Abstract

The resistance of sandwich cylinders with density-graded foam cores to internal blast loadings is investigated theoretically and numerically. Four kinds of density-graded foam core are designed, such as positive, negative, middle–high, and middle–low gradients. The deformation process of the sandwich cylinders is assumed to be split into three phases, i.e., fluid–structure interaction, combined deformation of core and inner wall, and sandwich stage of motion. Employing a rigid perfectly-plastic locking model of density-graded foam core, analytical models are proposed to predict the dynamic response of gradient sandwich cylinders. Finite element simulations of gradient sandwich cylinders subjected to internal blast loadings are carried out and agree well with the analytical predictions. Furthermore, the effects of the core density gradients and the wall thickness distributions on the blast resistance are explored and identified. It is shown that the thicker inner wall design can enhance the blast resistance of sandwich cylinders with the same mass.

References

1.
Gibson
,
L. J.
, and
Ashby
,
M. F.
,
1997
,
Cellular Solids: Structure and Properties
, Vol.
33
,
Cambridge University Press
,
Cambridge
, pp.
487
488
.
2.
Ashby
,
M. F.
,
Evans
,
A.
,
Fleck
,
N. A.
,
Gibson
,
L. J.
,
Hutchinson
,
J. W.
,
Wadley
,
H.
, and
Delale
,
F.
,
2000
, “
Metal Foams: A Design Guide
,”
Appl. Mech. Rev.
,
23
(
6
), p.
119
.
3.
Deshpande
,
V. S.
, and
Fleck
,
N. A.
,
2000
, “
High Strain Rate Compressive Behaviour of Aluminium Alloy Foams
,”
Int. J. Impact Eng.
,
24
(
3
), pp.
277
298
.
4.
Wu
,
Q.
,
Yang
,
C.
,
Ohrndorf
,
A.
,
Christ
,
H.-J.
,
Han
,
J.
, and
Xiong
,
J.
,
2020
, “
Impact Behaviors of Human Skull Sandwich Cellular Bones: Theoretical Models and Simulation
,”
J. Mech. Behav. Biomed. Mater.
,
104
, p.
103669
.
5.
Cooper
,
G. J.
,
Townend
,
D. J.
,
Cater
,
S. R.
, and
Pearce
,
B. P.
,
1991
, “
The Role of Stress Waves in Thoracic Visceral Injury From Blast Loading: Modification of Stress Transmission by Foams and High-Density Materials
,”
J. Biomech.
,
24
(
5
), pp.
273
285
.
6.
Wang
,
E.
,
Yao
,
R.
,
Li
,
Q.
,
Hu
,
X.
, and
Sun
,
G.
,
2024
, “
Lightweight Metallic Cellular Materials: A Systematic Review on Mechanical Characteristics and Engineering Applications
,”
Int. J. Mech. Sci.
,
270
, p.
108795
.
7.
Bayat
,
A.
, and
Gaitanaros
,
S.
,
2019
, “
Elastic Wave Propagation in Open-Cell Foams
,”
ASME J. Appl. Mech.
,
86
(
5
), p.
051008
.
8.
Fleck
,
N. A.
, and
Deshpande
,
V. S.
,
2004
, “
The Resistance of Clamped Sandwich Beams to Shock Loading
,”
ASME J. Appl. Mech.
,
71
(
3
), pp.
386
401
.
9.
Hutchinson
,
J. W.
, and
Xue
,
Z.
,
2005
, “
Metal Sandwich Plates Optimized for Pressure Impulses
,”
Int. J. Mech. Sci.
,
47
(
4–5
), pp.
545
569
.
10.
Deshpande
,
V.
, and
Fleck
,
N.
,
2005
, “
One-Dimensional Response of Sandwich Plates to Underwater Shock Loading
,”
J. Mech. Phys. Solids
,
53
(
11
), pp.
2347
2383
.
11.
Liang
,
Y.
,
Spuskanyuk
,
A. V.
,
Flores
,
S. E.
,
Hayhurst
,
D. R.
,
Hutchinson
,
J. W.
,
McMeeking
,
R. M.
, and
Evans
,
A. G.
,
2007
, “
The Response of Metallic Sandwich Panels to Water Blast
,”
ASME J. Appl. Mech.
,
74
(
1
), pp.
81
99
.
12.
Reid
,
S. R.
, and
Peng
,
C.
,
1997
, “
Dynamic Uniaxial Crushing of Wood
,”
Int. J. Impact Eng.
,
19
(
5–6
), pp.
531
570
.
13.
Tan
,
P. J.
,
Reid
,
S. R.
,
Harrigan
,
J. J.
,
Zou
,
Z.
, and
Li
,
S.
,
2005
, “
Dynamic Compressive Strength Properties of Aluminium Foams. Part II—‘Shock’ Theory and Comparison With Experimental Data and Numerical Models
,”
J. Mech. Phys. Solids
,
53
(
10
), pp.
2206
2230
.
14.
Ma
,
G. W.
, and
Ye
,
Z. Q.
,
2007
, “
Analysis of Foam Claddings for Blast Alleviation
,”
Int. J. Impact Eng.
,
34
(
1
), pp.
60
70
.
15.
Harrigan
,
J. J.
,
Reid
,
S. R.
, and
Seyed Yaghoubi
,
A.
,
2010
, “
The Correct Analysis of Shocks in a Cellular Material
,”
Int. J. Impact Eng.
,
37
(
8
), pp.
918
927
.
16.
Zheng
,
Z.
,
Yu
,
J.
, and
Li
,
J.
,
2005
, “
Dynamic Crushing of 2D Cellular Structures: A Finite Element Study
,”
Int. J. Impact Eng.
,
32
(
1–4
), pp.
650
664
.
17.
Wang
,
X.
,
Zheng
,
Z.
, and
Yu
,
J.
,
2013
, “
Crashworthiness Design of Density-Graded Cellular Metals
,”
Theoret. Appl. Mech. Lett.
,
3
(
3
), p.
031001
.
18.
Zhang
,
J.
,
Wang
,
Z.
, and
Zhao
,
L.
,
2016
, “
Dynamic Response of Functionally Graded Cellular Materials Based on the Voronoi Model
,”
Compos. Part B: Eng.
,
85
, pp.
176
187
.
19.
Yang
,
J.
,
Wang
,
S. L.
,
Zheng
,
Z. J.
, and
Yu
,
J. L.
,
2016
, “
Impact Resistance of Graded Cellular Metals Using Cell-Based Finite Element Models
,”
Key Eng. Mater.
,
703
, pp.
400
405
.
20.
Ma
,
G. W.
, and
Ye
,
Z. Q.
,
2007
, “
Energy Absorption of Double-Layer Foam Cladding for Blast Alleviation
,”
Int. J. Impact Eng.
,
34
(
2
), pp.
329
347
.
21.
Liao
,
S.
,
Zheng
,
Z.
, and
Yu
,
J.
,
2013
, “
Dynamic Crushing of 2D Cellular Structures: Local Strain Field and Shock Wave Velocity
,”
Int. J. Impact Eng.
,
57
, pp.
7
16
.
22.
Karagiozova
,
D.
, and
Alves
,
M.
,
2014
, “
Compaction of a Double-Layered Metal Foam Block Impacting a Rigid Wall
,”
Int. J. Solids Struct.
,
51
(
13
), pp.
2424
2438
.
23.
Karagiozova
,
D.
, and
Alves
,
M.
,
2015
, “
Stress Waves in Layered Cellular Materials—Dynamic Compaction Under Axial Impact
,”
Int. J. Mech. Sci.
,
101–102
, pp.
196
213
.
24.
Shen
,
C. J.
,
Yu
,
T. X.
, and
Lu
,
G.
,
2013
, “
Double Shock Mode in Graded Cellular Rod Under Impact
,”
Int. J. Solids Struct.
,
50
(
1
), pp.
217
233
.
25.
Shen
,
C. J.
,
Lu
,
G.
, and
Yu
,
T. X.
,
2014
, “
Investigation Into the Behavior of a Graded Cellular Rod Under Impact
,”
Int. J. Impact Eng.
,
74
, pp.
92
106
.
26.
Zheng
,
J.
,
Qin
,
Q.
, and
Wang
,
T. J.
,
2016
, “
Impact Plastic Crushing and Design of Density-Graded Cellular Materials
,”
Mech. Mater.
,
94
, pp.
66
78
.
27.
Chang
,
B.
,
Zheng
,
Z.
,
Zhang
,
Y.
,
Zhao
,
K.
,
He
,
S.
, and
Yu
,
J.
,
2020
, “
Crashworthiness Design of Graded Cellular Materials: An Asymptotic Solution Considering Loading Rate Sensitivity
,”
Int. J. Impact Eng.
,
143
, p.
103611
.
28.
Ding
,
Y.
,
Zheng
,
Y.
,
Zheng
,
Z.
,
Wang
,
Y.
,
He
,
S.
, and
Zhou
,
F.
,
2020
, “
Blast Alleviation of Sacrificial Cladding With Graded and Uniform Cellular Materials
,”
Materials
,
13
(
24
), p.
5616
.
29.
Gupta
,
V.
,
Kidane
,
A.
, and
Sutton
,
M.
,
2024
, “
Dynamic Characteristics of Density-Graded Cellular Materials for Impact Mitigation
,”
Int. J. Solids Struct.
,
296
, p.
112816
.
30.
Tilbrook
,
M. T.
,
Deshpande
,
V. S.
, and
Fleck
,
N. A.
,
2006
, “
The Impulsive Response of Sandwich Beams: Analytical and Numerical Investigation of Regimes of Behaviour
,”
J. Mech. Phys. Solids
,
54
(
11
), pp.
2242
2280
.
31.
