Robert K. Goldberg

Glenn Research Center, Cleveland, Ohio

Brina J. Blinzler and Wieslaw K. Binienda

University of Akron, Akron, Ohio

Modifi cation of a Macromechanical Finite-Element 

Based Model for Impact Analysis of TriaxiallyBraided Composites

NASA/TM—2010-216922

December 2010
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Robert K. Goldberg

Glenn Research Center, Cleveland, Ohio

Brina J. Blinzler and Wieslaw K. Binienda

University of Akron, Akron, Ohio

Modifi cation of a Macromechanical Finite-Element 

Based Model for Impact Analysis of TriaxiallyBraided Composites

NASA/TM—2010-216922

December 2010

National Aeronautics and

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NASA/TM—2010-216922 1 

Modification of a Macromechanical Finite-Element Based Model for 

Impact Analysis of Triaxially-Braided Composites 

Robert K. Goldberg 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Brina J. Blinzler and Wieslaw K. Binienda 

University of Akron 

Akron, Ohio 44325 

Abstract 

A macro level finite element-based model has been developed to simulate the mechanical and impact 

response of triaxially-braided polymer matrix composites. In the analytical model, the triaxial braid 

architecture is simulated by using four parallel shell elements, each of which is modeled as a laminated 

composite. For the current analytical approach, each shell element is considered to be a smeared 

homogeneous material. The commercial transient dynamic finite element code LS-DYNA is used to 

conduct the simulations, and a continuum damage mechanics model internal to LS-DYNA is used as the 

material constitutive model. The constitutive model requires stiffness and strength properties of an 

equivalent unidirectional composite. Simplified micromechanics methods are used to determine the 

equivalent stiffness properties, and results from coupon level tests on the braided composite are utilized to 

back out the required strength properties. Simulations of quasi-static coupon tests of several 

representative braided composites are conducted to demonstrate the correlation of the model. Impact 

simulations of a represented braided composites are conducted to demonstrate the capability of the model 

to predict the penetration velocity and damage patterns obtained experimentally. 

Introduction 

The use of textile (woven and braided) polymer composites is being actively investigated for 

application in aerospace structures, as an alternative to metals or traditional laminated composites. For 

example, triaxially-braided composites are being utilized in fan cases for jet engines. To be certified as 

flight-worthy, a full-scale engine blade-out test must be performed to demonstrate that the fan 

containment system can contain a released fan blade and that the fan case can maintain sufficient 

structural integrity during the engine spool down. As part of the design process, the need exists to 

simulate the blade and case deformation, along with the resulting damage and failure, during a blade-out 

event through the use of commercial explicit finite element codes. For metallic case systems, a sufficient 

ability to properly simulate the blade-out event exists due to the fact that adequate material databases and 

engineering experience in correlating analysis and test results are available. However, the capability to 

simulate the impact response of composite materials is much less mature. The ultimate goal of the current 

research is to improve the blade-out simulation capability for composite fan cases to a level comparable to 

that available for metallic cases. The work presented in this paper is a step towards that goal. 

There has been a significant amount of research conducted in the analysis and modeling of textile 

composites. The majority of the efforts have concentrated on various means to determine the effective 

mechanical properties of woven materials. Among the earliest attempts to model these materials was the 

work of Chou and Ishikawa (Ref. 1). In their original mosaic model, the woven composite was 

approximated as a one-dimensional series of laminated cross-ply composites, and classical laminate 

theory in combination with iso-stress or iso-strain assumptions were applied to obtain the effective 

stiffness properties of the material. They later extended the model to account for the fiber undulations that 
NASA/TM—2010-216922 2 

are present in an actual woven material (Ref. 1). This approach was extended to two-dimensions by Naik 

and Shembekar (Ref. 2), where a mixture of parallel and series assumptions were applied to obtain the 

effective properties of the material. To analyze more complicated fiber architectures, such as braided 

composites, researchers such as Pastore and Gowayed (Ref. 3) and Byun (Ref. 4) modeled the fibers as a 

series of rods at various angles, and utilized simple iso-strain assumptions to obtain the overall effective 

properties of the composite. More sophisticated analysis methods, such as those developed by Tanov and 

Tabiei (Ref. 5) and Bednarcyk and Arnold (Ref. 6), used an approach where a representative unit cell of a 

woven composite was created, and then micromechanics-based approaches were applied to compute the 

effective properties and response of the material. In the context of applying these methods within a finite 

element model, elements are created with a homogenized set of material properties, and the appropriate 

analysis method is used to generate the effective properties and response of the woven material. 

When many of these previously developed analytical methods have been used in combination with 

finite element analysis of a structure composed of woven or braided composite materials, homogenized 

elements are used, in which the architecture of the textile material is not directly accounted for within the 

finite element model. However, for triaxially-braided composites, experimental evidence has shown 

(Ref. 7) that when these materials are subject to impact, oftentimes the damage will propagate along the 

fiber directions. To best simulate these damage patterns, the braid architecture should be directly 

simulated within the finite element model. To account for the fiber architecture in a computationally 

efficient manner, Cheng (Ref. 8) created a “Braided Through the Thickness” approach, where the braided 

composite is modeled as a series of layered shell elements, where each element is a laminated composite 

with the appropriate fiber layup. The effective stiffness and strength material properties of the equivalent 

unidirectional composite then were included as input data for the finite element analysis. In the method 

developed by Cheng, fiber and matrix properties were combined using simple micromechanics-based 

approaches to obtain the required effective properties. The model was developed within the context of 

LS-DYNA (Ref. 9), a commercially available transient dynamic finite element code which is commonly 

used within the aerospace industry. A continuum damage mechanics-based composite constitutive model 

available within LS-DYNA was used as the material model. 

Littell et al. (Ref. 10) made two major extensions to the approach developed by Cheng. First of all, in 

actual braided composites, the layers of braid often do not directly sit on top of each other, but instead 

fiber shifting takes place. In their work, the discretization of the braid was adjusted to account for this 

phenomenon. More significantly, in the previously developed methods, the effective unidirectional 

composite properties of the materials utilized in a braided composite either had to be measured 

experimentally or computed by using micromechanics techniques. This approach requires an extensive 

additional experimental program, with tests on either the matrix constituent (for micromechanics 

approaches) or the equivalent unidirectional composites, besides tests on the braided composite, being 

required to obtain the needed data. These test programs can be quite complicated, with no guarantee that 

the experimental properties obtained are representative of the in-situ properties of the material. In the 

approach developed by Littell, equivalent unidirectional properties were obtained from coupon tests of the 

braided composite. In this manner, the in-situ properties were directly incorporated into the input for the 

material model, which could reduce the amount of testing required. Also, this approach has the potential 

to accurately simulate the deformation, damage and failure of a triaxially-braided composite in a 

computationally efficient manner. Alternatively, an approach of this type can be useful as a tool to verify 

more sophisticated analysis approaches. As described by Littell, et al. (Ref. 10), the stiffness and strength 

values obtained through simulations of quasi-static coupon tests correlated reasonably well to 

experimentally obtained values. However, when flat panel impact tests were simulated, while the 

predicted penetration velocity correlated reasonably well with experimentally obtained values, the 

predicted damage patterns did not correlate well to what was observed experimentally. 

