Homogenization Modeling for Mechanical 

Properties of Composite Conductor With 

Cooling Channel 

by Wei Sun and Jerome T. Tzeng 

ARL-TR-2872 November 2002

Approved for public release; distribution is unlimited. 
Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5069 

ARL-TR-2872 November 2002

Homogenization Modeling for Mechanical 

Properties of Composite Conductor With 

Cooling Channel 

Wei Sun and Jerome T. Tzeng 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited.
Abstract 

An electrical composite conductor may consist of a metallic core with a cooling channel and a 

multilayered insulating material. A model was developed to predict the mechanical properties of 

the composite conductor based on two-level homogenization hierarchies. A composite cylinder 

assembly model was developed in the level 1 homogenization for metallic core with a cooling 

channel, in which the cooling channel was analogized as a fiber void with null material 

properties. The effective mechanical properties of the composite insulation layers were

homogenized by smearing the properties of the multiple polymer coatings and fiber-reinforced 

composite. In the level 2 homogenization, combined homogenization sequences were used 

based on the requirement of the displacement- or the traction-prescribed continuity. The

developed model can calculate the nine effective mechanical constants of the conductor made of 

a metallic core and any angle (±θ°) plain-woven glass-fiber composite. The model predictions 

were compared well with the results obtained from the finite element analyses. The developed 

model provides a theoretical basis and an accurate calculation for effective mechanical constants

that are often difficult to be accurately determined through an experimental approach due to the

structural heterogeneity and material anisotropy of the composite conductor. 

ii
Contents 

List of Figures v

List of Tables vii

1. Introduction 1

2. Conductor Structural Layout and Homogenization Scheme 2

3. Homogenization Modeling 3

3.1 Homogenization of the Effective Metallic Core With Cooling Channel ........................3 

3.2 Homogenization of the Insulation Layers as Composite Blocks ....................................5 

3.3 Homogenization of EM Composite Conductor...............................................................8 

4. Results and Comparisons 11

4.1 Results of the Modeling Prediction...............................................................................11 

4.2 Comparison With the Numerical (Finite Element) Solution.........................................11 

4.3 Parametric Studies.........................................................................................................14 

5. Summary and Conclusion 15

6. References 17

Report Documentation Page 19 

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iv
List of Figures 

Figure 1. Schematic representation of a composite conductor unit cell. ........................................2 

Figure 2. Two-level homogenization scheme.................................................................................3 

Figure 3. Effective modeling of metallic core with cooling channel by CCAM............................4 

Figure 4. Section views of conductor and insulation composite blocks.........................................6 

Figure 5. Homogenization of composite conductor........................................................................9 

Figure 6. Combined sequences for composite conductor homogenization. ...................................9 

Figure 7. FEA mesh, loading, and boundary condition for determining CC EXX ..............................12 

Figure 8. Comparison of FEA and analytical predictions (conducting core with cross 

section: 1 H 1 in, insulation layer thickness: 0.02 in, D = 0.3 in). ............................................13 

Figure 9. Comparison of FEA and analytical predictions (conducting core with cross 

section: 1 H 1.5 in, insulation layer thickness: 0.02 in, D = 0.3 in). ........................................13 

Figure 10. Effect of the plain-woven fiber orientation on the conductor effective 

properties (conducting core with cross section: 0.75 H 1.0 in, insulation layer 

thickness: 0.015 in, D = 0.3 in)................................................................................................14 

Figure 11. Effect of cooling channel diameter on the conductor effective properties 

(conducting core with cross section: 0.75 H 1.0 in, insulation layer thickness: 

0.015 in). ..................................................................................................................................15 

Figure 12. Effect of insulation layer thickness on conductor effective properties 

(conducting core cross section: 1 H 1.25 in, D = 0.3 in).........................................................15 

Figure 13. Effect of conducting core cross section on effective properties (conducting 

core cross section: L H aL with L = 1 in, insulation layer thickness = 0.02 in, D = 

0.3 in). ......................................................................................................................................16 

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vi
List of Tables 

Table 1. Assumed constituent material properties and geometries...............................................11

Table 2. Homogenized elastic mechanical constants (L = 1 in, a = 1.5, b = c = d = 0.02, 

D = 0.3 in)................................................................................................................................11 

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viii
1. Introduction 

Electrical machinery, which ranges from electric drive vehicles to the electric launch system, is 

considered to be one of the most important components in the future combat systems. Compact, 

durable, and highly mobile power generators and motors are necessary for the success of all 

electrical systems [1, 2]. Extensive research has been conducted for electromagnetic (EM) 

structural design, analysis, and mechanics on various technical areas [3–9]. Because of the 

complex geometry and the heterogeneity of the conductor with insulation layers, the EM systems 

usually need to be analyzed using numerical techniques such as the finite element method. 

However, a conventional finite element analysis (FEA) cannot analyze each structural entity 

from the whole EM system because of the limit of computational time and machine capacity

limitations. Therefore, the EM structure must be analyzed separately at different levels, i.e., a 

global and local level. The analyses conducted at the global level use the homogenized effective 

properties derived from the representative volume element, or a unit cell of the EM conductor 

[10, 11]. At this level, the structure of the composite conductor is homogenized by smearing the 

distinctive phases of the constituents, and the effective properties of the EM conductor unit cell 

are derived. The unit cell properties are used to predict the global responses of the EM system

subjected to a given loading condition. The results derived from the global analysis will then be 

used in the local level analysis where the individual constituents, including their geometries and

properties, are considered, and the detail stress and deformation will be calculated. Clearly, an

accurate prediction of the conductor effective mechanical properties is critical because they

provide the fundamental material parameters in the design and analysis of the EM structural 

behavior under the combined mechanical, EM, and thermal loading, as well as the system

structural integrity, insulation, and service life. 

In this report, a homogenization modeling to predict the effective mechanical properties of EM 

composite conductor consisting of metallic core with cooling channel and multilayered

insulating materials is presented. The model was developed based on the two-level 

homogenization hierarchy schemes, in conjunction with the composite cylinder assembly model

(CCAM) and the combined homogenization sequences. The developed model was applied to 

predict the effective properties of the EM conductor made of metallic conducting core with 

cooling channel, insulation layers of different phase materials, and ±θ° plain-woven glass-fiber 

composite. These effective properties are composed of nine material constants that are often 

difficult to accurately determine through an experimental approach due to the structural

heterogeneity and material anisotropy. The model predictions were also compared and validated

with finite element calculation. 

The presentation of this report is organized as follows: Section 2 describes the conductor 

schematics, including its structural layout, geometric and material configuration, as well as the 

1
homogenization scheme used in the study; the analytical model to predict the conductor 

homogenized effective constants is derived and presented in section 3; the application of the 

model to predict the effective properties, the results, and comparisons will be presented in

section 4; a summary and conclusion follows in section 5. 

2. Conductor Structural Layout and Homogenization Scheme 

We consider a composite conductor consisting of an interior metallic conducting core with 

cooling channel and the exterior insulation layers made by different insulation materials and ±θ° 

plain-woven glass-fiber-reinforced composite. The metallic core conducts pulsating EM currents

that can cause rapid heating of the core material. The fiber-reinforced composite is used to 

provide desired mechanical and thermal properties, as well as an extra insulating protection. The

small cooling channel in the middle of the core lets a pressurized coolant circulate at a high

velocity in order to reduce the heat. The metallic conductor core with cooling channel, wrapped 

with the insulating composites, is packed into a winding assembly. A schematic representation 

of the constituent materials and geometries for such a composite conductor unit cell is presented 

in Figure 1. 

Insulation layer 2 (Phase 2) 

(thickness: cL) 

Insulation layer 3 (Phase 3) 

Glass/Epoxy plain-woven 

(thickness: dL) Insulation layer 1 (Phase 1) 

(thickness: bL) 

Metallic conducting Core

(L x aL) 

Cooling channel

(Diameter: D)

L

Figure 1. Schematic representation of a composite conductor unit cell.

For a composite conductor unit cell as shown in Figure 1, we used the following two-level 

homogenization schemes to derive its effective mechanical properties:

Level 1: Homogenization for effective metallic core and effective insulation composite

blocks; 

2
Level 2: Homogenization for effective composite conductor consisting of effective 

metallic core and effective insulation composite blocks. 

The level 1 homogenization is composed of two separate procedures: to determine the effective 

mechanical properties of metallic conducting core with cooling channel through composite

cylinder assembly model [12] and to determine the effective mechanical properties of the 

insulation layer, which consists of different phase insulation materials and glass composite. The 

results of the homogenized mechanical properties of the insulation layers and the metallic 

conducting core calculated from the level 1 homogenization will be used to derive the effective 

mechanical properties of the composite conductor in the level 2 homogenization. The 

homogenization scheme is illustrated in Figure 2, and the detail derivation is presented in the 

next section. 

Level 1 

Homogenization 

Level 2 

Homogenization 

Figure 2. Two-level homogenization scheme. 

3. Homogenization Modeling 

3.1 Homogenization of the Effective Metallic Core With Cooling Channel

We analogize the metallic core containing cooling channel in Figure 3 as a composite cylinder 

assembly, which is composed of a matrix (metallic core) and a cylindrical fiber (cooling channel 

as void). For this type of composite assembly, we apply a CCAM [12] to calculate its

homogenized mechanical properties. 

As shown in the derivation of the CCAM [12], the effective mechanical constants of the 

conducting core containing a cooling channel can be expressed by 

1 1

2

2

1

1 2

2

2 1

1 1 2 2 1

4( )

k G

V

k

V

V V

E E V E V M

A

+ +

− = + +ν ν

; (1)

3
Homogenized conducting 

core by CCAM

Conducting core 

with cooling channel

r 

Original 

metallic core Equivalent 

metallic 

cylinder 

Cooling Channel

Volume of homogenized metallic core = Volume of equivalent metallic cylinder 

= Volume of original metallic core 

Figure 3. Effective modeling of metallic core with cooling channel by CCAM. 

1 1

2

2

1

1 2

1 2

2 1

1 1 2 2 1

) 1 1 ( )(

k G

V

k

V

V V

k k

V V M

A

+ +

− −

= + +

ν ν

ν ν ν ; (2)

1 2 2 1

1 1 2 2

1 (1 )

(1 )

G V G V

G V G V G G M

A

+ +

+ + = ; (3)

2

( ) ( )

M

T

M

M T

T

G G

G + + − = ; (4)

2

)

4

) (

4

(

( )

( )

( )

( )

M

T

M

M

T

M

M

T

M

M

T

M

M

T

k mG

k G

k mG

k G

E −

−

+

+

+

+

+ = ; (5)

M

T

M

M

T

M

M

T k mG

k mG

+

− ν = ; (6)

with 

2 2

2 2 1

2 1

3 2 1

2

2 2

2 2 1

2 1

3 2 1

2

( ) 1

(1 )( ) 3

(1 )( ) 3

β βα

β β βα

V V V

G G

G G

V

V V V

G G

G G

V

G G M

T

− − −

+

+

+ − −

+

+

+ = ; (7)

]

1

[1

1

2 1

1

2

( ) 1

+ β

+ −

− = +

V

G G

G

V G G M

T ; (8)

4
2

2

1

2

2

1

1

3 4

3 4 3 4

− ν

+

− ν − − ν

α = G G

G G

; (9)

3 4 1

1

ν

β − = ; (10)

1 1

1

2 1

2

1 1

k G

V

k k

V k k M

+

+ −

= + ; (11)

M

A

M

A

M

E

k

m

2 4 ( ) 1

ν = + . (12)

The nomenclatures used in equations (1)–(12) are defined as follows: superscript M denotes 

metallic core; subscripts A and T denote the effective properties in the channel axial direction (in 

Z direction) and in the transverse direction (in X or Y direction), respectively; T(+) and T(!) 

stand for the upper and lower bounds; 1 and 2 stand for homogenized metallic core, original

metallic core, and cooling channel (fiber); E is for Young's modulus; G is for shear modulus; k is 

for bulk modulus; υ is for Poisson’s ratio, and V is for volume fraction. 

If we analogize the cooling channel as a cylindrical void in the CCAM as shown in Figure 3, E2, 

G2, k2, and υ2 will be equal to zero. Substituting these values into equations (1)–(12) obtain 

(1 ) , (13) E E1V1 E1 V2

M

A = = −

, (14) ν =ν 1

M

A

(1 )

(1 )

2

2

1 V

V G G M

A

+

− = , (15)

3 4 1

1

ν

α β − = = , (16)

1 1 2

1 1 2 (1 )

G k V

k G V k M

+

− = , (17)

with the transverse constants being defined by equations (4)–(8). 

3.2 Homogenization of the Insulation Layers as Composite Blocks 

Because of the different fiber orientations in the plain-woven composite with respect to the 

global conductor coordinate system, we homogenize the over-wrapped insulation layers as two 

different composite blocks: CB1 at the horizontal surfaces of the conducting core and CB2 at the 

vertical surfaces. The difference between CB1 and CB2 is in the fiber orientation of the 

5
plain-woven composite with respect to the global coordinate system XYZ, as indicated in 

Figure 4. The detail section views of the insulation composite block CB1 and CB2 are shown in 

Figure 4b and Figure 4c, and the relationship between the local composite coordinate system xyz

for a typical insulation composite block and the conductor global structural coordinate system 

XYZ is shown in Figure 4d, respectively. 

c) Section view of composite 

block 2 - CB2 

(G/E ± 450 in YZ-plane) 

b) Section view of composite block 1 - CB1

(G/E ± 450 in XZ-plane) 

Y 

X

a) Section view of composite

conductor

X 

Glass 

Composite

Phase 2

Phase 1 

Z

Y

x z

y

0

0

d) Coordinate systems 

xyz: local composite coordinate system

XYZ: global conductor coordinate system

X

Y

P11 P2

Phase 1 (P1)

Phase 2 (P2)

G

Glass Composite (G)

CB2 CB2

CB

CB1

Y

X

Metallic Core 

Figure 4. Section views of conductor and insulation composite blocks. 

Based on the composite mechanics and homogenization theory [14–16], we can derive an 

analytical expression for elastic constants of the typical composite block shown in Figure 4d. Its 

nine elastic constants in the global coordinate system XYZ can be expressed in terms of the 

elastic constants of its constituent layers and their volume fractions as: 

; (18) G

P P P P G yy

CB EXX = V E +V E +V E 1 1 2 2

1 2 2 1 1 2

1 2

G P P

G

P P zz G

P P zz

G

CB P P zz

YY

V E E V E E V E E

E E E

E

+ + = ; (19)

; (20) G

P P P P G xx CB EZZ = V E +V E +V E 1 1 2 2

; (21) G

P P P P G yz

CB

XY

CB ν XY =ν = V ν +V ν +V ν 1 1 2 2

6
1 2 2 1 2 1

1 2

G P P

G

P P yz

G

P P yz

G

CB P P yz

XY

V G G V G G V G G

G G G

G

+ + = ; (22)

1 2 2 1 2 1

1 2

G P P

G

P P xz G

P P xz

G

CB P P xz

YZ

V G G V G G V G G

G G G

G

+ + = ; (23)

; (24) G

P P P P G xy

CB GXZ = V G +V G +V G 1 1 2 2

; (25) G

P P P P G xz CB ν YZ = V ν +V ν +V ν 1 1 2 2

1 2 2 1 1 2

1 2

G P P

G

P P xy

G

P P xy

G

CB P P xy

XZ

V ν ν V ν ν V ν ν

ν ν ν

ν

+ + = . (26)

The elastic constants of the plain-woven glass/epoxy composite in the local coordinate system

(xyz) can be determined by 

θ θ + θ ν θ + −

= 4

11

2 2

11

12

12

11 22

4

22

11 22

)sin cos sin 1 2

cos ( E

G E

E E E

E E

E G

xx ; (27) 

θ θ + θ ν θ + −

= 4

22

2 2

11

12

12

11 22

4

11

11 22

)sin cos sin 1 2cos ( E

G E

E E E

E E E G

yy ; (28) 

)sin cos ] 1 1 1 [ (sin cos ) ( 2 2

11 22 12

4 4

11

12 θ + θ − + − θ θ ν

ν = E E E GExx

G

xy ; (29) 

)sin cos (sin cos ) 2 2 4 1 2 ( 2 2 4 4

11 12

12

11 22

12

12

− θ θ + θ + θ ν+ +

=

E E E G

G

G GG

xy ; (30) 

)] 1 ) 0.5(1 )( 1 [ (

0.5[ 0.5(1 )]

23

m

m

f m

m m

f

f

f

f

f

m f m

G

yz

E E E

E

V

E E

V

E

E

V V

G G

ν

+ × + +

ν

+

+ × +

= = ; (31) 

f m m f

G f m

zz V E V E

E E

E E

+ = = 33 ; (32)

m m ; (33) f f

G ν yz =ν 23 = V ν +V ν

m m ; (34) f f

G ν xz =ν 13 = V ν +V ν

7
)] 1 ) 0.5(1 )( 1 [ (

0.5[ 0.5(1 )]

13

m

m

f m

m m

f

f

f

f

f

m f m

G

xz

E E E

E

V

E E

V

E

E

V V

G G

ν

+ × + +

ν

+

+ × +

= = . (35) 

The detail derivation for glass composite mechanical properties have been addressed by Sun and 

Tzeng [10], and Huang [13]. The additional nomenclatures in equations (18)–(35), as well as in

the following expressions, are defined as follows: the superscripts CB1 and CB2 denote

composite blocks 1 and 2; the subscripts 1, 2, and 3 are for the composite principle coordinate 

system; x, y, or z denote components in the composite local coordinate system; X, Y, and Z 

denote the conductor global structural coordinate system; P1, P2, and G denote phase 1, phase 2, 

and glass composite insulation materials; the subscripts f and m denote constituent fiber and

matrix in glass composite materials; Vi

Pj denotes the volume fraction of individual insulation

material in the composite blocks, with i = 1, 2 for CB1 and CB2, and j = 1, 2, 3 for phase 1, 

phase 2, and phase 3 material, respectively; and Vf and Vm denote the volume fraction of the fiber 

and matrix in glass composites. 

From equations (18)–(26), we can determine the effective elastic constants for composite blocks

CB1 and CB2 as shown in Figures 4b and 4c. Their relations to the constants of the typical 

composite block (Figure 4d) are: 

(36)

CB

XZ

CB

XZ

CB

YZ

CB

YZ

CB

XY

CB

XY

CB

XZ

CB

XZ

CB

YZ

CB

YZ

CB

XY

CB

XY

CB

ZZ

CB

ZZ

CB

YY

CB

YY

CB

XX

CB

XX

v

G G G G G G

E E E E E E

= = =

= = =

= = =

1 1 1

1 1 1

1 1 1

; ;

; ;

; ;

υ υ υ υ υ

for composite block CB1, and 

(37)

CB

YZ

CB

XZ

CB

XZ

CB

YZ

CB

XY

CB

XY

CB

YZ

CB

XZ

CB

XZ

CB

YZ

CB

XY

CB

XY

CB

ZZ

CB

ZZ

CB

XX

CB

YY

CB

YY

CB

XX

v

G G G G G G

E E E E E E

= = =

= = =

= = =

2 2 2

2 2 2

2 2 2

; ;

; ;

; ;

υ υ υ υ υ

for composite block CB2. 

3.3 Homogenization of EM Composite Conductor 

Homogenization for effective mechanical properties of the composite conductor is accomplished 

by homogenizing the effective metallic conducting core with the composite insulation blocks.

The schematic of the homogenization is illustrated in Figure 5. 

To homogenize the mechanical properties of the composite conductor, we consider using a 

two-sequence model as shown in Figure 6. Namely, the homogenized mechanical properties of 

the composite conductor are determined through a combined sequence operations. In sequence 

1, we first homogenize the insulation composite block and the metallic conducting core to 

8
Homogenized Composite Conductor

(Composite blocks + Metallic core)

X

Z

Y 

0

Insulation Composite Block 1

G/E ± 45° in XZ-plane

Insulation Composite Block 2

G/E ± 45° in YZ-plane

Insulation Composite Block 1 

G/E ± 45° in XZ-plane

Insulation Composite Block 2 

G/E ± 45° in YZ-plane

Metallic

Core

Figure 5. Homogenization of composite conductor.

Sequence 2

Y 

CB1

CB1

CB2 CB2

Sequence 1 X

{ , } 2 2 M

ij

CB

ij

CB M Eij = E E −

CB1

CB1

CB2

CB2

X

Y 

Sequence 1

Sequence 2 

{ , } 1 1 M

ij CBij CB M Eij = E E −

a) { , } 1 CB2 M

ij

CB

ij

CC Eij E E − = b) { , } 2 CB1 M

ij

CB

ij

CC Eij E E − =

Figure 6. Combined sequences for composite conductor homogenization.

determine the effective mechanical properties (Figure 6a) or (Figure 6b). In 

sequence 2, we add the remaining insulation composite blocks to the results of the sequence 1 

homogenization to derive the effective mechanical properties of the composite conductor . 

Depending on the responses of the constituents to the prescribed deformation, the effective 

constants derived from the sequence operations or 

 will be calculated either through a displacement-prescribed relation: 

CB M Eij2− CB M Eij1−

{(E , E CBi

ij

CC Eij

= ), = 1, 2} − E i M

ij

CBi M

ij

= {( , ), = 1, 2} − E E E i CBi M

ij

CBi

ij

CC

ij

9 
.... (38) 1 1 2 2 = ij + ij + effective Eij V E V E

or a stress-prescribed relation:

...

...

1 2 2 1

1 2

+ + =

ij ij

effective ij ij

ij V E V E

E E

E . (39)

Based on the previously mentioned analogies, we establish the following mathematical 

formulations to calculate the homogenized mechanical properties of the composite conductor: 

2 2

2

1 1

CB

XX

CB M M

CB

XX

M

CB

XX

CC CB

XX

V E V E

E E

E V E

+ = + ; (40)

1 1

1

2 2

CB

YY

CB M M

CB

YY

M

CB

YY

CC CB

YY

V E V E

E E

E V E

+ = + ; (41)

; (42) 1 1 2 CB2

ZZ

CB CB

ZZ

CC M M CB EZZ = V E +V E +V E

( ) ( ) 2 1 2 1 2 2

1 2

CB

XY

CB CB M M

XY

CB M CB CB M

XY

CB M

XY

CB

CC XY

XY G G V V V G V G V G

G G G G

+ + + = ; (43) 

( ) ( )

( )

2 1 1 2 2

1 1 2

CB M M

YZ

CB CB CB

YZ

CB M

CB M M

YZ

CB CB

CC YZ

YZ

V V G V V G V G

G V G V G G

+ + +

+ = ; (44)

( ) ( )

( )

1 2 2 2 1

2 1 1

CB M M

XZ

CB CB CB

XZ

CB M

CB M M

XZ

CB CB

CC XZ

XZ

V V G V V G V G

G V G V G G

+ + +

+ = ; (45) 

2 2

2

1 1

CB

XY

CB M M

CB

XY

M

CB

XY

CC CB

XY

V V

V

ν ν

ν ν

ν ν

+ = + ; (46)

1 2 2 1 1 2

1 2

CB

YZ

CB

YZ

CB M M

YZ

CB M CB

YZ

CB

CB

YZ

CB

YZ

M

CC

YZ

V ν ν V ν ν V ν ν

ν ν ν

ν

+ + = ; (47) 

1 2 2 1 1 2

1 2

CB

XZ

CB

XZ

CB M M

XZ

CB M CB

XZ

CB

CB

XZ

CB

XZ

M

CC

XZ

V ν ν V ν ν V ν ν

ν ν ν

ν

+ + = . (48) 

In equations (40)–(48), the homogenized mechanical properties of metallic conducting core are 

determined by the CCAM model and are related to the global coordinate system as: 

, ; M

T

M

YY

M EXX = E = E M

A

M EZZ = E

, G ; (49) M

T

M GXY = G M

A

M

YZ

M

XZ = G = G

, . M

T

M ν XY =ν M

A

M

YZ

M ν XZ =ν =ν

10 
4. Results and Comparisons 

4.1 Results of the Modeling Prediction

The assumed constituent material properties and the designed geometry in the conductor unit cell 

(Figure 1) are listed in Table 1. 

Table 1. Assumed constituent material properties and geometries. 

Constituent Material Dimension Material Properties 

Metallic Conducting Core Width H height H depth 

(L H aL H L)

Young’s modulus EM: 10.0 (106

 psi)

Poisson’s ratioυΜ: 0.32 

Diameter of cooling channel: D 

Phase 1 

Insulation Material 

Thickness 

bL 

Young’s modulus EP1: 0.5 (106 psi)

Poisson’s ratio υP1: 0.35

Phase 2 

Insulation Material 

Thickness 

cL 

Young’s modulus EP2: 0.075 (106 psi)

Poisson’s ratio υP2: 0.35

Phase 3 

Glass/Epoxy Composite 

Thickness 

dL 

±45° plain woven 

E-glass fiber: Ef: 10.5 (106

 psi); υf: 0.22 

Epoxy: Em: 0.5 (106

 psi); υm: 0.35

Fiber volume fraction Vf: 0.5 

From the equations defined in the level 1 and level 2 homogenization, we obtain the following 

homogenized elastic material constants for metallic conducting core with the cooling channel, 

for composite insulation blocks, and for composite conductor. These results are summarized in 

Table 2. 

Table 2. Homogenized elastic mechanical constants (L = 1 in, a = 1.5, b = c = d = 0.02, D = 0.3 in).

Homogenized Conductor Core Composite Block 

CB1

Composite Block 

CB2

Composite Conductor 

EM

A = 8.115 Mpsi

EM

T = 6.252 Mpsi

GM

A = 2.586 Mpsi 

GM

T = 2.424 Mpsi 

υM

A = 0.320

υM

T= 0.290 

ECB1XX = 0.675 Mpsi 

ECB1YY = 0.183 Mpsi 

ECB1ZZ = 0.675 Mpsi 

GCB1XY = 0.069 Mpsi 

GCB1YZ = 0.069 Mpsi 

GCB1XZ = 0.417 Mpsi 

υCB1XY = 0.089

υCB1YZ = 0.328 

υCB1XZ = 0.378 

ECB2XX = 0.183 Mpsi 

ECB2YY = 0.675 Mpsi 

ECB2ZZ = 0.675 Mpsi 

GCB2XY = 0.069 Mpsi 

GCB2XZ = 0.417 Mpsi 

GCB2YZ = 0.069 Mpsi 

υCB2XY = 0.328

υCB2YZ = 0.378 

υCB2XZ = 0.328 

ECCXX = 1.485 Mpsi 

ECCYY = 2.011 Mpsi 

ECCZZ = 6.826 Mpsi 

GCCXY = 0.368 Mpsi 

GCCYZ = 0.694 Mpsi 

GCCXZ = 0.522 Mpsi 

υCCXY = 0.322 

υCCYZ = 0.326 

υCCXZ = 0.324 

4.2 Comparison With the Numerical (Finite Element) Solution

The finite element model is developed based on the designed computer-aided design (CAD)

geometry. The FEA software used in the analysis is ANSYS 5.6.3. A total of 6300 8-node brick 

11 
elements was generated in ANSYS for the unit cell CAD model. Out of the 6300 elements, there 

are 1260 8-node Solid64-type structural anisotropic elements in CB1, 1440 8-node Solid64-type

structural anisotropic elements in CB2, and 3600 8-node Solid45-type structural brick elements

in the metallic core. The material properties of CB1 and CB2 are determined from the equations

derived in section 3. The FEA mesh, loading, and boundary condition for determining is 

presented in Figure 7. For the purpose of description, we present only one case of determining 

the effective constant by using the FEA model and numerical calculation. A description of 

using the FEA model and numerical approach to calculate all nine mechanical constants was 

detailed by Hashin [12]. 

CC EXX

CC EXX

X

Y

Ux

UX = 0.001LX @ SX1

UX = 0 @ SX2 

LY

SX1 

LX

SY2

SY1

SX2

Z

Y 

X 

SZ2

SZ2

Figure 7. FEA mesh, loading, and boundary condition for determining . CC EXX

Based on the prescribed loading and boundary condition as shown in Figure 7, the conductor 

effective constant can be determined as CC EXX

2

2 0.001

( )

( )

SX

X

X

X

SX

X

X

CC X

XX A

R

L

U

A

R

E = = × ε

σ = , (50)

and 

R N dA , (51) X

Sx

X ∫ =

2

with 

U X LX = 0.001 on SX1, (52) 

= 0.0 U X on SX2, (53) 

12 
where Ux is the prescribed displacement on the surface SX1 and SX2; ASX1 and ASX2 are the areas 

of the surface SX1 and SX2, respectively; LX is the dimension of the unit cell in the X direction; a 

scale of 0.001 in the application displacement on the surface SX1 produces a uniform strain at the 

value of 0.1%, and RX is the X-component of the average reaction force produced on the surface

SX2 as a result of the prescribed displacement UX on the surface SX1. 

Comparisons of the analytical predictions to the numerical calculations based on the FEA are 

presented in Figures 8 and 9 for the composite conductor with different core cross sections. It 

can be seen that the mechanical constants predicted from the analytical model agree well with

the finite element predictions for both cases, except for a slight difference between the 

predictions of the in-plane Poisson’s ratio υxy. 

0.00E+00

1.00E+06

2.00E+06

3.00E+06

4.00E+06

5.00E+06

6.00E+06

7.00E+06

Exx Eyy Ezz Gxy Gyz Gxz

FEA Prediction Analytical Model

0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

uxy uyz uxz

FEA Prediction Analytical Model

Figure 8. Comparison of FEA and analytical predictions (conducting core with cross section: 1 H 1 in, insulation

layer thickness: 0.02 in, D = 0.3 in). 

0.00E+00

1.00E+06

2.00E+06

3.00E+06

4.00E+06

5.00E+06

6.00E+06

7.00E+06

Exx Eyy Ezz Gxy Gyz Gxz

FEA Prediction Analytical Model

0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

uxy uyz uxz

FEA Prediction Analytical Model

Figure 9. Comparison of FEA and analytical predictions (conducting core with cross section: 1 H 1.5 in, insulation

layer thickness: 0.02 in, D = 0.3 in). 

13 
4.3 Parametric Studies 

The effects of the fiber orientation in the composite layer and the change of the channel diameter 

on the effective properties of the conductor are studied, and the results are presented in 

Figures 10 and 11, respectively. It seems that the homogenized effective properties of the 

conductor are not sensitive to the fiber orientations, except for a slight variation for axial 

modulus, , and the axial Poisson’s ratio, and , as shown in Figure 10. The increase 

of the channel diameter will decrease the axial modulus, , , and G , as well as the

transverse Poisson’s ratio, , but will produce less of an effect on the transverse modulus, 

, , and G , and has no effect on the axial Poisson’s ratio, and , as shown in 

Figure 11. We believe that this trend of change is caused by the reduction of the axial modulus

and the transverse Poisson’s ratio of the metallic core due to the increase of the channel 

diameter. 

CC EZZCC υ XZCC υYZ

CC EZZCC GXZCC

YZ

υ

CC υ XY

CC EXXCC EYYCC

XY

CC υ XZCC

YZ

0.00E+00

2.00E+06

4.00E+06

6.00E+06

8.00E+06

1.00E+07

0 15 30 45

Fiber woven angle (degree)

Modulus (psi)

Exx

Eyy

Ezz

Gxy

Gyz

Gxz

2.50E-01

2.75E-01

3.00E-01

3.25E-01

3.50E-01

3.75E-01

4.00E-01

0 15 30 45

Fiber woven angle (degree)

Poisson ratio

Uxy

Uyz

Uxz

Figure 10. Effect of the plain-woven fiber orientation on the conductor effective properties (conducting core with

cross section: 0.75 H 1.0 in, insulation layer thickness: 0.015 in, D = 0.3 in). 

The variation of the conductor geometry, such as the change of the insulation layer thickness and

change of the conductor core cross section on the effective properties of the conductor are also 

studied and the results are presented in Figures 12 and 13, respectively. It can be observed that 

the increase in the insulation layer thickness will, in general, decrease the effective modulus of 

the conductor because of the decrease of the conducting core volume. The three Young’s 

modulus, , , and , and the in-plane Poisson’s ratio, , are particularly sensitive to 

this change, while the shear modulus and the axial Poisson’s ratios are less sensitive, as shown in 

Figure 12. Geometric variation, i.e., increasing the core height dimension, will affect the axial 

Young’s modulus, , and in-plane Poisson’s ratio, , but will not dramatically affect other

conductor effective mechanical properties, as shown in Figure 13. 

CC EXXCC EYY

E

CC EZZCC υ XY

CC

ZZ

CC υ XY

14 
0.00E+00

2.00E+06

4.00E+06

6.00E+06

8.00E+06

1.00E+07

0 0.1 0.2 0.3 0.4 0.5

Diameter of cooling channel (inch)

Modulus (psi)

Exx

Eyy

Ezz

Gxy

Gyz

Gxz

2.50E-01

3.00E-01

3.50E-01

4.00E-01

0 0.1 0.2 0.3 0.4 0.5

Diameter of cooling channel (inch)

Poisson ratio

Uxy

Uyz

Uxz

Figure 11. Effect of cooling channel diameter on the conductor effective properties (conducting core with cross 

section: 0.75 H 1.0 in, insulation layer thickness: 0.015 in). 

0.00E+00

2.00E+06

4.00E+06

6.00E+06

8.00E+06

0.005 0.01 0.02 0.04 0.06 0.08 0.1

Insulation Layer Thickness (inch)

Modulus (psi)

Ezz

Exx

Eyy

Gyz

Gxz

Gxy

0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

0.005 0.01 0.02 0.04 0.06 0.08 0.1

Insulation Layer Thickness (inch)

Poisson Ratio

Uxy

Uxz

Uyz

Figure 12. Effect of insulation layer thickness on conductor effective properties (conducting core cross section:

1 H 1.25 in, D = 0.3 in). 

5. Summary and Conclusion 

A homogenization modeling to predict the effective mechanical properties of EM composite 

conductor consisting of metallic core with cooling channel and insulating layers of different 

materials and ±θ° plain woven glass-fiber composite was presented. The homogenization 

scheme was developed based on the following two-level homogenization hierarchies: the 

homogenization of the metallic core with cooling channel and composite insulation blocks and 

the homogenization of the EM composite conductor. The CCAM was applied in the level 1 

15 
0.00E+00

2.00E+06

4.00E+06

6.00E+06

8.00E+06

0.75 1 1.25 1.5

a

Core Cross Section (L x aL, L = 1")

Modulus (psi)

Ezz

Exx

Eyy

Gyz

Gxz

Gxy

2.80E-01

2.90E-01

3.00E-01

3.10E-01

3.20E-01

3.30E-01

3.40E-01

3.50E-01

0.75 1 1.25 1.5

a

Core Cross Section (L x aL, L = 1")

Poisson Ratio

Uxy

Uxz

Uyz

Figure 13. Effect of conducting core cross section on effective properties (conducting core cross section: L H aL

with L = 1 in, insulation layer thickness = 0.02 in, D = 0.3 in). 

homogenization process to derive the effective properties of the conducting core with the cooling 

channel. In the CCAM-based modeling, the cooling channel was analogized as a fiber void with 

null material properties. The effective mechanical properties of the composite insulation blocks 

were homogenized by smearing the properties of the insulating layers. In the derivation of the 

homogenization model to predict the effective mechanical properties of the composite conductor, 

combined sequences of the homogenization were used and the homogenization algorithms were

executed based on either the displacement prescribed or the traction prescribed boundary 

conditions. 

The developed homogenization model was applied to predict the effective mechanical properties

of the EM composite conductor. The mechanical properties of the homogenized EM composite

conductor behave anisotropically due to the material anisotropy and the structural anisotropy of

the conductor. The material anisotropy is primarily caused by the constituent anisotropic 

properties of the insulation layer originated from the glass fiber plain-woven composite. The 

structural anisotropy is caused by the transverse dimensional difference in the conductor global 

structure. Both anisotropies contribute a significant difference between the transverse modules

( , , ) and the axial modules ( , G , G ), as shown in Table 2. The slight

difference between and in Table 2 is due to the geometric difference of the conducting 

core in the X and Y directions, while this difference vanishes if the dimensions of the conducting 

core in X and Y are the same, as shown in Figure 13, where a = 1 for a conducting core with a 

square cross section. However, the effective Poisson’s ratios of the conductor are not too 

sensitive to the material anisotropy and the structural anisotropy. There is no significant 

difference between the three principal Poisson’s ratios, as observed in both Table 2 and in the 

subsequent figures. The good agreement between the analytical and numerical predictions as 

shown in Figures 8 and 9 demonstrates the applicability and accuracy of the developed

homogenization model. 

CC EXXCC EYYCC GXYCC EZZCC

XZ

CC

YZ

CC EXXCC EYY

16 
6. References 

1. Fair, H. D., and E. M. Schmidt. “The Science and Technology of Electric Launch, A U.S. 

Perspective.” IEEE Transaction on Magnetics, vol. 35, no. 1, pp. 11–18, 1999. 

2. Walls, W. A., W. F. Weldon, S. B. Pratap, M. Palmer, and D. Adams. “Application of 

Electromagnetic Guns to Future Naval Platforms.” IEEE Transaction on Magnetics, vol. 37, 

pp. 262–267, 1999. 

3. Rosenwasser, S., G. Nagy, and G. Mehle. “The Design, Fabrication and Characterization of 

an Advanced Graphite Composite Structure for High Speed Rotating Machines.” IEEE 

Transaction on Magnetics, vol. 35, no. 1, pp. 307–311, 1999. 

4. Satapathy, S., and C. Persad. “Thermal Stress in EML Rail-Conductor Overlays.” IEEE 

Transaction on Magnetics, vol. 37, no. 1, pp. 269–274, 2001. 

5. Becherini, G., M. Raugi, and A. Tellini. “Thermal and Mechanical Stress in Induction 

Coilguns.” IEEE Transaction on Magnetics, vol. 35, pp. 130–135, 1999. 

6. Liu, H. P., Y. L. Ting, and R. C. Zowarka. “Electromagnetic and Structural Analyses of an 

Integrated Launch Package.” IEEE Transaction on Magnetics, vol. 35, pp. 74–78, 1999. 

7. Myatt, R. L., and P. H. Titus. “3D, Coupled Electromagnetic, Thermal, Current Diffusion in 

the Finger Joints of the Alcator C-Mod Toroidal Field Coils.” IEEE Transaction of 

Magnetics, vol. 34, pp. 713–716, 1998. 

8. Tzeng, J. T. “Mechanics of Composite Rotating Machines for Pulsed Power Applications.” 

IEEE Transaction on Magnetics, vol. 37, no. 1, pp. 328–331, 2001. 

9. Tzeng, J. T. “Dynamic Responses and Fracture of Composite Cylinders.” Journal of 

Composite Science and Technology, vol. 58, no. 9, pp. 1443–1452, 1998. 

10. Sun, W., and J. T. Tzeng. “Effective Mechanical Model of Electromagnetic (EM) 

Composite Conductor.” ARL-TR-2674, U.S. Army Research Laboratory, Aberdeen Proving 

Ground, MD, February 2002. 

11. Sun, W., and J. T. Tzeng. “Global-Local FEA Modeling for EM Composite Conductor With 

Cooling Channel.” U.S. Army Research Laboratory, Aberdeen Proving Ground, MD, to be 

published. 