Yin
,
C.
,
Jin
,
Z.
,
Chen
,
Y.
, and
Hua
,
H.
,
2016
, “
One-Dimensional Response of Single/Double-Layer Cellular Cladding to Water Blast
,”
Int. J. Impact Eng.
,
88
, pp.
125
138
.
32.
Feng
,
H.
,
Huang
,
W.
,
Deng
,
S.
,
Yin
,
C.
,
Wang
,
P.
, and
Liu
,
J.
,
2022
, “
Dynamic Fluid-Structure Interaction of Graded Foam Core Sandwich Plates to Underwater Blast
,”
Int. J. Mech. Sci.
,
231
, p.
107557
.
33.
Xiang
,
C.
,
Qin
,
Q.
,
Wang
,
F.
,
Yu
,
X.
,
Wang
,
M.
,
Zhang
,
J.
, and
Wang
,
T. J.
,
2018
, “
Impulsive Response of Rectangular Metal Sandwich Plate With a Graded Foam Core
,”
Int. J. Appl. Mech.
,
10
(
6
), p.
1850064
.
34.
Yang
,
Y.
,
Qin
,
Q.
,
Zheng
,
J.
, and
Wang
,
T. J.
,
2021
, “
Uniaxial Crushing of Sandwich Plates With Continuously Density-Graded Cellular Cores Subjected to Impulsive Loading
,”
Eur. J. Mech. A/Solids
,
90
, p.
104361
.
35.
Yin
,
C.
,
Jin
,
Z.
,
Chen
,
Y.
, and
Hua
,
H.
,
2020
, “
Effects of Sacrificial Coatings on Stiffened Double Cylindrical Shells Subjected to Underwater Blasts
,”
Int. J. Impact Eng.
,
136
, p.
103412
.
36.
Mao
,
W.
,
Zhong
,
M.
,
Xie
,
X.
,
Ma
,
H.
,
Yang
,
G.
, and
Fan
,
L.
,
2024
, “
Dynamic Response of a Hollow Cylindrical Shell Subjected to a Near-Field Underwater Explosion
,”
J. Appl. Phys.
,
135
(
22
), p.
4701
.
37.
Shen
,
J.
,
Lu
,
G.
,
Zhao
,
L.
, and
Zhang
,
Q.
,
2013
, “
Short Sandwich Tubes Subjected to Internal Explosive Loading
,”
Eng. Struct.
,
55
, pp.
56
65
.
38.
Karagiozova
,
D.
,
Langdon
,
G. S.
,
Nurick
,
G. N.
, and
Niven
,
T.
,
2016
, “
The Influence of a Low Density Foam Sandwich Core on the Response of a Partially Confined Steel Cylinder to Internal Air-Blast
,”
Int. J. Impact Eng.
,
92
, pp.
32
49
.
39.
Liang
,
M.
,
Zhang
,
G.
,
Lu
,
F.
, and
Li
,
X.
,
2017
, “
Blast Resistance and Design of Sandwich Cylinder With Graded Foam Cores Based on the Voronoi Algorithm
,”
Thin-Wall. Struct.
,
112
, pp.
98
106
.
40.
Liang
,
M.
,
Lu
,
F.
,
Zhang
,
G.
, and
Li
,
X.
,
2017
, “
Experimental and Numerical Study of Aluminum Foam-Cored Sandwich Tubes Subjected to Internal Air Blast
,”
Compos. Part B: Eng.
,
125
, pp.
134
143
.
41.
Liang
,
M.
,
Li
,
X.
,
Lin
,
Y.
,
Zhang
,
K.
, and
Lu
,
F.
,
2020
, “
Theoretical Analysis of Blast Protection of Graded Metal Foam-Cored Sandwich Cylinders/Rings
,”
Materials
,
13
(
17
), p.
3903
.
42.
Zhang
,
T.
,
Liu
,
Z.
,
Li
,
S.
,
Lei
,
J.
, and
Wang
,
Z.
,
2023
, “
Dynamic Response and Energy Absorption Performance of Aluminum Foam-Filled Sandwich Circular Tubes Under Internal Blast Loading
,”
Int. J. Impact Eng.
,
173
, p.
104458
.
43.
Zhang
,
T.
,
Liu
,
Z.
,
Li
,
S.
,
Lei
,
J.
, and
Wang
,
Z.
,
2024
, “
Elastic-Plastic Response for the Foam-Filled Sandwich Circular Tube Under Internal Blast Loading
,”
Int. J. Impact Eng.
,
188
, p.
104945
.
44.
Tan
,
P. J.
,
Reid
,
S. R.
,
Harrigan
,
J. J.
,
Zou
,
Z.
, and
Li
,
S.
,
2005
, “
Dynamic Compressive Strength Properties of Aluminium Foams. Part I—Experimental Data and Observations
,”
J. Mech. Phys. Solids
,
53
(
10
), pp.
2174
2205
.
You do not currently have access to this content.