In this paper, first the “Braided Through the Thickness” analysis method, and the differences between 

the approach utilized in this paper and the original methods developed by Cheng (Ref. 7) and Littell, et al. 

(Ref. 10) will be summarized and explained. Specifically, the original geometry as developed by Cheng 

(Ref. 7) (i.e., not accounting for the fiber shifting between layers) was utilized. However, as will be 
NASA/TM—2010-216922 3 

described later in this paper, instead of utilizing a layered shell approach within each shell element to 

approximate the composite architecture, a semi-analytical approach was applied to determine the 

equivalent properties of each element based on the composite layup. The element itself was then modeled 

as a smeared continuum shell element. The philosophy developed by Littell, et al. (Ref. 10) of utilizing a 

“top-down” approach to determine the required strength properties for the material model is applied once 

again. However, the methodology was adjusted to reflect the different geometry of the analysis model and 

to account for the varying geometry within the composite unit cell in a more theoretically consistent 

manner. Simulations of quasi-static coupon tests and the correlation of the simulations to experimental 

results, for several representative composites will be described. Simulations of a flat panel impact test for 

a representative braided composite, and the comparison of the simulated penetration velocity and damage 

patterns to experimentally-obtained results will be described. 

Overview of Analysis Approach 

The “Braided Through the Thickness” analysis approach as developed by Cheng (Ref. 7) and Littell, 

et al. (Ref. 10) has currently been designed to analyze triaxially-braided polymer composites with a 

[0°/60°/–60°] braid architecture. In the braided composites, the 0° fibers have 24 k filaments per tow, 

while the 60° and –60° fibers have 12 k filaments per tow. Other triaxially-braided fiber architectures or 

theoretically any textile composite architecture can be analyzed using this approach. A unit cell of a 

typical triaxially-braided fiber preform is shown in Figure 1(a). In the figure, the 60° bias fibers are 

visible on the surface. Portions of the 0° axial fibers that lie below the bias fibers can be seen in the open 

spaces between the bias fibers. An assumption in the methodology is that the fiber bundle spacing and 

number of fibers per fiber bundle are adjusted such that the fiber volume fractions in both the axial and 

bias directions are equal. In actuality, this particular fiber architecture is quasi-isotropic in-plane. 

Therefore the global in-plane stiffness should be the same in all directions, but this condition is not 

actually enforced within the context of the analysis model. 
NASA/TM—2010-216922 4 

To apply the analysis approach, the braided-fiber architecture is idealized. As a first step in this 

process, a schematic of the top view of the fiber architecture is shown in Figure 1(b), where the –60° bias 

fibers are green, the 60° bias fibers are red, and the 0° axial fibers are blue. As shown in the figure, the 

unit cell can be divided into four equal length parallel subcells. Next, each subcell is approximated to be a 

laminated composite composed of a stack of fiber bundles at various orientations that are determined by 

the braid architecture. Subcell A is modeled as a [60°/0°/–60°] composite (bottom layer listed first). 

Subcell B is modeled as a [60°/–60°] composite, subcell C is modeled as a [–60°/0°/60°] composite, and 

subcell D is modeled as a [–60°/60°] composite. This idealization is shown in Figure 1(c). For subcells A 

and C, the fact that the 0° fiber tows have twice as many filaments per tow as the 60° and –60° layers is 

accounted for by making the 0° layer twice as thick as the remaining two layers. Each subcell can be 

modeled as an individual shell element in a finite element model. A unit cell then consists of four shell 

elements. Shell elements can be used since the length and width of the composite structures typically 

considered are much greater than the thickness. This conclusion can be justified based on impact tests 

discussed by Littell (Ref. 11), where the out-of-plane deformation in a flat panel impact test was found to 

be relatively small in relation to the panel dimensions. A full structure can then be modeled by replicating 

this four element unit cell throughout the finite element mesh. Each subcell is assumed to be equal 

thickness. In the one-layer model as described here, the plies in subcells B and D have lower overall fiber 

volume fractions due to the lack of axial fibers, resulting in these subcells only having two plies while 

subcells A and C have three plies. Note also that while each subcell is approximated as an anti-symmetric 

composite, the normal-bending coupling that is normally associated with a composite architecture of this 

type is assumed to be negligible. Due to the overall architecture of the braided composite, such coupling 

was not observed experimentally in composites of this type (Ref. 11). As a result, the portion of the 

laminate stiffness matrix (commonly referred to as the “B” matrix) that relates the in-plane loads to outof-plane curvatures is assumed to be equal to zero. This approximation can be enforced due to the nature 

of the method used to model each subcell in the analysis model. Specifically, for this particular study, 

instead of modeling each subcell as a layered shell element, with each layer modeled explicitly within the 

finite element model (as was done by Cheng (Ref. 8) and Littell, et al. (Ref. 10)), each subcell was 

modeled as a smeared continuum shell element, with the effective stiffness properties determined using a 

combination of mechanics of materials-based micromechanics methods and classical laminate theory. The 

strength properties of each shell element are determined based on global coupon data from the braided 

composite. The details of how the stiffness and strength properties are determined will be described later 

in this paper. Applying a layered shell approach would allow for simulating the growth of damage in each 

layer independently, which could lead to an improved prediction of the damage patterns in the material 

due to impact. However, the approach of using smeared continuum shell elements for each subcell was 

chosen due to the fact that for the analyses in this paper difficulties were encountered in obtaining valid 

analytical results for a layered shell model using the applied constitutive model (to be discussed below). 

The assumption was made that even with using smeared continuum shell elements the overall damage 

patterns could be predicted adequately. Furthermore, another potential advantage of using smeared 

continuum elements for each subcell as opposed to a layered shell model would be an increase in 

computational efficiency. Computational efficiency is of key importance in simulating impact events on a 

full structure when the fiber tow dimensions are large enough that the composite architecture needs to be 

accounted for in the model. 

The actual braided composites which were examined in this study had six layers of braided fibers 

(Fig. 2). For this study, a six layer model was created by stacking six of the single-layer models 

(Fig. 1(c)) on top of each other. The fiber shifting that sometimes occurs between layers, identified by 

Littell, et al. (Ref. 10), was not accounted for in this approach. By not accounting for the fiber shifting, 

and thus ensuring that the geometry of each subcell is different, the architecturally dependent damage that 

occurs during impact is more likely to be captured. 
NASA/TM—2010-216922 5 

Constitutive Model Overview 

Due to the desire to apply this analysis methodology to the simulation of impact problems, the model 

was implemented within the context of LS-DYNA (Ref. 9), a commercially available transient dynamic 

explicit finite element code that is widely used within the aerospace industry to conduct impact analyses. 

