Relative merits of single-cell, multi-cell and foam-filled thin-walled structures in energy absorption
Introduction
Over the past twenty years, enormous efforts have been made by the academia and industry to understand the mechanisms of structural collapse in axial crushing of thin-walled metal tubes. The axial progressive folding deformation of the tubes is known to be an efficient energy absorbing mechanism. It is recognized that the number of “angle” elements on a tube's cross-section decides, to a large extent, on the efficiency of the energy absorption [1], [2]. It is therefore desirable to design thin-walled sheet metal profiles or extrusion with internal webs for weight-efficient energy absorption. Chen and Nardini [3] carried out experimental studies on the axial crushing behavior of single-hat and double-hat with an internal flange sections, and found that the latter one improves the Specific Energy Absorption (SEA, energy absorption per unit structural mass) by about 20% compared to the former one.
The axial crushing of single-cell, double-cell and triple-cell aluminum extrusion was studied analytically and numerically in this paper. Based on the Super Folding Element theory [1], [2], an analytical solution for mean crushing force of multi-cell sections was developed. Numerical simulations using non-linear explicit finite element code were then conducted. The numerical results were compared to the analytical solutions.
The axial crushing of aluminum foam-filled multi-cell columns was also addressed in this paper. The applications of cellular solids such as aluminum foam and honeycomb as reinforcement to thin-walled structures, and as cores for sandwich panels, have received increasing interest in recent years. Aluminum foam is of particular practical interest because of its mass efficiency, its attractive mechanical behavior, and the recent developments of cost-effective production process. A typical compressive stress-strain curve of aluminum foam consists of three regions: a linear elasticity at small strains, a long distinct plateau of almost constant stress, and a final densification region at very large strains (60∼90% nominal strain). This makes the aluminum foam an ideal material for energy absorbing.
Extensive studies have been carried out by a number of authors on the axial crushing behavior of foam-filled columns [4], [5], [6], [7], [8], [9], and it was revealed that the crushing resistance and energy absorption of thin-walled columns are improved dramatically by filling it with aluminum foam. This is due to the interaction between the tube wall and the foam core which changes the local buckling mode of the tube wall. Seitzberger et al. [4], [5] conducted experimental studies on the axial crushing of steel columns filled with aluminum foam. Various cross-sections were considered in their studies, including square, hexagonal, octagonal and bitubal arrangements of these cross-sections (two concentrically oriented profiles with aluminum foam in between). They reported that considerable mass efficiency improvements with respect to energy absorption were obtained by foam filling, particularly the bitubal arrangements. Comprehensive experimental studies on the effect of filling thin-walled square and circular aluminum extrusions with aluminum foam was carried out by Hanssen et al. [6], [7]. Santosa et al. [8], [9] conducted numerical investigations on the effect of foam filling undergoing axial crushing. Aluminum foam filling was found to be preferable to thickening the column wall in terms of specific energy absorption. Based on their numerical simulations, simple closed-form solution was developed to calculate the mean crushing force of foam-filled square sections. It was found that the increase of mean crushing force of a filled column has a linear dependency on the foam compressive resistance and cross-sectional area. Chen and Nardini [3] found in their study that significant gain in specific energy absorption can be achieved by filling the closed-hat profiles with aluminum foam, as long as the progressive folding deformation developed without premature joint failure.
Numerical analyses were carried out in the present paper to simulate the axial crushing of double-cell and triple-cell extrusions filled with aluminum foam. Based on the numerical results and the analytical solutions to non-filled sections, closed-form solutions were derived to calculate the mean crushig force of foam-filled multi-cell sections. The relative merits of filled sections on energy absorption and weight saving were discussed.
Section snippets
Non-filled multi-cell columns
Theoretical solutions to the mean crushing force of multi-cell columns undergoing axial crushing were derived based on the Super Folding Element method [1], [2]. Numerical analyses using explicit finite element code PAM-CRASH were then carried out, and the results were compared to the theoretical solutions.
Foam-filled multi-cell columns
In order to achieve higher weight efficiency in energy absorption, the lightweight cellular materials such as aluminum foam was utilized to fill the thin-walled structures. Significant increases in the crushing resistance and energy absorption were obtained from the direct compressive strength of the foam and from the interaction between the foam and the column wall. The foam filler functions as an elastic–plastic foundation to the column wall, and accordingly reduces the folding wavelength and
Discussion and conclusion
The axial crushing of hollow multi-cell columns were addressed in the present paper. Based on the Super Folding Element theory, an analytical solution for the mean crushing force of multi-cell sections were derived, and the solution was compared very well with the numerical predictions.
Numerical studies were also carried out on the axial crushing of foam-filled double-cell and triple-cell columns. Based upon the numerical results of filled columns and the closed-form solutions for non-filled
Acknowledgements
The present research was conducted for the Project of the “Ultralight” Consortium at MIT. The financial support of all members of the Consortium is gratefully acknowledged. Thanks are also due to Altair Computing and Engineering System International for providing free academic licenses of the programs HYPERMESH and PAM-CRASH.
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