12. Hashin, Z. “Theory of Fiber-Reinforced Materials.” NASA-CR-1974, National Aeronautics 

and Space Administration, Washington, DC, 1974. 

17 
13. Huang, Z. M. “The Mechanical Properties of Composites Reinforced With Woven and 

Braided Fabrics.” Composite Science and Technology, vol. 60, pp. 479–498, 2000. 

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the Mechanics and Physics of Solids, vol. 11, pp. 357–372, 1963. 

15. Hassani, B., and E. Hinton. “A Review of Homogenization and Topology Optimization I – 

Homogenization Theory for Media With Periodic Structure.” Computer & Structures, 

vol. 69, pp. 707–717, 1998. 

16. Hassani, B., and E. Hinton. “A Review of Homogenization and Topology Optimization II – 

Analytical and Numerical Solution of Homogenization Equations.” Computer & Structures, 

vol. 69, pp. 719–738, 1998. 

18 
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PO BOX LIVERMORE CA 94550 12211

RESEARCH TRIANGLE PARK NC 

1 AFRL MLS OL 27709-2211 L COULTER 

5851 F AVE 1 AFRL MLBC 

BLDG 849 RM AD1A 2941 P ST RM 136 

WRIGHT HILL AFB UT 84056-5713 PATTERSON AFB OH 

 45433-7750 

 1 DIRECTOR 

LOS ALAMOS NATIONAL LAB 8 NAVAL SURFACE WARFARE CTR 

F L ADDESSIO T 3 MS 5000 J FRANCIS CODE G30 

PO BOX 1633 D WILSON CODE G32 LOS ALAMOS NM 87545 R D COOPER CODE G32 

J FRAYSSE CODE G33 1 OSD E ROWE CODE G33 JOINT CCD TEST FORCE T DURAN CODE G33 OSD JCCD L DE SIMONE CODE G33 R WILLIAMS R HUBBARD CODE G33 3909 HALLS FERRY RD DAHLGREN VA 22448 VICKSBURG MS 29180-6199

2 NAVAL SURFACE WARFARE CTR 3 DARPA CARDEROCK DIVISION M VANFOSSEN 

R CRANE CODE 2802 S WAX 

C WILLIAMS CODE 6553 L CHRISTODOULOU 3A LEGGETT CIR 3701 N FAIRFAX DR BETHESDA MD 20054-5000 ARLINGTON VA 22203-1714

 1 AFRL MLSS 2 SERDP PROGRAM OFC R THOMSON PM P2 

2179 12TH ST RM 122 C PELLERIN

WRIGHT PATTERSON AFB OH B SMITH 45433-7718 901 N STUART ST STE 303 

 ARLINGTON VA 22203 

 2 AFRL 

 F ABRAMS 1 OAK RIDGE NATIONAL J BROWN LABORATORY BLDG 653 R M DAVIS 2977 P ST STE 6 PO BOX 2008 WRIGHT PATTERSON AFB OH OAK RIDGE TN 37831-6195 45433-7739 