The constitutive model resident within LS-DYNA that was chosen for use with the analysis method is a 

continuum damage mechanics-based model for unidirectional composites, based on a theory developed 

by Matzenmiller, et al. (Ref. 12), that is implemented in LS–DYNA as MAT_58. The failure criterion 

implemented in the model is based on the Hashin failure criterion. For this material model, the required 

input stiffness parameters include the unidirectional-ply-level (or material axis system-based) axial and 

transverse modulus, in-plane shear modulus, and the in-plane Poisson’s ratio. The unidirectional-ply-level 

(or material axis system-based) strength data that is required includes the axial tensile and axial 

compressive failure stress and failure strain, the transverse tensile and transverse compressive failure 

stress and failure strain, and the in-plane shear failure stress and failure strain. The stiffness values are 

used by the material model to simulate the initial linear portion of the composite response. The ply-level 

strength and ultimate strain values are used to determine the nonlinear portion of the material response 

and to determine how the damage parameters used as internal variables within the material model evolve 

over the loading cycle. Furthermore, the user may specify a “stress-limiting factor” in the longitudinal 

and/or transverse directions. If the value of the “stress-limiting factor” is set to zero, the failure stress 

value is assumed to occur at the specified failure strain, and the material model then “connects the dots” 

(including enforcing any required material nonlinearity) in order to create the best-fit stress strain curve 

that accounts for the specified stiffness and strength values. If the “stress limiting factor” is set to one, the 

stress-strain curve of the composite is assumed to increase linearly until the maximum strength value is 

reached. At that point, the material is assumed to act as if it were a perfectly plastic material, with the 

strain in the specified direction increasing with no increase in stress until such point as the specified strain 

level is reached, at which point material failure is assumed to occur. These ideas are shown schematically 

in Figure 3. 
NASA/TM—2010-216922 6 

For this study, since each subcell was modeled as a smeared homogeneous continuum, the properties 

that were input for the constitutive model were the effective stiffness and strength properties for each 

subcell, not the properties of the individual composite layers represented within the subcell. For each 

element, the longitudinal material direction was assumed to be along the axial (0°) fibers, and the in-plane 

transverse material direction was assumed to be perpendicular to this direction. Therefore, the composite 

unit cell was approximated as four orthotropic subcells (one element per subcell) joined together. The 

constitutive behavior of each subcell was simulated using the above-described material model. Two sets 

of material properties were required to analyze the unit cell. Subcells A and C required one set of stiffness 

and strength properties, since they represented a composite with 0°, 60°, and –60° layers. Since the 

composites were balanced, even though the location of the 60° and –60° layers were different for 

subcells A and C, the effective stiffness and strength properties were assumed to be the same. In a similar 

manner, stiffness and strength properties had to be defined for subcells B and D. Again, since these two 

subcells both represented a composite with a 60° layer and a –60° layer, the properties of both subcells 

were assumed to be the same. Note that the properties of subcells A and B were different not only because 

of the different fiber layups, but due to the fact that the local fiber volume fractions of the two subcells 

were different due to the presence or lack of axial fibers and pure matrix pockets in the subcell (Fig. 1(b)). 

The properties required by the model described above are the properties of the subcell, which is 

treated as an effective orthotropic material. A fundamental problem in the analysis of textile composites is 

that the representative lamina properties are not known and cannot be directly measured. Attempts can be 

made to fabricate unidirectional laminates using the same fiber tows that are used to make the preform. 

This approach is often not easy to accomplish, and the properties of the unidirectional lamina could be 

different from the properties of the fiber tows within the textile composite because of processing 

differences. For these reasons, a method was chosen that utilizes an approach based on a combination of 

classical laminate theory and concepts from composite micromechanics theory to calculate the lamina 

stiffness properties using a “bottom-up” approach, where the constituent properties were homogenized 

through the use of micromechanics theory to obtain the effective ply level properties, and then classical 

laminate theory was applied to obtain the effective stiffness properties of the subcell. To determine the 

strength properties for each subcell, properties from experimental data obtained on the braided composite 

were applied using a “top-down” approach to determine the required parameters. The details on this 

methodology will be discussed later in this paper. Although there are also some limitations in using this 

approach to determine the strength properties, the experimental requirements are simplified, and the 

calculated lamina properties represent the in-situ properties of each subcell within the braided composite. 
NASA/TM—2010-216922 7 

Determination of Material Properties 

A computer program was developed to compute the effective stiffness and strength properties for 

each subcell based on the input of the fiber volume ratio of each subcell, fiber and matrix constitutive 

properties, and failure stress and failure strain data for the braided composite obtained through coupon 

level tests. Details of the procedures incorporated into the program are given below. 

Stiffness Properties 

Determining the stiffness properties to input into the constitutive model is a two-step procedure. First, 

given the fiber and matrix stiffness properties as listed in Littell (Refs. 10 and 11) and the subcell fiber 

volume ratio, micromechanics methods were used to determine the effective unidirectional stiffness 

properties of a single ply of the composite in the subcell. For this study, a micromechanics method 

developed by Sun and Chen (Ref. 13) was utilized due to the combination of accuracy of the method 

combined with the availability of simple analytical expressions to determine the effective stiffness 

properties. This combination was deemed beneficial in terms of utilizing the procedures in the context of 

a standalone program. The input data required by the micromechanics method includes the fiber volume 

ratio, the longitudinal, transverse, and shear fiber modulus, the fiber Poisson’s ratio, and the matrix 

modulus and Poisson’s ratio. For the micromechanical calculations, the average fiber volume ratio for 

each subcell was determined based on high fidelity finite element models of triaxially-braided composites 

developed by Li, et al. (Ref. 14), which were generated based on detailed measurements of representative 

braided composite geometries. From the finite element models, volumes corresponding to the equivalent 

subcell volumes in the “Braided Through the Thickness” simplified model were identified. The equivalent 

average fiber volume ratio in the selected volumes (corresponding to the subcells) was then calculated 

numerically from the mesh of the high-fidelity finite element model, based on the volume of fiber tows, 

local fiber volume fraction of the fiber tows (identified in Li, et al. (Ref. 14)), and the volume of any pure 

resin regions present in the identified volume. For the composites analyzed in this study, subcells A and C 

were found to have an average fiber volume ratio of 0.65, and subcells B and D were found to have an 

average fiber volume ratio of 0.50. 

Once the unidirectional stiffness properties for each subcell were computed, classical laminate theory 

(Ref. 15) was applied to obtain the overall effective stiffness for the subcell. For this study, only in-plane 

loads were assumed to be applied, which resulted in the moment curvature relations of classical laminate 

theory being neglected. In-plane normal-shear couplings were absent since the subcells were 

approximated as balanced laminates. Furthermore, as discussed earlier, even though the composite layups 

were anti-symmetric, tension-bending coupling was neglected. For purposes of computation, the 

composites were assumed to have unit thickness, so the loads per unit length could be approximated as 

stresses. The above assumptions were applied to write the constitutive equation for each subcell, such as 

is shown below for subcell A 

11 11 12 11

22 12 22 22

12 66 12

0

0

0 0

A AA A

A AA A

A AA

A A

A A

A

           

   

 

        

(1)

where Aij

A

 represents the stiffness matrix components for subcell A, σij

A represents the stresses in 

subcell A, εij

A represents the normal strains in subcell A and γijA represents the engineering shear strains in 

subcell A. In this and all following equations, the “11” direction is assumed to be along the 0° fibers, the 

“22” direction is assumed to be perpendicular to the 0° fibers in the plane of the composite, and the “12” 

direction is assumed to be the in-plane shear direction. The stiffness matrix components were computed 

using the usual procedures of classical laminate theory (Ref. 15). Specifically, the unidirectional stiffness 
NASA/TM—2010-216922 8 

matrix for a single ply of each subcell was computed based on the computed effective engineering 

properties. Next, the A matrix terms are written in terms of Q-bar, the transformed stiffness terms for a 

unidirectional ply in the structural axis system and the ratio of the ply thickness to the overall thickness in 

the manner of classical laminate theory as follows 

* ij ij k

k

A Qt  (2)

where the sum is taken over the layers k, and tk is the thickness ratio of the k

th layer. For subcell A, the 

expansion can be written as follows 

60deg 0deg 60deg

11 11 11 11

60deg 0deg 60deg

12 12 12 12

60deg 0deg 60deg

22 22 22 22

* *2 *

* *2 *

* *2 *

A

A

A

A Q tQ tQ t

A Q tQ tQ t

A Q tQ tQ t







 



 

(3)

and in a similar manner the expansion for subcell B can be written. Note that for subcells A and C the 

thickness ratio of the 0° (axial) layer was taken to be 0.5 and the thickness ratio of the 60° and –60° (bias) 

layers were taken to be 0.25. This is due to the fact that the axial fiber tows for the composites used in this 

study were composed of 24 k flattened tows and the bias fiber tows were composed of 12 k flattened 

tows, leading to the axial fiber tows having a greater number of fibers. This fact is reflected in the “2t” 

terms in the “A” matrix calculations relating to the 0° layers. For subcells B and D, due to the lack of 

axial fibers the thickness ratio for both the 60° and –60° (bias) layers was taken to be 0.50. Based on the 

computed stiffness matrix terms, the required engineering constants for each subcell could then be 

determined using the usual procedures of orthotropic elasticity theory (Ref. 15). 

Strength Properties 

To compute the strength properties for each subcell required by the LS-DYNA MAT_58 constitutive 

model (Ref. 9), data obtained from global axial tension and compression (loading along the direction of 

the axial fibers), transverse tension and compression (loading perpendicular to the direction of the axial 

fibers), and in-plane shear coupon level tests were utilized. Note that for the constitutive model that is 

utilized for this study both the stresses and strains in the various component directions at failure are 

required to be input. As shown in Figure 3, the failure stresses and strains are used along with the “stresslimiting parameter” to construct the appropriate stress-strain response for the composite. Particularly in 

simulating an impact event, where the stresses are highly multiaxial, properly determining all of the 

strength parameters is critical. The key step in the algorithm was utilizing a mechanics of materials 

approach to specify what the stresses and strains in each subcell were given an applied global stress. In 

this way, global failure stresses and strains were related to the local stresses and strains in the individual 

subcells at points of failure. These local stresses and strains were then utilized as the failure stresses and 

strains in the subcell for the MAT_58 constitutive model. Referring back to the subcell architecture as 

defined in Figures 1(b) and (c), and assuming each subcell had equal width (equal to 0.25 of the total 

width of the composite), the following iso-stress and iso-strain assumptions, referred to as the mechanics 

of materials assumptions (Ref. 15) were defined 
NASA/TM—2010-216922 9 

11 11 11 11 11

22 22 22 22 22

12 12 12 12 12

11 11 11 11 11

22 22 22 22 22

12 12 12 12 12

0.25 0.25 0.25 0.25

0.25 0.25 0.25 0.25

0.25 0.25 0.25 0.25

ABCD

ABCD

ABCD

ABCD

ABCD

ABCD

    

       

       

       

    

    

(4)

where stress and strain values without superscripts represent the global stress and strain values, and 

superscripted values represent the stresses and strains in the particular subcell. Note that due to the 

assumptions of the analysis approach, the stresses and strains in subcells A and C are equal, as are the 

stresses and strains in subcells B and D. As will be described below, for different types of loading the 

expressions in Equation (4) were manipulated and combined with the stiffness matrix equations for each 

subcell to relate the failure stresses and strains for each subcell to the global failure stresses and strains 

observed for the composite. 

To compute the axial tension failure stress and failure strain for each subcell, data obtained from axial 

tension tests on the braided composite were utilized. Representative results from an axial tension test on a 

T700S/E-862 triaxially-braided composite obtained by Littell (Ref. 11) (to be described in more detail 

later in this paper) are shown in Figure 4. As can be seen in the figure, the axial tension stress-strain curve 

became nonlinear at a stress level of approximately 495 MPa, and failed at a stress level of approximately 

800 MPa. To relate the global stresses to subcell stresses, Equation (4) was combined with the subcell 

stiffness matrix equations. For the special case of axial tension loading, all of the stresses except the 

longitudinal tension stress (σ11) were set equal to zero. As shown in Equation (4), due to the simplified 

nature of the discretization of the unit cell the transverse and shear stresses in each subcell are assumed to 

 
NASA/TM—2010-216922 10 

be equal and equal to the global stress. For the case of uniaxial tensile loading, the global applied 

transverse and shear stresses are equal to zero. The following expressions relating the stresses in 

subcells A and B to the global applied longitudinal tension stress were obtained as follows: 

11 11

11 11 11

11 11

11

,

0.5 1

B

B A B

B A

A

S

S S

S



           

(5)

where S11 is the “11” component of the compliance matrix (inverse of the stiffness matrix) for the 

appropriate subcell (A or B). Since the ultimate failure in an axial tension test of a triaxially-braided 

composite has been found to be primarily due to the failure of the axial fibers (Ref. 10), the axial failure 

stress for subcell A (and by extension subcell C) (which has axial fibers) was determined using 

Equation (5) with the ultimate composite failure stress being utilized as the global applied stress. The 

axial failure stress for subcell B (and by extension subcell D) was computed using the global stress level 

at which the axial tension stress-strain curve became nonlinear. The rationale for making this assumption 

was based on observations made by Littell (Ref. 11) on the local response of braided composites during 

an axial tension test. During the course of an axial tension test, large strains in the bias fiber tows in the 

direction perpendicular to the load were observed by using digital image correlation methods to view fullfield surface strains, indicating that local matrix microcracking within the bias fiber tows leading to bias 

fiber tow failure (at least in the transverse direction) occurred well before the ultimate strength of the 

composite was reached. In addition, local delaminations were observed to take place in the bias fiber tows 

during axial loading. For this study, the assumption was made that the effects of these bias fiber tow 

failures would be most pronounced in subcells B and D since no axial fibers were present in those 

subcells. Furthermore, the assumption was made that the stress level at which these local failures in the 

bias fiber tows occurred (or at least became significant) was at least loosely correlated to the stress level 

at which the global stress-strain curve became nonlinear. These assumptions are justified based on 

observations made by Littell (Ref. 11). For composites where the bias fiber tow failure was not as 

pronounced and initiated at higher stress levels, the stress level at which the global axial tension stressstrain curve became nonlinear was much higher. Furthermore, the global stress level at which the stressstrain curve became nonlinear was at least loosely correlated to the stress level at which fiber splitting and 

out-of-plane delaminations occurred (Ref. 11). Therefore, as mentioned above, the local axial stress in 

subcell B (and subcell D) at the global stress level where the axial tension stress-strain curve became 

nonlinear was used as the failure stress for the subcell. Even though on a local level the bias fiber failure 

occurred in the transverse fiber direction, due to the large fiber angle of the bias fibers on the global 

homogeneous subcell level the effects were most pronounced in the global axial direction. Since the 

failure stresses for subcells B and D were much lower than the failure stresses for subcells A and C, the 

“stress-limiting parameter” was set to one (1) for subcells B and D. In this manner, once the failure stress 

in these subcells was reached, the stress would be held at a constant level, but strain could accumulate 

until the ultimate failure strain was reached. This behavior is displayed schematically in Figure 3. By 

applying this approach, premature failure of the simulations (since the composite could still accumulate 

strain even after the bias fibers failed) would be avoided and the analysis would be consistent with the 

approximations applied in the theory. To determine the axial failure strain for each subcell, which is also 

required for the constitutive model, based on the uniform strain assumptions shown in Equation (4), the 

axial tension failure strain for all of the subcells was set equal to the global axial tension failure strain of 

the composite. 

To compute the axial compression failure stress and failure strain for each subcell, data obtained from 

axial compression tests on the braided composite were utilized. Representative results from an axial 

compression test on a T700S/E-862 triaxially-braided composite obtained by Littell (Ref. 11) (to be 

described in more detail later in this paper) are shown in Figure 5. For the case of axial compression, 
NASA/TM—2010-216922 11 

detailed examination of full-field strain data obtained during the tests by Littell (Ref. 11) indicated that 

the strain field was nearly uniform throughout the gage section, indicating that no local fiber tow damage 

was occurring before the final failure of the composite. Therefore, all of the subcells were assumed to fail 

simultaneously when the global axial compression-failure stress was reached. To compute the local axial 

compression-failure stress in each subcell, the global axial compression stress was used in Equation (5) to 

compute the local subcell stresses. Even though the stress-strain curve shown in Figure 5 is nonlinear and 

the expressions in Equation (5) are based on a linear elastic response, the assumption was made that the 

ratio of the local subcell stresses to the global applied stress remained constant. To remain consistent with 

the approximations of the theory, the axial compression-failure strain for each subcell was set equal to the 

global axial compression-failure strain. With the specification of the initial modulus, failure stress and 

failure strain of each subcell, the MAT_58 constitutive model used for the analysis was then capable of 

enforcing the required nonlinearities in the material response. 

To compute the transverse tension-failure stress and-failure strain for each subcell, data obtained from 

transverse tension tests on the braided composite (along with data from the axial tension tests for reasons 

to be described below) were utilized. Representative results from a transverse tension test on a T700S/ 

E-862 triaxially-braided composite obtained by Littell (Ref. 11) (to be described in more detail later in 

this paper) are shown in Figure 4. As can be seen in the figure, while the initial stiffness of the axial and 

transverse curves are the same, the transverse tension results become nonlinear at a much lower stress as 

compared to the axial tension results and the material fails at a much lower stress in transverse tension as 

compared to axial tension. Theoretically, since the triaxially-braided composites are nominally quasiisotropic, the axial tension- and transverse tension-failure stresses should be much closer to each other. 

The reasons for this discrepancy were discussed in detail by Littell, et al. (Refs. 10 and 11). As discussed 

in these papers, premature failure near fiber bundles that terminate at free edges can influence the shape 

of the stress-strain curve and the measured failure strain. A large amount of edge damage was observed in 

both axial and transverse tensile tests. In an axial tensile test the axial braid fibers lie along the specimen 

axis and are gripped on both ends during a test. Since these axial braid fibers carry most of the load, the 

reduction in strength caused by edge damage is small for the axial tensile test. The edge damage has a 

larger effect on the measured strength for the transverse tensile test because all of the axial braid fibers are 
NASA/TM—2010-216922 12 

perpendicular to the applied load. There is no continuous load path between the grips through fibers 

because all axial and bias fiber bundles terminate at a free edge. The edge damage contributes to the 

nonlinearity of the experimental transverse-tensile stress-strain curve and also contributes to the reduced 

transverse-failure stress compared with the axial failure stress. Full-field strain measurements during the 

transverse tensile tests revealed regions of low strain up to 10 percent of the specimen width that were not 

carrying load because of edge damage. Since the damaged region did not carry load, the stress in the 

undamaged region was about 10 percent higher than the stress that was calculated based on the initial 

cross-sectional area of the specimen. The experimental transverse stress-strain curve was therefore not an 

accurate representation of the transverse tensile properties. 

Due to the fact that the transverse tensile results obtained experimentally were not accurate 

indications of the actual behavior of the material under transverse tensile loading conditions, indirect 

methods were utilized to obtain the transverse tensile failure stress and failure strain for each subcell. As a 

first approximation, the global transverse tension failure stress was assumed to be equal to the global 

axial-tension failure stress. For a quasi-isotropic material, this approximation theoretically should be valid 

and anecdotal evidence (Refs. 10 and 11) indicates that in actual structures the transverse tensile strength 

should be very close to the axial tensile strength. Following the approximations specified in Equation (4), 

the transverse tensile-failure stress in each subcell was set equal to the global axial-tension failure stress. 

To relate the global transverse stress to the subcell strains, Equation (4) was combined with the subcell 

constitutive equations. The following expressions relating the strains in subcells A and B to the global 

applied transverse-tension stress were obtained as follows: 

12 12

22 12 22 22 22

11 11

12 12

22 12 22 22 22

11 11

B A

AA A

A B

A B

BB B

A B

S S S S

S S

S S S S

S S

       

  

       

  

 (6)

where Sij is the “ij” component of the compliance matrix (inverse of the stiffness matrix) for the 

appropriate subcell (A or B). To apply Equation (6) to compute the transverse tensile failure strain for 

each subcell, a phenomenon that was discovered by Littell, et al. (Refs. 10 and 11) was incorporated into 

the algorithm. During the transverse tensile tests, large strains in the transverse direction in the axial fiber 

tows were observed, indicating that local matrix microcracking within the axial fiber tows leading to axial 

fiber tow failure (at least in the transverse direction) occurred well before the ultimate strength of the 

composite was reached. These results indicated that the behavior of subcells A and C in the transverse 

direction likely resembled an “elastic-plastic” response, where before the “fiber splitting” occurred the 

transverse stiffness was equal to the initial elastic value, but once “fiber splitting” occurred the subcells 

could accumulate strain but not stress, and the local modulus was reduced to a very small value. 

