Open-cell metallic foams exhibit properties desirable in engineering applications requiring mitigation of the adverse effects resulting from impact loading; however, the history dependent dynamic response of these cellular materials has not been clearly elucidated. This article contributes an approach for modeling the response of dynamically loaded open-cell metallic foams from ligament level to unit cell level to specimen level. The effective response captures the localized chaotic collapse phenomena through ligament reorientation at cell level while maintaining the history of plastic deformation at ligament level. First, the phenomenological elastoplastic constitutive behavior of the ligaments composing the unit cell is modeled. Then, using the constitutive ligament model, the effective unit cell response is obtained from a micromechanical model that enforces the principle of minimum action on a representative 3D unit cell. Finally, the macroscopic specimen response is predicted utilizing a finite element analysis program, which obtains the response at every Gauss point in the mesh from the microscopic unit cell model. The current communication focuses on the ability of the model to capture the yielding and collapse behaviors, as well as the strain rate effects, observed during impact loading of metallic foams.

1.
Weaire
,
D.
, and
Hutzler
,
S.
, 1999,
The Physics of Foam
,
Oxford University Press
,
New York
.
2.
Banhart
,
J.
, 2003, “
Aluminum Foams: On the Road to Real Application
,”
MRS Bull.
0883-7694,
28
(
4
), pp.
290
295
.
3.
Gibson
,
L.
, 2000, “
Mechanical Behavior of Metallic Foams
,”
Annu. Rev. Mater. Sci.
0084-6600,
30
, pp.
191
227
.
4.
Ashby
,
M. F.
,
Evans
,
T.
,
Fleck
,
N.
,
Gibson
,
L.
,
Hutchinson
,
J.
, and
Wadley
,
H.
, 2000,
Metal Foams: A Design Guide
,
1st ed.
,
Butterworth-Heinemann
,
Boston
.
5.
Gibson
,
L. J.
, and
Ashby
,
M. F.
, 1997,
Cellular Solids Structure and Properties
,
2nd ed.
,
Cambridge University Press
,
Cambridge
.
6.
Evans
,
A. G.
,
Hutchinson
,
J. W.
, and
Ashby
,
M. F.
, 1999, “
Multifunctionality of Cellular Metal Systems
,”
Prog. Mater. Sci.
0079-6425,
43
, pp.
171
221
.
7.
Bardenhagen
,
S. G.
,
Brydon
,
A. D.
, and
Guilkey
,
J. E.
, 2005, “
Insight Into the Physics of Foam Densification Via Numerical Simulation
,”
J. Mech. Phys. Solids
0022-5096,
53
, pp.
597
617
.
8.
Gong
,
L.
,
Kyriakides
,
S.
, and
Jang
,
W. -Y.
, 2005, “
Compressive Response of Open-Cell Foams. Part I: Morphology and Elastic Properties
,”
Int. J. Solids Struct.
0020-7683,
42
, pp.
1355
1379
.
9.
Zhou
,
J.
,
Gao
,
Z.
,
Cuitiño
,
A. M.
, and
Soboyejo
,
W. O.
, 2004, “
Effects of Heat Treatment on the Compressive Deformation Behavior of Open Cell Aluminum Foams
,”
Mater. Sci. Eng., A
0921-5093,
386
, pp.
118
128
.
10.
Mukai
,
T.
,
Kanahashi
,
H.
,
Miyoshi
,
T.
,
Mabushi
,
M.
,
Nieh
,
T. G.
, and
Higashi
,
K.
, 1999, “
Dynamic Compressive Behavior of an Ultra-Lightweight Magnesium Foam
,”
Scr. Mater.
1359-6462,
41
(
4
), pp.
365
371
.
11.
Mukai
,
T.
,
Kanahashi
,
H.
,
Yamada
,
Y.
,
Shimojima
,
K.
,
Mabuchi
,
M.
,
Nieh
,
T. G.
, and
Higashi
,
K.
, 1999, “
Experimental Study of the Energy Absorption in a Closed-Celled Aluminum Foam Under Dynamic Loading
,”
Scr. Mater.
1359-6462,
40
(
8
), pp.
921
927
.
12.
Shimojima
,
K.
,
Chino
,
Y.
,
Yamada
,
Y.
,
Wen
,
C.
, and
Mabuchi
,
M.
, 2001, “
Compression Test Simulation of Controlled Cell Shape Open Cellular Magnesium Alloy Under Dynamic Loading
,”
J. Inst. Met.
0020-2975,
41
, pp.
1326
1331
.
13.
Dannemann
,
K. A.
, and
Lankford
,
J.
, Jr.
, 2000, “
High Strain Rate Compression of Closed-Cell Aluminum Foams
,”
Mater. Sci. Eng., A
0921-5093,
293
, pp.
157
164
.
14.
Kanahashi
,
H.
,
Mukai
,
T.
,
Yamada
,
Y.
,
Shimojima
,
K.
,
Mabuchi
,
M.
,
Nieh
,
T.
, and
Higashi
,
K.
, 2001, “
Experimental Study for the Improvement of Crashworthiness in az91 Magnesium Foam Controlling Its Microstructure
,”
Mater. Sci. Eng., A
0921-5093,
308
, pp.
