Macro Scale Independently Homogenized 

Subcells for Modeling Braided Composites

NASA/TM—2012-217621

July 2012

AIAA–2011–1911

Brina J. Blinzler

University of Akron, Akron, Ohio

Robert K. Goldberg

Glenn Research Center, Cleveland, Ohio

Wieslaw K. Binienda

University of Akron, Akron, Ohio 
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Macro Scale Independently Homogenized 

Subcells for Modeling Braided Composites

NASA/TM—2012-217621

July 2012

AIAA–2011–1911

Brina J. Blinzler

University of Akron, Akron, Ohio

Robert K. Goldberg

Glenn Research Center, Cleveland, Ohio

Wieslaw K. Binienda

University of Akron, Akron, Ohio 

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

52nd Structures, Structural Dynamics, and Materials Conference

cosponsored by the AIAA, ASME, ASCE, AHS, and ASC

Denver, Colorado, April 4–7, 2011
Acknowledgments

This work was funded by the Vehicle Systems Safety Technologies Program of the Aviation Safety Project, 

and NASA Graduate Student Researchers Program grant no. NNXD9AL95H.

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either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2012-217621 1

Macro Scale Independently Homogenized Subcells for 

Modeling Braided Composites

Brina J. Blinzler

University of Akron

Akron, Ohio 44325

Robert K. Goldberg

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Wieslaw K. Binienda

University of Akron

Akron, Ohio 44325

Abstract

An analytical method has been developed to analyze the 

impact response of triaxially braided carbon fiber composites, 

including the penetration velocity and impact damage patterns.

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. Currently, each shell 

element is considered to be a smeared homogeneous material.

The commercial transient dynamic finite element code LSDYNA is used to conduct the simulations, and a continuum 

damage mechanics model internal to LS-DYNA is used as the 

material constitutive model. To determine the stiffness and 

strength properties required for the constitutive model, a topdown approach for determining the strength properties is

merged with a bottom-up approach for determining the 

stiffness properties. The top-down portion uses global 

strengths obtained from macro-scale coupon level testing to 

characterize the material strengths for each subcell. The 

bottom-up portion uses micro-scale fiber and matrix stiffness 

properties to characterize the material stiffness for each 

subcell. Simulations of quasi-static coupon level tests for 

several representative composites are conducted along with 

impact simulations.

Nomenclature

σ11 global axial (ultimate) tension stress

σ11A axial tension strength for subcells ‘A’ and ‘C’

σ11A(pon) axial tension strength for subcells ‘A’ and ‘C’ (pointof-nonlinearity)

σ11(pon) global axial (point-of-nonlinearity) tension stress

σ11B axial tension strength for subcells ‘B’ and ‘D’

σ22 global transverse tension strength

σ22A transverse tension strength subcells ‘A’ and ‘C’

σ22B transverse tension strength subcells ‘B’ and ‘D’

ε11A axial tension failure strain subcells ‘A’ and ‘C’

ε11B axial tension failure strain subcells ‘B’ and ‘D’

ε22B transverse tension failure strain subcells ‘B’ and ‘D’

ε22A transverse tension failure strain subcells ‘A’ and ‘C’

S compliance matrix

[S]mod modified compliance

S11A compliance matrix (axial component) subcells ‘A’ 

and ‘C’

S11B compliance matrix (axial component) subcells ‘B’ 

and ‘D’

S12B compliance matrix (Poisson component) subcells ‘B’ 

and ‘D’

S12A compliance matrix (Poisson component) subcells ‘A’ 

and ‘C’

S22B compliance matrix (transverse component) subcells 

‘B’ and ‘D’

S22A compliance matrix (transverse component) subcells 

‘A’ and ‘C’

E22A transverse elastic modulus subcells ‘A’ and ‘C’

E11 longitudinal elastic modulus

E22 transverse elastic modulus

ν12 in-plane Poisson’s ration

G12 in-plane shear modulus

G shear modulus

E elastic modulus

β decay constant

υ Poisson’s ratio

ε strain rate

σult ultimate stress

Introduction

Polymer matrix composite materials are utilized for a 

variety of aerospace applications because of their comparatively lower weight, and versatile material properties.

Composite structures may undergo a variety of loading 

conditions during service life. In order to be used as protective 

structures, composites are required to resist ballistic impact 

loading. For these types of applications, it is necessary to have 

a model that accurately simulates both ballistic limit and 
NASA/TM—2012-217621 2

damage patterns for the impact region. The ballistic limit of a 

structure is the point at which a projectile travels completely 

through the material but the projectile’s residual velocity 

nominally equals zero. The ballistic limit is generally a range 

determined from a full array of impact experiments. Every 

composite material behaves differently under impact loading 

conditions. The ballistic limit and damage mechanisms are 

highly dependent on the material constituents, the structure’s 

layup, the textile architecture, and the shape of the projectile.

Specifically, in a braided composite, numerous micromechanical phenomena occur contributing to both the ballistic limit 

and the damage patterns.

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 material 

was the work of Chou and Isikawa (Ref. 1). In their original 

mosaic model, the woven composite was approximated as a 

one-dimensional series of laminated cross-ply composites, and 

classical lamination theory in combination with iso-stress or 

iso-strain assumptions was applied to obtain the effective

stiffness properties of the material. They later extended the 

model to account for the fiber undulations that 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. Using 

a different approach, Rao et al. (Ref. 5) developed a method 

where each subcell possesses a modified geometry of the 

portion of the textile geometry. Also, Walter et al. (Ref. 6)

discusses an experimental study which details how the global 

response of textile composites can be correlated to the local 

damage mechanism in the matrix and fiber tows. More 

sophisticated analysis methods, such as those developed by 

Tanov and Tabiei (Ref. 7), Bednarcyk and Arnold (Ref. 8), 

Sankar and Marrey (Ref. 9), and Jenq and Mo (Ref. 10) 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.

Traditionally, when these analytical methods are 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. The braided composites analyzed in this paper have a 

Figure 1.—Identification of the unit cell (a)specimen photograph, (b) four shell elements (A,B,C,D), (c) through thickness layers

large unit cell size, as can be seen in Figure 1 (unit cell: 17.8- by 

5.1-mm). Because of this large unit cell size, the materials

experience strain and damage more like structures rather than 

homogenized materials. For this reason the high velocity 

impact damage patterns are highly dependent on the material 

architecture and projectile shape. Classical analysis methods 

cannot account for these architecture and shape effects. In an 

attempt to develop a capability to simulate the architecturallydependent damage patterns observed in triaxially-braided 

composites under impact conditions, Cheng created a 

“Braided through the Thickness Approach” (Ref. 11), where a 

braided composite was modeled as a series of layered shell 

elements, and each element was a laminated composite with 

the appropriate layup. The approach was developed to analyze 

triaxially-braided composites with a [+60°/0°/–60°] braid 

architecture. A limitation of Cheng’s method was that it had to 

be calibrated with full impact testing for each material 

analyzed. