This review covers studies dealing with simplified analytical models for ballistic penetration of an impactor into different solid media, namely, metals, soil, concrete, and composites at high speeds, but not at hypervelocities. The overview covers mainly papers that were published in the last decade, but not analyzed in previous reviews on impact dynamics. Both mathematical models and their engineering applications are considered. The review covers 280 citations.

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,
R. P.
, 1976, “
A Review of Procedures for the Analysis and Design of Concrete Structures to Resist Missile Impact Effects
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, and
Goldsmith
,
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, and
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,
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, 1982, “
Penetration and Perforation of Solids
,”
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,
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Zukas
,
T.
Nicholas
,
H. F.
Swift
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, and
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, 1986, “
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,”
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202
.
6.
Anderson
,
C. E.
, Jr.
, and
Bodner
,
S. R.
, 1988, “
Ballistic Impact: The Status of Analytical and Numerical Modeling
,”
Int. J. Impact Eng.
0734-743X,
11
(
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), pp.
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40
.
7.
Heuzé
,
F. E.
, 1989, “
An Overview of Projectile Penetration Into Geological Materials, With Emphasis on Rocks
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8.
Recht
,
R. F.
, 1990, “
High Velocity Impact Dynamics: Analytical Modeling of Plate Penetration Dynamics
,”
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,
J. A.
Zukas
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Wiley
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9.
Zukas
,
J. A.
, and
Walters
,
W. P.
, 1990, “
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,” In:
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,
J. A.
Zukas
(ed),
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, New York.
10.
Abrate
,
S.
, 1991, “
Impact on Laminated Composite Materials
,”
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44
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), pp.
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190
.
11.
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,
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, 1994, “
Impact on Laminated Composites: Recent Advances
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47
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), pp.
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544
.
12.
Dancygier
,
A. N.
, and
Yankelevsky
,
D. Z.
, 1996, “
High Strength Concrete Response to Hard Projectile Impact
,”
Int. J. Impact Eng.
0734-743X,
18
(
6
), pp.
583
599
.
13.
Corbett
,
G. G.
,
Reid
,
S. R.
, and
Johnson
,
W.
, 1996, “
Impact Loading of Plates and Shells by Free-Flying Projectiles: A Review
,”
Int. J. Impact Eng.
0734-743X,
18
(
2
), pp.
141
230
.
14.
Abrate
,
S.
, 1998,
Impact on Composite Structures
,
Cambridge Univ. Press
, Cambridge.
15.
Teland
,
J. A.
, 1998, “
A Review of Empirical Equations for Missile Impact Effects on Concrete
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16.
Børvik
,
T.
,
Langseth
,
M.
,
Hopperstad
,
O. S.
, and
Malo
,
K. A.
, 1998, “
Empirical Equations for Ballistic Penetration of Metal Plates
,” Fortifikatorisk Notat No. 260/98, The Norwegian Defence Construction Service, Central Staff—Technical Division, Oslo, Norway.
17.
Kasano
,
H.
, 1999, “
Recent Advances in High-Velocity Impact Perforation of Fiber Composite Laminates
,”
JSME Int. J., Ser. A
1340-8046,
42
(
2
), pp.
147
157
.
18.
Goldsmith
,
W.
, 1999, “
Non-Ideal Projectile Impact on Targets
,”
Int. J. Impact Eng.
0734-743X,
22
(
2-3
), pp.
95
395
.
19.
Cheeseman
,
B. A.
, and
Bogetti
,
T. A.
, 2003, “
Ballistic Impact Into Fabric and Compliant Composite Laminates
,”
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61
(
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), pp.
161
173
.
20.
Phoenix
,
S. L.
, and
Porwal
,
P. K.
, 2003, “
A New Membrane Model for the Ballistic Impact Response and v50 Performance of Multi-Ply Fibrous Systems
,”
Int. J. Solids Struct.
0020-7683,
40
(
24
), pp.
6723
6765
.
21.
Bunimovich
,
A.
, and
Dubinsky
,
A.
, 1995,
Mathematical Models and Methods of Localized Interaction Theory
,
World Scientific
, Singapore.
22.
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,
A.
, and
Dubinsky
,
A.
, 1996, “
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,”
Fluid Dyn. Res.
0169-5983,
31
(
3
), pp.
339
349
.
23.
Ben-Dor
,
G.
,
Dubinsky
,
A.
, and
Elperin
,
T.
, 1997, “
Shape Optimization of High Velocity Impactors Using Analytical Models
,”
Int. J. Fract.
0376-9429,
87
(
1
), pp.
L7
L10
.
24.
Ben-Dor
,
G.
,
Dubinsky
,
A.
, and
Elperin
,
T.
, 1997, “
Area Rules for Penetrating Bodies
,”
Theor. Appl. Fract. Mech.
0167-8442,
26
(
3
), pp.
193
198
.