Therefore, at the point of transverse-tensile failure the overall transverse stiffness of subcells A and C was 

most likely not equal to the initial elastic stiffness value, but instead was reduced due to the transverse 

failure in the axial fiber tows. As a first approximation to account for this effect, when Equation (6) was 

applied in the property calculation algorithm the transverse compliance matrix value for subcell A (S22

A

) 

was doubled from the initial elastic value to reflect the reduced stiffness due to the local microcracking in 

the axial fiber tows. 

To compute the transverse compression-failure stress and failure strain for each subcell, data obtained 

from transverse compression tests on the braided composite were utilized. Representative results from a 

transverse compression test on a T700S/E-862 triaxially braided composite obtained by Littell (Ref. 11) (to 

be described in more detail later in this paper) are shown in Figure 5. For the case of transverse 

compression, similar to the case for axial compression, detailed examination of full-field strain data obtained 

during the tests by Littell (Ref. 11) indicated that the strain field was uniform throughout the gage section, 
NASA/TM—2010-216922 13 

indicating that no local fiber tow damage was occurring before the final failure of the composite. Therefore, 

all of the subcells were assumed to fail simultaneously when the global transverse compression-failure stress 

was reached. To compute the local transverse compression-failure stress in each subcell, once again the 

assumptions given in Equation (4) were applied and the subcell failure stresses were assumed to be equal to 

the global composite transverse compression-failure stress. To compute the subcell transverse compressionfailure strains, an expression similar to Equation (6) was used with some modifications. First, Equation (6) 

was used directly with the global transverse compression-failure stress as input. However, the strains 

computed using Equation (6) could not be utilized directly due to the fact that, as observed in Figure 5, the 

transverse compression response of the composite is nonlinear, and Equation (6) was developed assuming a 

linear elastic response. Next, the ratio of each subcell strain to the total transverse compression strain under 

elastic conditions (computed using the second expression in Equation (4)) was determined. The assumption 

was then made that the strain ratio under elastic conditions was identical to the actual strain ratio. Therefore, 

the strain ratio for each subcell was scaled using the actual transverse compression-failure strain to obtain 

the transverse compression failure strain for each subcell. 

To compute the in-plane shear failure stress and failure strain for each subcell, a procedure very 

similar to that utilized for the case of transverse compression was utilized. Once again, detailed 

examination of full-field strain data obtained during coupon level tests by Littell (Ref. 11) indicated that 

the strain field was uniform throughout the gage section, indicating that no local fiber tow damage was 

occurring before the final failure of the composite. Therefore, all of the subcells were assumed to fail 

simultaneously when the global in-plane shear failure stress was reached. To compute the local in-plane 

shear failure stress in each subcell, once again the assumptions given in Equation (4) were applied and the 

subcell failure stresses were assumed to be equal to the global composite in-plane shear failure stress. To 

compute the subcell in-plane shear-failure strains, Equation (6) was used with some modifications. First, 

Equation (6) was used directly with the in-plane shear failure stress as input. However, the strains 

computed using Equation (6) could not be utilized directly due to the fact that, while not shown here, the 

in-plane shear response of the composite is nonlinear, and Equation (6) was developed assuming a linear 

elastic response. Next, the ratio of each subcell strain to the total in-plane shear strain under elastic 

conditions was determined. The assumption was then made that the strain ratio under elastic conditions 

was identical to the actual strain ratio. Therefore, the strain ratio for each subcell was scaled using the 

actual in-plane shear-failure strain to obtain the in-plane shear-failure strain for each subcell. 

Simulation of Quasi-Static Tension Tests 

A series of simulations was conducted to evaluate the analysis methods described above. Specifically, 

quasi-static axial and transverse coupon-level tensile tests on two representative triaxially-braided 

composites were simulated. At this time, only the tensile response was simulated due to the relative 

simplicity of the finite element models. In the future, to fully evaluate the material model compressive 

and shear tests will also be simulated. The materials were composed of a two-dimensional triaxial-braided 

preform and a 177 °C (350 °F) cure epoxy resin. For both materials, TORAYCA T700S fibers (Toray 

Carbon Fibers America, Inc.), a high strength, standard modulus carbon fiber was used. For the first 

material, EPICOTE Resin 862/EPIKURE Curing Agent W system (Hexion Specialty Chemicals) 

(E-862 for short), a two-part low viscosity system was used. For the second material, CYCOM PR 520 

(Cytec Industries, Inc.), a one part toughened resin, was used. 

A [0°/60°/–60°] triaxial-braid architecture was manufactured. The 0° axial fibers were 24 k flattened 

tows while the ±60° bias fibers were 12 k flattened tows. Although larger fiber bundles were used in the 

axial direction, the fiber bundle spacing in the axial and bias directions were adjusted to give the same 

fiber volume in the axial and bias directions. This is a nominally quasi-isotropic in-plane fiber 

architecture, so the global in-plane stiffness is expected to be the same in all directions when the region of 

 
NASA/TM—2010-216922 14 

interest includes several unit cells of the braid material. Composite panels were fabricated by placing six 

layers of the braided preform into a mold with the 0° fibers aligned in the same direction. Although the 

axial (0°) fibers in the various layers were aligned, the lateral position of the axial tows in the six layers 

was random. Resin was injected into the closed mold and cured according to processing conditions 

recommended by the resin manufacturer. The global fiber-volume ratio of the cured composites was 

measured using the acid digestion technique. Both the T700S/PR520 and T700S/E-862 composites had a 

global fiber volume of 55.9±0.18 percent. 

The finite element meshes used in the study are shown in Figure 6. The finite element model for the 

axial tension test was 30.48 cm (12.0 in.) long and 3.56 cm (1.40 in.) wide and had 369 nodes and 320 

shell elements. The model for the transverse tensile test was 30.48 cm (12 in.) long and 3.56 cm (1.40 in.) 

wide and had 522 nodes and 476 elements. The fixed end of the model was constrained in all three 

displacement and rotation directions. The loading was displacement-controlled at the rate of 0.0635 cm/s 

(0.025 in./s), which was consistent with the test conditions. Each subcell was modeled as a shell element, 

which allowed the braid architecture to be explicitly modeled with the finite element mesh of the coupon. 

