for assessing the barrier displacement and related variables prior to entering the design phase (Ulker et al, 2008).
Researches performed on the characteristics of energy absorber structures using AN Y ® O .’ ed oblong tube energy absorbers. The implicit version of ANSYS® was used to simulate the quasi–static lateral compression of nested systems (Olabi et al., 2008). Morris et al. also used the implicit ANSYS® in 2006 in the analysis of nested tube type energy absorbers with different indenters and exterior constraints. In a more recent study at Dalian University of Technology in China, ANSYS® was used to investigate the
crashworthiness of kagome honeycomb sandwich cylindrical energy absorber columns under axial crushing loads (Zhang et al, 2010).
A group of researchers used the nonlinear ANSYS/LS–DYNA® code to analyse and simulate the inversion processes of a specific type of tube under axial compression (Zhang 2009). Another group used ANSYS/LS–DYNA® to investigate the relations between configuration parameters of double–walled hexagonal honeycomb cores and their out–of–plane dynamic plateau stresses at various impact velocities (Deqiang, 2010), all achieving satisfactory predictions of the experiments.
Within the Cellbond Composites Company, preliminary work has already been carried out looking at the finite element modelling of some egg–box geometries. Depending on the area of application, based on the maximum temperature, the level and angle of impact, and the boundary conditions that the structure will be subjected to, egg-boxes can be produced from metallic or non-metallic (polymeric) material (Ashmead et al, 2000).
Furthermore, Zupan et al. (2003) proposed a 3D finite element shell model of the egg-box since, despite the correct collapse modes, the calculations that had been made using their original axisymmetric finite element model gave less accurate ’ . In this study, 3D FE models were developed and validated against the results of experiments in order to further analyse the geometrical features of egg-box structures and their effect on the deformation pattern of the absorber. Although their predictions were improved with the 3D simulation, the material model they defined to model the aluminium alloy, lacked adequacy in taking into account the rate sensitivity and failure of the material. This issue is addressed in the study in hand.