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COPIES ORGANIZATION COPIES ORGANIZATION

1 OAK RIDGE NATIONAL 1 USDOT FEDERAL RAILRD 

 LABORATORY M FATEH RDV 31 

C EBERLE MS 8048 WASHINGTON DC 20590 

PO BOX 2008 

OAK RIDGE TN 37831 3 CYTEC FIBERITE 

 R DUNNE 

 3 DIRECTOR D KOHLI 

 SANDIA NATIONAL LABS R MAYHEW 

APPLIED MECHANICS DEPT 1300 REVOLUTION ST 

 MS 9042 HAVRE DE GRACE MD 21078 

 J HANDROCK

Y R KAN 1 DIRECTOR 

 J LAUFFER NATIONAL GRND INTLLGNC CTR 

PO BOX 969 IANG TMT 

 LIVERMORE CA 94551-0969 2055 BOULDERS RD 

 CHARLOTTESVILLE VA 

1 OAK RIDGE NATIONAL 22911-8318 

 LABORATORY 

C D WARREN MS 8039 1 SIOUX MFG 

PO BOX 2008 B KRIEL 

OAK RIDGE TN 37831 PO BOX 400 

FT TOTTEN ND 58335 

 4 NIST 

M VANLANDINGHAM MS 8621 2 3TEX CORPORATION 

J CHIN MS 8621 A BOGDANOVICH 

J MARTIN MS 8621 J SINGLETARY 

D DUTHINH MS 8611 109 MACKENAN DR 

 100 BUREAU DR CARY NC 27511 

GAITHERSBURG MD 20899 

 1 3M CORPORATION 

 1 HYDROGEOLOGIC INC J SKILDUM 

SERDP ESTCP SPT OFC 3M CENTER BLDG 60 IN 01 

 S WALSH ST PAUL MN 55144-1000 

1155 HERNDON PKWY STE 900 

HERNDON VA 20170 1 DIRECTOR 

DEFENSE INTLLGNC AGNCY 

3 NASA LANGLEY RSCH CTR TA 5 

 AMSRL VS K CRELLING

W ELBER MS 266 WASHINGTON DC 20310 

F BARTLETT JR MS 266 

G FARLEY MS 266 1 ADVANCED GLASS FIBER YARNS 

HAMPTON VA 23681-0001 T COLLINS 

281 SPRING RUN LANE STE A 

1 NASA LANGLEY RSCH CTR DOWNINGTON PA 19335 

T GATES MS 188E 

HAMPTON VA 23661-3400 1 COMPOSITE MATERIALS INC 

 D SHORTT 

 1 FHWA 19105 63 AVE NE 

 E MUNLEY PO BOX 25 

6300 GEORGETOWN PIKE ARLINGTON WA 98223 

 MCLEAN VA 22101 

8 
NO. OF NO. OF

COPIES ORGANIZATION COPIES ORGANIZATION

 1 JPS GLASS 2 MILLIKEN RSCH CORP 

 L CARTER H KUHN

PO BOX 260 M MACLEOD

 SLATER RD PO BOX 1926 

SLATER SC 29683 SPARTANBURG SC 29303 

 1 COMPOSITE MATERIALS INC 1 CONNEAUGHT INDUSTRIES INC 

 R HOLLAND J SANTOS 

11 JEWEL CT PO BOX 1425 

ORINDA CA 94563 COVENTRY RI 02816 

1 COMPOSITE MATERIALS INC 1 ARMTEC DEFENSE PRODUCTS 

 C RILEY S DYER 

14530 S ANSON AVE 85 901 AVE 53

SANTA FE SPRINGS CA 90670 PO BOX 848 

 COACHELLA CA 92236 

 2 SIMULA 

J COLTMAN 1 NATIONAL COMPOSITE CENTER 

 R HUYETT T CORDELL 

10016 S 51ST ST 2000 COMPOSITE DR 

PHOENIX AZ 85044 KETTERING OH 45420 

 2 PROTECTION MATERIALS INC 3 PACIFIC NORTHWEST LAB 

M MILLER M SMITH 

 F CRILLEY G VAN ARSDALE 

14000 NW 58 CT R SHIPPELL 

MIAMI LAKES FL 33014 PO BOX 999 

RICHLAND WA 99352 

 2 FOSTER MILLER 

 M ROYLANCE 8 ALLIANT TECHSYSTEMS INC 

 W ZUKAS C CANDLAND MN11 2830 

195 BEAR HILL RD C AAKHUS MN11 2830 

WALTHAM MA 02354-1196 B SEE MN11 2439 

N VLAHAKUS MN11 2145 

1 ROM DEVELOPMENT CORP R DOHRN MN11 2830 

R O MEARA S HAGLUND MN11 2439 

136 SWINEBURNE ROW M HISSONG MN11 2830 

BRICK MARKET PLACE D KAMDAR MN11 2830 

 NEWPORT RI 02840 600 SECOND ST NE 

HOPKINS MN 55343-8367 

 2 TEXTRON SYSTEMS 

 T FOLTZ 1 SAIC 

 M TREASURE M PALMER 

1449 MIDDLESEX ST 1410 SPRING HILL RD STE 400 

 LOWELL MA 01851 MS SH4 5 

MCLEAN VA 22102 

1 O GARA HESS & EISENHARDT 

 M GILLESPIE

9113 LESAINT DR 

FAIRFIELD OH 45014 

9 
NO. OF NO. OF

COPIES ORGANIZATION COPIES ORGANIZATION

 1 APPLIED COMPOSITES 1 BRIGS COMPANY 

 W GRISCH J BACKOFEN 

333 NORTH SIXTH ST 2668 PETERBOROUGH ST 

ST CHARLES IL 60174 HERNDON VA 22071-2443 

 1 CUSTOM ANALYTICAL 1 ZERNOW TECHNICAL SERVICES 

ENG SYS INC L ZERNOW 

 A ALEXANDER 425 W BONITA AVE STE 208 

13000 TENSOR LANE NE SAN DIMAS CA 91773 

 FLINTSTONE MD 21530 

1 GENERAL DYNAMICS OTS

 1 AAI CORPORATION L WHITMORE 

DR N B MCNELLIS 10101 NINTH ST NORTH 

PO BOX 126 ST PETERSBURG FL 33702 

HUNT VALLEY MD 21030-0126 

2 GENERAL DYNAMICS OTS

1 OFC DEPUTY UNDER SEC DEFNS FLINCHBAUGH DIV 

 J THOMPSON K LINDE 

1745 JEFFERSON DAVIS HWY T LYNCH 

CRYSTAL SQ 4 STE 501 PO BOX 127 

 ARLINGTON VA 22202 RED LION PA 17356 

 3 ALLIANT TECHSYSTEMS INC 1 GKN WESTLAND AEROSPACE 

 J CONDON D OLDS 

 E LYNAM 450 MURDOCK AVE 

 J GERHARD MERIDEN CT 06450-8324 

WV01 16 STATE RT 956 

PO BOX 210 5 SIKORSKY AIRCRAFT 

ROCKET CENTER WV 26726-0210 G JACARUSO 

 T CARSTENSAN 

1 PROJECTILE TECHNOLOGY INC B KAY 

515 GILES ST S GARBO MS S330A 

HAVRE DE GRACE MD 21078 J ADELMANN 

 6900 MAIN ST

 1 HEXCEL INC PO BOX 9729 

 R BOE STRATFORD CT 06497-9729 

PO BOX 18748

SALT LAKE CITY UT 84118 1 PRATT & WHITNEY 

C WATSON 

5 AEROJET GEN CORP 400 MAIN ST MS 114 37 

 D PILLASCH EAST HARTFORD CT 06108

 T COULTER 

 C FLYNN 1 AEROSPACE CORP 

 D RUBAREZUL G HAWKINS M4 945 

 M GREINER 2350 E EL SEGUNDO BLVD 

1100 WEST HOLLYVALE ST EL SEGUNDO CA 90245 

AZUSA CA 91702-0296 

 2 CYTEC FIBERITE 

1 HERCULES INC M LIN 

 HERCULES PLAZA W WEB 

WILMINGTON DE 19894 1440 N KRAEMER BLVD 

ANAHEIM CA 92806 

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NO. OF NO. OF

COPIES ORGANIZATION COPIES ORGANIZATION

 2 UDLP 1 NORTHRUP GRUMMAN CORP 

 G THOMAS ELECTRONIC SENSORS 

 M MACLEAN & SYSTEMS DIV 

PO BOX 58123 E SCHOCH MS V 16 

SANTA CLARA CA 95052 1745A W NURSERY RD 

 LINTHICUM MD 21090 

1 UDLP WARREN OFC 

A LEE 1 GDLS DIVISION

31201 CHICAGO RD SOUTH D BARTLE 

 SUITE B102 PO BOX 1901 

WARREN MI 48093 WARREN MI 48090 

 2 UDLP 2 GDLS 

 R BRYNSVOLD D REES 

P JANKE MS 170 M PASIK 

4800 EAST RIVER RD PO BOX 2074 

MINNEAPOLIS MN 55421-1498 WARREN MI 48090-2074 

 2 BOEING ROTORCRAFT 1 GDLS 

 P MINGURT MUSKEGON OPERATIONS

 P HANDEL M SOIMAR 

800 B PUTNAM BLVD 76 GETTY ST 

WALLINGFORD PA 19086 MUSKEGON MI 49442 

 1 BOEING 1 GENERAL DYNAMICS 

 DOUGLAS PRODUCTS DIV AMPHIBIOUS SYS 

L J HART SMITH SURVIVABILITY LEAD

3855 LAKEWOOD BLVD G WALKER 

 D800 0019 991 ANNAPOLIS WAY 

LONG BEACH CA 90846-0001 WOODBRIDGE VA 22191 

 1 LOCKHEED MARTIN 6 INST FOR ADVANCED 

SKUNK WORKS TECH 

 D FORTNEY H FAIR 

1011 LOCKHEED WAY I MCNAB 

PALMDALE CA 93599-2502 P SULLIVAN 

 S BLESS 

 1 LOCKHEED MARTIN W REINECKE 

 R FIELDS C PERSAD 

 5537 PGA BLVD 3925 W BRAKER LN STE 400

 SUITE 4516 AUSTIN TX 78759-5316 

ORLANDO FL 32839 

1 ARROW TECH ASSO 

1233 SHELBURNE RD STE D8 

 SOUTH BURLINGTON VT 

 05403-7700 