283
287
.
15.
Han
,
F.
,
Zeu
,
Z.
, and
Gao
,
J.
, 1998, “
Compressive Deformation and Energy Absorbing Characteristics of Foamed Aluminum
,”
Metall. Mater. Trans.
,
29
, pp.
2497
2502
.
16.
Hall
,
I. W.
,
Guden
,
M.
, and
Yu
,
C. J.
, 2000, “
Crushing of Aluminum Closed Cell Foams: Density and Strain Rate Effects
,”
Scr. Mater.
1359-6462,
43
, pp.
515
521
.
17.
Yi
,
F.
,
Zhu
,
Z.
,
Zu
,
F.
,
Hu
,
S.
, and
Yi
,
P.
, 2001, “
Strain Rate Effects on the Compressive Property and the Energy-Absorbing Capacity of Aluminum Alloy Foams
,”
Mater. Charact.
1044-5803,
47
, pp.
417
422
.
18.
Kanahashi
,
H.
,
Mukai
,
T.
,
Yamada
,
Y.
,
Shimojima
,
K.
,
Mabuchi
,
M.
,
Nieh
,
T. G.
, and
Higashi
,
K.
, 2000, “
Dynamic Compression of an Ultra-Low Density Aluminum Foam
,”
Mater. Sci. Eng., A
0921-5093,
280
, pp.
349
353
.
19.
Deshpande
,
V. S.
, and
Fleck
,
N. A.
, 2000, “
High Strain Rate Compressive Behavior of Aluminum Alloy Foams
,”
Int. J. Impact Eng.
0734-743X,
24
, pp.
277
98
.
20.
Lee
,
S.
,
Barthelat
,
F.
,
Moldovan
,
N.
,
Espinosa
,
H. D.
, and
Wadley
,
H. N. G.
, 2006, “
Deformation Rate Effects on Failure Modes of Open-Cell Al Foams and Textile Cellular Materials
,”
Int. J. Solids Struct.
0020-7683,
43
, pp.
53
73
.
21.
Lee
,
S.
,
Barthelat
,
F.
,
Hutchinson
,
J. W.
, and
Espinosa
,
H. D.
, 2006, “
Dynamic Failure of Pyramidal Truss Core Materials—Experiments and Modeling
,”
Int. J. Plast.
0749-6419,
22
, pp.
2118
2145
.
22.
Chen
,
W.
,
Lu
,
T. J.
, and
Fleck
,
N. A.
, 1999, “
Effect of Imperfections on the Yielding of Two-Dimensional Foams
,”
J. Mech. Phys. Solids
0022-5096,
47
, pp.
2235
2272
.
23.
Meguid
,
S. A.
,
Cheon
,
S. S.
, and
El-Abbasi
,
N.
, 2002, “
FE Modelling of Deformation Localization in Metallic Foams
,”
Finite Elem. Anal. Design
0168-874X,
38
, pp.
631
643
.
24.
Zhang
,
J.
,
Kikuchi
,
N.
,
Li
,
V.
,
Yee
,
A.
, and
Nusholtz
,
G.
, 1998, “
Constitutive Modeling of Polymeric Foam Material Subjected to Dynamic Crashloading
,”
Int. J. Impact Eng.
0734-743X,
21
(
5
), pp.
369
386
.
25.
Demiray
,
S.
,
Becker
,
W.
, and
Hohe
,
J.
, 2007, “
Numerical Determination of Initial and Subsequent Yield Surfaces of Open-Celled Model Foams
,”
Int. J. Solids Struct.
0020-7683,
44
, pp.
2093
2108
.
26.
Wang
,
Y.
, and
Cuitiño
,
A. M.
, 2000, “
Three-Dimensional Nonlinear Open-Cell Foams With Large Deformations
,”
J. Mech. Phys. Solids
0022-5096,
48
, pp.
961
988
.
27.
Romero
,
P. A.
,
Zheng
,
S. F.
, and
Cuitiño
,
A. M.
, 2008, “
Modeling the Dynamic Response of Viscoelastic Open-Cell Foams
,”
J. Mech. Phys. Solids
0022-5096,
56
, pp.
1916
1943
.
28.
Cuitiño
,
A. M.
, and
Ortiz
,
M.
, 1992, “
A Material-Independent Method for Extending Stress Update Algorithms From Small-Strain Plasticity to Finite Plasticity With Multiplicative Kinematics
,”
Eng. Comput.
0263-4759,
9
, pp.
437
451
.
29.
Ortiz
,
M.
, and
Stainer
,
L.
, 1999, “
The Variational Formulation of Viscoplastic Constitutive Updates
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
171
, pp.
419
444
.
30.
Gioia
,
G.
,
Wang
,
Y.
, and
Cuitiño
,
A. M.
, 2001, “
The Energetics of Heterogeneous Deformation in Open-Cell Solid Foams
,”
Proc. R. Soc. London, Ser. A
0950-1207,
457
, pp.
1079
1096
.
31.
Ericksen
,
J. L.
, 1998,
Introduction to the Thermodynamics of Solids
, revised ed.,
Springer-Verlag
,
New York
.
You do not currently have access to this content.