In Figure 6, the red elements represent subcell A, the blue elements represent subcell B, the green 

elements represent subcell C, and the yellow elements represent subcell D. The unit cell orientations for 

both of the modeling conditions are highlighted in Figure 6 for reference. In the axial test simulation, the 

unit cell is oriented parallel to the direction of the applied load. In the transverse test simulation, the unit 

cell is oriented perpendicular to the direction of the applied load. While not discussed in this report, the 

entire specimen was modeled as opposed to a single unit cell in order to investigate the ability of the 

method to simulate the damage patterns that occur during a coupon test. 

 
NASA/TM—2010-216922 15 

To compute the stiffness properties for each subcell, first the subcell fiber volume ratios were 

determined as discussed earlier. In applying the micromechanics analysis methods, the stiffness properties 

for the fiber and matrix given in Table 1 were applied. Given the observations made by Littell (Ref. 11) 

that the measured stiffness properties for both of the braided composites were approximately the same, 

identical stiffness properties for both of the resin systems were used (based on values listed by Littell 

(Ref. 11) for the PR520 resin). The equivalent stiffness properties (along with the equivalent strength 

properties) for each subcell for each of the two material systems are given in Table 2. To determine the 

equivalent strength properties for each subcell, the methods and procedures discussed in the previous 

section were applied. The numerical values of the global failure stresses and failure strains that were 

utilized to compute the equivalent subcell strength properties for each of the two materials are given in 

Table 3. The equivalent strength values that were computed for each of the two materials are given in 

Table 2. 

TABLE 1.—CONSTITUENT PROPERTIES 

 E11 (GPa) E22 (GPa) ν12 G12 (GPa) 

T700 (Fiber) 230.00 15.00 0.20 27.00 

E-862 (Resin) 4.00 4.00 0.36 1.47 

PR520 (Resin) 4.00 4.00 0.36 1.47 

TABLE 2.—MATERIAL PROPERTY VALUES USED FOR THE QUASI-STATIC COUPON SIMULATIONS 

Material T700–E862 T700–PR520 

Material Parameter Name (LS-DYNA name) (MPa) (MPa) 

Subcell A&C B&D A&C B&D 

Axial modulus (EA) 80815 8111 80815 8111 

Transverse modulus (EB) 47215 37536 47215 37536 

In plane shear modulus (GAB) 14982 23041 14982 23041 

In plane Poisson ratio (PRBA) 0.175 1.464 0.175 1.464 

Axial tensile failure strain (E11T) 0.018 0.018 0.024 0.024 

Axial compressive failure strain (E11C) 0.012 0.012 0.019 0.019 

Transverse tensile failure strain (E22T) 0.035 0.013 0.045 0.017 

Transverse compressive failure strain (E22C) 0.009 0.007 0.014 0.010 

In plane shear failure strain (GMS) 0.024 0.016 0.029 0.019 

Axial tensile stress at failure (XT) 1454 90 1905 191 

Axial compressive stress at failure (XC) 613 62 687 69 

Transverse tensile stress at failure (YT) 800 800 1048 1048 

Transverse compressive stress at failure (YC) 305 305 346 346 

In plane shear stress at failure (SC) 257 257 308 308 

Stress limiting parameter for axial tension (SLIMT1) 0 1 0 1 

Stress limiting parameter for transverse tension (SLIMT2) 0 0 0 0 

Stress limiting parameter for axial compression (SLIMC1) 0 0 0 0 

Stress limiting parameter for transverse compression (SLIMC2) 0 0 0 0 

Stress limiting parameter for shear (SLIMS) 0 0 0 0 

TABLE 3.—GLOBAL STRESS VALUES USED IN CALCULATIONS 

(MPa) T700/E862 T700/PR520 

Global stress at failure (Axial tension) 800 1048 

Global stress at failure (Transverse tension) 800 1048 

Global stress at failure (Axial compression) 337 378 

Global stress at failure (Transverse compression) 305 346 

Global stress at failure (Shear) 257 308 

Stress at pt. of nonlinearity (Axial tension) 495 1048 

Global strain at failure (Axial compression) 0.012 0.019 

Global strain at failure (Transverse compression) 0.008 0.012 

Global strain at failure (Shear) 0.020 0.024 
NASA/TM—2010-216922 16 

Tensile stress versus strain curves were generated for both the T700S/E-862 and T700S/PR520 

materials in the axial and transverse directions to examine the correlation of the analysis model to the test 

data. Even though the coupon level test data was used to obtain the input data applied to the model, due to 

the complexity of the material model and the ways that the various stiffness and strength parameters 

interact, the stiffnesses and strengths predicted by the analytical simulations may not necessarily 

correspond to the parameters determined from the test data. Specimen failure was deemed to occur when 

all of the elements in a row failed. The element failure occurred nearly simultaneously in the simulations, 

leading to a fairly abrupt ultimate failure. The resulting stress-strain curves for the E-862 system are 

shown in Figure 7 (axial tension) and Figure 8 (transverse tension). The resulting stress-strain curves for 

the PR520 system are shown in Figure 9 (axial tension) and Figure 10 (transverse tension). In these 

figures the test data is as determined by Littell, et al. (Ref. 10). 

 
NASA/TM—2010-216922 17 

For the axial tension test, for both materials the deformation response and ultimate failure stress 

computed by the simulations correlated well with the experimental results. The initial stiffness was well 

correlated for both materials. The nonlinearity in the stress-strain curve for the E-862 material was 

correlated well. The simulation of the axial tension response of the PR520 material displayed some 

nonlinearity that was not present in the experimental response, but the maximum error was approximately 

7 percent. The reasons for this discrepancy are unclear and need to be explored further. The ultimate 

strength of the transverse tensile specimen was significantly overpredicted, and the simulated response of 

the transverse tensile test was much more linear than observed in the experiments for both materials. As 

mentioned earlier, the most likely cause of the discrepancy in the transverse tensile results is due to the 

edge damage and low strain zones that were observed in the experimental transverse-tension tests, leading 

to the experimental transverse stress-strain curve not being an accurate representation of the true 

composite tensile response. Due to the way in which the braid architecture was discretized and simulated 

in the analytical model, with the fiber tows not being modeled in a continuous manner, these local effects 

could not be captured in the simulations as each subcell in a sense is an independent laminated composite. 

As a result, the simulated results from the transverse tension test in all likelihood were more 
NASA/TM—2010-216922 18 

representative of the response that would be observed if the response was measured at a location far away 

from where edge effects would be significant. Therefore, the fact that the simulated transverse-tension 

response of the material was more linear than the experimental results, with a transverse-failure stress 

only slightly lower than the axial-failure stress, was consistent with the strength properties input into the 

constitutive model (with the assumptions discussed above) and most likely actually more representative 

of the response of the material as utilized in an engineering structure. In a qualitative sense, the simulated 

transverse tension results are consistent with the expected response of the material, but a full detailed 

quantitative examination of the transverse tension simulation results will only be possible when improved 

experimental results are obtained. 

Simulation of Impact Tests 

The composite materials presented in this research are sometimes used in impact situations. This 

section presents preliminary investigations which use the developed composite models for impact 

simulations for the detection and prediction of impact velocity thresholds and failure depictions. The 

T700/E862 material system was examined for the impact simulations. 