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COPIES ORGANIZATION COPIES ORGANIZATION

1 R EICHELBERGER 2 PENN STATE UNIV 

 CONSULTANT R MCNITT 

409 W CATHERINE ST C BAKIS 

BEL AIR MD 21014-3613 212 EARTH ENGR 

 SCIENCES BLDG 

 1 SAIC UNIVERSITY PARK PA 16802 

 G CHRYSSOMALLIS 

8500 NORMANDALE LAKE BLVD 1 PENN STATE UNIV 

 SUITE 1610 R S ENGEL 

BLOOMINGTON MN 55437-3828 245 HAMMOND BLDG 

UNIVERSITY PARK PA 16801 

1 UCLA MANE DEPT ENGR IV

H T HAHN 1 PURDUE UNIV

LOS ANGELES CA 90024-1597 SCHOOL OF AERO & ASTRO 

C T SUN 

2 UNIV OF DAYTON W LAFAYETTE IN 47907-1282 

 RESEARCH INST 

R Y KIM 1 STANFORD UNIV 

A K ROY DEPT OF AERONAUTICS 

300 COLLEGE PARK AVE & AEROBALLISTICS 

 DAYTON OH 45469-0168 S TSAI

 DURANT BLDG

1 UMASS LOWELL STANFORD CA 94305 

 PLASTICS DEPT 

 N SCHOTT 1 UNIV OF MAINE 

1 UNIVERSITY AVE ADV STR & COMP LAB 

LOWELL MA 01854 R LOPEZ ANIDO 

5793 AEWC BLDG 

1 IIT RESEARCH CENTER ORONO ME 04469-5793 

D ROSE 

 201 MILL ST 1 JOHNS HOPKINS UNIV 

ROME NY 13440-6916 APPLIED PHYSICS LAB 

 P WIENHOLD

1 GA TECH RSCH INST 11100 JOHNS HOPKINS RD

GA INST OF TCHNLGY LAUREL MD 20723-6099 

 P FRIEDERICH 

ATLANTA GA 30392 1 UNIV OF DAYTON 

J M WHITNEY

1 MICHIGAN ST UNIV COLLEGE PARK AVE 

 MSM DEPT DAYTON OH 45469-0240 

 R AVERILL 

 3515 EB 1 NORTH CAROLINA STATE UNIV 

EAST LANSING MI 48824-1226 CIVIL ENGINEERING DEPT

 W RASDORF 

1 UNIV OF WYOMING PO BOX 7908 

 D ADAMS RALEIGH NC 27696-7908 

PO BOX 3295 

LARAMIE WY 82071 

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NO. OF NO. OF

COPIES ORGANIZATION COPIES ORGANIZATION

5 UNIV OF DELAWARE ABERDEEN PROVING GROUND

CTR FOR COMPOSITE MTRLS 

 J GILLESPIE 1 US ARMY MATERIEL 

 M SANTARE SYSTEMS ANALYSIS ACTIVITY 

 S YARLAGADDA P DIETZ 

 S ADVANI 392 HOPKINS RD 

 D HEIDER AMXSY TD 

 201 SPENCER LABORATORY APG MD 21005-5071 

 NEWARK DE 19716 

1 US ARMY ATC 

 1 DEPT OF MATERIALS W C FRAZER 

 SCIENCE & ENGINEERING CSTE DTC AT AC I

 UNIVERSITY OF ILLINOIS 400 COLLERAN RD 

 AT URBANA CHAMPAIGN APG MD 21005-5059 

 J ECONOMY 

1304 WEST GREEN ST 115B 1 DIRECTOR 

URBANA IL 61801 US ARMY RESEARCH LAB 

AMSRL OP AP L 

 1 UNIV OF MARYLAND APG MD 21005-5066 

DEPT OF AEROSPACE ENGNRNG

A J VIZZINI 84 DIR USARL 

COLLEGE PARK MD 20742 AMSRL CI

AMSRL CI S 

 1 DREXEL UNIV A MARK 

A S D WANG AMSRL CS IO FI 

32ND & CHESTNUT ST M ADAMSON

 PHILADELPHIA PA 19104 AMSRL SL BA

 AMSRL SL BL

3 UNIV OF TEXAS AT AUSTIN D BELY 

CTR FOR ELECTROMECHANICS R HENRY 

 J PRICE AMSRL SL BG 

 A WALLS AMSRL SL I 

 J KITZMILLER AMSRL WM

10100 BURNET RD J SMITH 

AUSTIN TX 78758-4497 AMSRL WM B

 A HORST 

 3 VA POLYTECHNICAL AMSRL WM BA

INST & STATE UNIV D LYON 

 DEPT OF ESM AMSRL WM BC

M W HYER P PLOSTINS 

 K REIFSNIDER J NEWILL 

 R JONES S WILKERSON 

BLACKSBURG VA 24061-0219 A ZIELINSKI

AMSRL WM BD

 1 SOUTHWEST RSCH INST B FORCH 

ENGR & MATL SCIENCES DIV R FIFER 

 J RIEGEL R PESCE RODRIGUEZ 

6220 CULEBRA RD B RICE 

 PO DRAWER 28510 AMSRL WM BE

SAN ANTONIO TX 78228-0510 C LEVERITT 

AMSRL WM BF

 J LACETERA 

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ABERDEEN PROVING GROUND (CONT) ABERDEEN PROVING GROUND (CONT)

AMSRL WM BR AMSRL WM TA

 C SHOEMAKER W GILLICH 

 J BORNSTEIN T HAVEL 

 AMSRL WM M J RUNYEON 

 D VIECHNICKI M BURKINS 

 G HAGNAUER E HORWATH

 J MCCAULEY B GOOCH 

 AMSRL WM MA W BRUCHEY 

 L GHIORSE M NORMANDIA 

 S MCKNIGHT AMRSL WM TB

 AMSRL WM MB D KOOKER 

 B FINK P BAKER 

 J BENDER AMSRL WM TC

 T BOGETTI R COATES 

 R BOSSOLI AMSRL WM TD

 L BURTON A DAS GUPTA 

 K BOYD T HADUCH 

 S CORNELISON T MOYNIHAN 

 P DEHMER F GREGORY 

 R DOOLEY M RAFTENBERG

 W DRYSDALE M BOTELER 

 G GAZONAS T WEERASOORIYA 

 S GHIORSE D DANDEKAR 

 D GRANVILLE AMSRL WM TE 

 D HOPKINS A NIILER 

 C HOPPEL J POWELL 

 D HENRY 

 R KASTE 

 M KLUSEWITZ 

 M LEADORE 

 R LIEB 

 E RIGAS 

 J SANDS 

 D SPAGNUOLO 

 W SPURGEON 

 J TZENG 

 E WETZEL 

 AMRSL WM MC 

 J BEATTY 

 E CHIN

 J MONTGOMERY 

 A WERECZCAK 

 J LASALVIA

 AMSRL WM MD 

 W ROY 

 S WALSH 

AMSRL WM T

 B BURNS 

 M ZOLTOSKI 

14 
NO. OF NO. OF

COPIES ORGANIZATION COPIES ORGANIZATION

 1 LTD 1 DYNAMEC RESEARCH AB 

 R MARTIN AKE PERSSON 

 MERL BOX 201 

 TAMWORTH RD SE 151 23 SODERTALJE 

HERTFORD SG13 7DG SWEDEN 

 UK 

1 ISRAEL INST OF

 1 SMC SCOTLAND TECHNOLOGY

 P W LAY S BODNER 

 DERA ROSYTH FACULTY OF MECHANICAL 

ROSYTH ROYAL DOCKYARD ENGR

DUNFERMLINE FIFE KY 11 2XR HAIFA 3200 

 UK ISRAEL

 1 CIVIL AVIATION 1 DSTO 

 ADMINSTRATION WEAPONS SYSTEMS DIVISION 

 T GOTTESMAN N BURMAN RLLWS 

PO BOX 8 SALISBURY 

BEN GURION INTERNL AIRPORT SOUTH AUSTRALIA 5108 

 LOD 70150 AUSTRALIA

 ISRAEL

 1 DEF RES ESTABLISHMENT 

 1 AEROSPATIALE VALCARTIER

 S ANDRE A DUPUIS

A BTE CC RTE MD132 2459 BOULEVARD PIE XI NORTH 

316 ROUTE DE BAYONNE VALCARTIER QUEBEC 

 TOULOUSE 31060 CANADA 

 FRANCE PO BOX 8800 COURCELETTE

GOA IRO QUEBEC 

1 DRA FORT HALSTEAD CANADA 

P N JONES 

SEVEN OAKS KENT TN 147BP 1 INSTITUT FRANCO ALLEMAND 

 UK DE RECHERCHES DE SAINT 

 LOUIS 

1 DEFENSE RESEARCH ESTAB DE M GIRAUD 

 VALCARTIER 5 RUE DU GENERAL 

 F LESAGE CASSAGNOU

 COURCELETTE QUEBEC BOITE POSTALE 34 

 COA IRO F 68301 SAINT LOUIS CEDEX 

 CANADA FRANCE

 1 SWISS FEDERAL ARMAMENTS 1 ECOLE POLYTECH 

 WKS J MANSON 

 W LANZ DMX LTC 

 ALLMENDSTRASSE 86 CH 1015 LAUSANNE 

 3602 THUN SWITZERLAND 

 SWITZERLAND 

15 
NO. OF

COPIES ORGANIZATION

1 TNO DEFENSE RESEARCH

 R IJSSELSTEIN

ACCOUNT DIRECTOR 

 R&D ARMEE 

PO BOX 6006 

2600 JA DELFT

 THE NETHERLANDS 

2 FOA NATL DEFENSE RESEARCH 

 ESTAB 

DIR DEPT OF WEAPONS & 

 PROTECTION 

 B JANZON 

 R HOLMLIN 

S 172 90 STOCKHOLM 

 SWEDEN 

2 DEFENSE TECH & PROC AGENCY 

 GROUND

 I CREWTHER

GENERAL HERZOG HAUS 

 3602 THUN 

 SWITZERLAND 

 1 MINISTRY OF DEFENCE 

 RAFAEL 

 ARMAMENT DEVELOPMENT 

 AUTH 

 M MAYSELESS

PO BOX 2250 

 HAIFA 31021 

 ISRAEL

1 TNO DEFENSE RESEARCH

I H PASMAN 

 POSTBUS 6006

2600 JA DELFT

 THE NETHERLANDS 

 1 B HIRSCH 

TACHKEMONY ST 6 

 NETAMUA 42611 

 ISRAEL

1 DEUTSCHE AEROSPACE AG

 DYNAMICS SYSTEMS 

 M HELD 

PO BOX 1340 

D 86523 SCHROBENHAUSEN 

 GERMANY 

16