Experimental And Numerical Studies Of Foam-"Lled Sections

* Corresponding author. Tel.:#1-617-253-2104; fax: #1-617-253-1962.

E-mail address: wierz@mit.edu (T. Wierzbicki)

International Journal of Impact Engineering 24 (2000) 509}534

Experimental and numerical studies of foam-"lled sections

Sigit P. Santosa!, Tomasz Wierzbicki!,*, Arve G. Hanssen", Magnus Langseth"

!Impact & Crashworthiness Laboratory, Massachusetts Institute of Technology, Room 5-218,

77 Massachusetts Avenue, Cambridge, MA-02139, USA

"Department of Structural Engineering, The Norwegian University of Science and Technology,

N-7034, Trondheim, Norway

Received 30 September 1998; received in revised form 29 June 1999

Abstract

A comprehensive experimental and numerical studies of the crush behavior of aluminum foam-"lled

sections undergoing axial compressive loading is performed. Non-linear dynamic "nite element analyses are

carried out to simulate quasi-static test conditions. The predicted crushing force and fold formation are

found to be in good agreement with the experimental results. Based on the numerical simulations, simple

closed-form solution is developed to calculate the mean crushing force of the foam-"lled sections. It is found

that the increase of mean crushing force of a "lled column has a linear dependence with the foam compressive

resistance and cross-sectional area of the column. The proposed solution is within 8% of the experimental

data for wide range of column geometries, materials and foam strengths. ( 2000 Elsevier Science Ltd. All

rights reserved.

Keywords: Thin-walled column; Aluminum foam; Axial crush

1. Introduction

Recent developments of cost-e!ective processes for the production of low-density metallic

cellular material, such as aluminum foam, have cleared the way for using it in light-weight

structural members. This is due to the unique characteristics of the cellular material which can

undergo large strain deformation while maintaining its low stress level before the densi"cation,

which occurs at the densi"cation strain in the range of 60}90%. One potential application of this

type of material is to reinforce thin-walled prismatic columns in space frame structures. It has been

0734-743X/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved.

PII: S 0 7 3 4 - 7 4 3 X ( 9 9 ) 0 0 0 3 6 - 6

Nomenclature

E Young's modulus

H half-wave folding length

P instantaneous crushing force

b column width

n strain hardening exponent

t column thickness

CI foam strengthening constant

EH elastic modulus of foam material

F0, F& characteristic load of empty and "lled column

GH foam shear modulus

P. mean crushing force of empty column

P.,& mean crushing force for "lled column

P.,&' mean crushing force for bonded-"lled column

*P. increase of the mean crushing force

d instantaneous shortening distance

l Poisson's ratio

h rotation angle of superfolding element

eD densi"cation strain

oH foam density

os density of solid cell wall of foam

p0 plastic #ow stress

p6 ultimate strength

p: yield stress

p& crushing strength of foam

pH1- plastic collapse stress of foam

p&!*- tensile strength of adhesive

qH1- plastic shear strength of foam

q&!*- shear strength of adhesive

shown through numerical studies that the crushing characteristics of a thin-walled column are

improved dramatically by "lling it with aluminum foam [1].

A comprehensive experimental study on the e!ect of "lling thin-walled columns with aluminum

foam was done by Hanssen et al. [2,3]. They investigated the axial crushing behavior of the

foam-"lled aluminum extrusion under quasi-static loading condition. They found that signi"cant

increases of crushing force were obtained from the direct compressive strength of the foam and

from the interaction between the foam and wall column. The interaction at the foam}wall interface

decreases the folding length, and therefore increases the crushing force. For a typical column with

a length to width ratio of 3, the non-"lled extrusion formed 5 lobes, while the foam-"lled sections

formed as many as 9 lobes. Similar experimental results were obtained by Seitzberger et al. [4], on

the axially compressed steel tubes "lled with aluminum foam. The experimental results on the

510 S.P. Santosa et al. / International Journal of Impact Engineering

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