In the impact tests, which were conducted in the NASA Glenn Research Center Ballistic Impact 

Laboratory and which are described in detail in Reference 16, a single stage compressed-gas gun was 

used to propel an aluminum 2024 projectile into 30.5 cm (12 in.) by 30.5 cm (12 in.) by 3.2 mm 

(0.125 in.) composite panels. The composite panel was held in a circular fixture with an aperture of 

20.54 cm (10 in.). The projectile was a thin-walled hollow AL 2024 cylinder with a nominal mass of 

50 gm and a front face with a compound radius. The overall length of the projectile was 4.95 cm 

(1.947 in.), the wall thickness was 0.076 cm (0.030 in.), and the nominal diameter was 5.067 cm 

(1.995 in.). Tests were performed over a range of impact velocities to determine the velocity for onset of 

damage, the growth of damage with increasing velocities, the penetration threshold, and the damage 

pattern induced by penetration. Twelve panel tests were conducted using impact velocities ranging from 

157 m/s (515 ft/s) to 175 m/s (573 ft/s). The threshold velocity for penetration was between 161 m/s 

(530 ft/s) and 168 m/s (550 ft/s). 

To conduct simulations of the impact tests described above, the flat panels used in the impact tests 

were modeled using a finite element mesh 0.3048 m (12 in.) wide, 0.3048 m (12 in.) tall and 0.3175 cm 

(0.125 in.) thick with 2700 shell elements. The finite element model of the panel, including the circular 

boundary conditions that were applied to simulate the experimental conditions, is shown in Figure 11. 

The simulated panels had a clamped boundary in a 25.4 cm (10 in.) diameter circle at the center. The 
NASA/TM—2010-216922 19 

nodes in this boundary had all six degrees-of-freedom constrained. The panel was made up of 810 unit 

cells; 15 unit cells across and 54 unit cells vertically. The alternating patterns of pink, blue, green, and 

yellow represent the four subcells of the unit cell used to simulate the composite braid geometry. The 

projectile was modeled as a linear elastic material to accurately account for energy absorption due to 

elastic deformation of the projectile. The density and stiffness of the projectile in the simulation were 

measured from the aluminum used in the experimental tests (Ref. 16). The contact algorithm that used 

was the LS-DYNA contact “Contact_Automatic_Single_Surface,” (Ref. 9). 

Simulations were run for various impact velocities above and below the penetration threshold. The 

penetration threshold in the simulations was defined as the velocity at which the projectile fully 

penetrated the plate with a residual projectile velocity of zero. The model predicted penetration taking 

place at an impact velocity of 160 m/s (525 ft/s), which was only slightly below the experimental 

threshold velocity of 161 to 168 m/s (530 to 550 ft/s). The reason for the slight discrepancy could be 

related to the fact that quasi-static properties were utilized to compute the equivalent strength parameters 

applied in the analysis. The actual response and properties of the material may be a function of strain rate, 

with the various failure stresses and strains being higher at higher strain rates. Future efforts will 

investigate the effects on the predictions of using strain rate-dependent material properties. 

A photograph of the damage patterns that were obtained in a panel impacted near the threshold 

velocity is shown in Figure 12, with a diagram of the simulated impact damage patterns shown next to it. 

The unsymmetric damage patterns observed in the simulation results was due to the fact that the projectile 

rotated during the simulations and did not impact exactly head on. The projectile rotation has also been 

observed in the experimental tests (Ref. 16). In the experimental impact test failure initiated along the 

axial fibers in the center of the specimen and then propagated outward along both the axial and the bias 

fibers. The simulated results predicted a similar damage pattern with the failure initiating along the bias 

fibers around the edges of the damage area, then propagating horizontally, and finally zipping vertically 

near the center of the damage area. However, in the simulation, a more rounded opening than that seen in 

the experimental tests was created. It is possible this difference could be due again to the use of quasistatic properties. There may be some anisotropic stiffening due to rate effects. Further research will be 

done to investigate the effects of strain rate. 
NASA/TM—2010-216922 20 

Conclusions 

A macro-level finite element-based approach has been developed which allows for the simulation of 

the response of a triaxially-braided composite in a manner which takes into account the architecture of the 

braided material within a structure. The input material properties utilized for the analysis can be 

determined based on experimental tests conducted on the braided composite. The correlation between the 

analysis results and results obtained from quasi-static tensile coupon tests was reasonably good. A 

representative flat panel test was simulated using the analysis model. The penetration velocity was 

slightly underpredicted, and the damage patterns obtained were similar to those obtained experimentally. 

The discrepancy between the experimental and analytical results is most likely due to the effects of strain 

rate on the material properties which is not currently accounted for within the material model. The 

analysis model, which utilizes LS-DYNA shell elements, appears promising in its ability to simulate the 

axial and transverse deformation and failure of the braided material. Future efforts will involve 

incorporating the effects of strain rate into the model, as well as investigating in more detail the capability 

of the model to simulate impact events. 

References 

1. Chou, T.W. and Ishikawa, T.: “Analysis and Modeling of Two-Dimensional Fabric Composites,” in 

Textile Structural Composites, Composite Material Series, vol. 3, T.W. Chou and F.K. Ko, Eds., 

Elsevier Science Publishers B.V., Amsterdam, 1989, ch. 7, pp. 209–277. 

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Analysis,” Journal of Composite Materials, vol. 26, no. 15, pp. 2196–2225, 1992. 

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4. TITLE AND SUBTITLE

Modification of a Macromechanical Finite-Element Based Model for Impact Analysis of 

Triaxially-Braided Composites 

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6. AUTHOR(S)

Goldberg, Robert, K.; Blinzler, Brina, J.; Binienda, Wieslaw, K. 

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WBS 698259.02.07.03.03.01 

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14. ABSTRACT

A macro level finite element-based model has been developed to simulate the mechanical and impact response of triaxially-braided polymer 

matrix composites. In the analytical model, the triaxial braid architecture is simulated by using four parallel shell elements, each of which is 

modeled as a laminated composite. For the current analytical approach, each shell element is considered to be a smeared homogeneous 

material. The commercial transient dynamic finite element code LS-DYNA is used to conduct the simulations, and a continuum damage 

mechanics model internal to LS-DYNA is used as the material constitutive model. The constitutive model requires stiffness and strength 

properties of an equivalent unidirectional composite. Simplified micromechanics methods are used to determine the equivalent stiffness 

properties, and results from coupon level tests on the braided composite are utilized to back out the required strength properties. Simulations 

of quasi-static coupon tests of several representative braided composite are conducted to demonstrate the correlation of the model. Impact 

simulations of a represented braided composites are conducted to demonstrate the capability of the model to predict the penetration velocity 

and damage patterns obtained experimentally. 

15. SUBJECT TERMS

Polymer matrix composites; Braided composites; Finite element method; Micromechanics 

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