Research Papers

A New FEM Approach for Simulation of Metal Foam Filled Tubes

[+] Author and Article Information
Matteo Strano

 Politecnico di Milano, Dipartimento di Meccanica, Via La Masa 1, 20156 Milan, Italymatteo.strano@polimi.it

J. Manuf. Sci. Eng 133(6), 061003 (Nov 28, 2011) (11 pages) doi:10.1115/1.4005354 History: Received March 29, 2011; Revised October 12, 2011; Published November 28, 2011

The combination of thin metal cases or tubes with a filling made of metal foams is interesting and promising for many applications in mechanical engineering. Components made of an outer hollow thin compact metal structure and a cellular lightweight core are especially suited to energy absorption applications. In order to allow for an efficient product/process design with a concurrent engineering approach, reliable and computationally affordable finite element method (FEM) calculations are required by both product and process engineers. The structural performance of these complex composite parts must be numerically predicted, in order to find the optimal combination of outer structure and metal foam properties. While FEM simulation at large deformations of bending, crushing, etc. of thin sheets and tubes is state of the art, the accurate FEM simulation of the mechanical behavior of metal foams cannot be considered fully established. In this paper the three most common methods for FEM simulation of metal foam materials are discussed: (a) homogenization approach, (b) realistic reconstruction of tomographic data, and (c) repetition of standard unit cells. A new effective approach is proposed, suited for simulation of composite, metal foam filled, structures of realistic dimensions. The approach is based on meshing the metal foam by replicating a unit cell made of 32 triangular shell elements, and then by randomizing the nodal position in order to emulate the intrinsic homogeneity of foam morphology. The method is validated by means of different experimental tests. The results show that the proposed method correctly predicts the behavior of foam structures in axial compression. The method slightly overestimated the actual load registered in three point bending tests. Several improvements are described and discussed in the paper, such as randomization of nodal positions of the mesh, in order to reduce the overestimation of forces. An FEM approach for the simulation of large deformations of metal foam filled metal structure (e.g., tubes) suited for the design of realistic large dimensions structural components has been presented. The proposed method shows some innovative features with respect to the available scientific literature, such as a configuration based on octahedral unit cells with low number of triangular shell elements. Randomization of nodal positions of each unit cell has been implemented as a method for better representing the intrinsic variability of metal foams and for reducing the stiffness of the simulated structure.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Stainless steel round tube after three point bending, filled by an aluminum foam, longitudinal cross section

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Figure 2

Unit cells; (a) realistically reproduced by solid elements; (b) with shell elements forming ellipsoids connected by a truncated pyramid; (c) with shell elements forming spheres joined by a triangular flat surface

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Figure 3

Examples of space partitions

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Figure 4

Modeling options for FEM mesh (see Table 1)

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Figure 5

Metal foam filled t-shape

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Figure 6

Regular and random octahedral u.c.

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Figure 7

Two layers of repeated u.c.

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Figure 8

Example of final foam mesh

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Figure 9

Two colors pictures of foam sections for image processing: (a) free expansion; (b) contained expansion

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Figure 10

FEM and experimental results of axial compression tests, regular octahedral u.c. with eight elements

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Figure 11

Effective stress-strain curve of the outer tube

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Figure 12

FEM and experimental results of three point bending tests

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Figure 13

Initial assembly of split tube

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Figure 14

Deformations of cells measured by image processing analysis at non dimensional stroke Sp_nd intervals of 0.0667, starting from 0.0667

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Figure 15

Load versus Sp_nd for bending of a split and rejoined steel tube filled by aluminium foam

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Figure 16

Effective plastic strain of structure measured by FEM at Sp_nd intervals of 0.0667, starting from 0.0667 (only ¼ of the model is shown, due to symmetry)

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Figure 17

Numerical load versus Sp_nd curves for comparison with Fig. 1

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Figure 18

Alternative unit cells: (a) hexahedral u.c., shown with no skin after insertion inside a tube; (b) double shaped u.c. 1 sphere—20 double pyramids




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