25.
Li
,
Q. M.
,
Weng
,
H. J.
, and
Chen
,
X. W.
, 2004, “
A Modified Model for the Penetration Into Moderately Thick Plates by a Rigid, Sharp-Nosed Projectile
,”
Int. J. Impact Eng.
0734-743X,
30
(
2
), pp.
193
204
.
26.
Ben-Dor
,
G.
,
Dubinsky
,
A.
, and
Elperin
,
T.
, 1997, “
Optimal 3D Impactors Penetrating Into Layered Targets
,”
Theor. Appl. Fract. Mech.
0167-8442,
27
(
3
), pp.
161
166
.
27.
Ben-Dor
,
G.
,
Dubinsky
,
A.
, and
Elperin
,
T.
, 1998, “
On the Ballistic Resistance of Multi-Layered Targets With Air Gaps
,”
Int. J. Solids Struct.
0020-7683,
35
(
23
), pp.
3097
3103
.
28.
Ben-Dor
,
G.
,
Dubinsky
,
A.
, and
Elperin
,
T.
, 2001, “
Shape Optimization of Penetrator Nose
,”
Theor. Appl. Fract. Mech.
0167-8442,
35
(
3
), pp.
261
270
.
29.
Chen
,
X. W.
, and
Li
,
Q. M.
, 2002, “
Deep Penetration of a Non-Deformable Projectile With Different Geometrical Characteristics
,”
Int. J. Impact Eng.
0734-743X,
27
(
6
), pp.
619
637
.
30.
Nishiwaki
,
J.
, 1951, “
Resistance to the Penetration of a Bullet Through an Aluminium Plate
,”
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, pp.
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378
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31.
Chernyi
,
G. G.
, 1969,
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,
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, New York.
32.
Vitman
,
F. F.
, and
Stepanov
,
V. A.
, 1959, “
Effect of the Strain Rate on the Resistance of Metals to Deformation at Impact Velocities of 100-1000m∕s
,” In:
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221
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33.
Golubev
,
V. K.
, and
Medvedkin
,
V. A.
, 2001, “
Penetration of a Rigid Rod Into a Thick Steel Plate at Elevated Velocities
,”
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33
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), pp.
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.
34.
Landgrov
,
I. F.
, and
Sarkisyan
,
O. A.
, 1984, “
Piercing Plastic-Material Barriers With a Rigid Punch
,”
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, pp.
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35.
Heimdahl
,
O. E. R.
, and
Schulz
,
J. C.
, 1986, “
A Note on the Obtainment of Instantaneous Penetration Information From Final Penetration Data
,”
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.
36.
Mileiko
,
S. T.
, and
Sarkisyan
,
O. A.
, 1981, “
Phenomenological Model of Punch-Through
,”
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37.
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S. T.
,
Sarkisyan
,
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, and
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,
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, 1994, “
Ballistic Limits of Al-6% Mg Allow Laminated by Diffusion Bonding
,”
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38.
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,
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,
Lee
,
L. M.
,
Jenrette
,
B. D.
, and
Setchell
,
R. E.
, 1984, “
Gas-Gun Experiments Determine Forces on Penetrators Into Geological Targets
,”
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51
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39.
Forrestal
,
M. J.
,
Lee
,
L. M.
, and
Jenrette
,
B. D.
, 1986, “
Laboratory-Scale Penetration Experiments Into Geological Targets to Impact Velocities of 2.1km∕s
,”
ASME J. Appl. Mech.
0021-8936,
53
(
2
), pp.
317
320
.
40.
Ben-Dor
,
G.
,
Dubinsky
,
A.
, and
Elperin
,
T.
, 2002, “
Optimal Nose Geometry of the Impactor Against FRP Laminates
,”
Compos. Struct.
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55
(
1
), pp.
73
80
.
41.
Ben-Dor
,
G.
,
Dubinsky
,
A.
, and
Elperin
,
T.
, 2002, “
Optimization of the Nose Shape of an Impactor Against a Semi-Infinite FRP Laminate
,”
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62
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42.
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,
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,
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,
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, and
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,
T.
, 2002, “
A Model for Predicting Penetration and Perforation of FRP Laminates by 3-D Impactors
,”
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56
(
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), pp.
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248
.
43.
Sagomonyan
,
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, 1960, “
Penetration of Sharp Bodies of Revolution Into Soils
,”
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44.
Rakhmatulin
,
Kh. A.
,
Sagomonian
,
A. Ya.
, and
Alekseev
,
N. A.
, 1964,
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,
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45.
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,
D. Z.
, and
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,
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,”
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Bishop
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,
Hill
,
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, and
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,”
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,”
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,
Anderson
,
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,
Asay
,
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,
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,
Grady
,
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, and
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,
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54.
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, and
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, and
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57.
Hetherington
,
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,”
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,
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, 1996, “
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, and
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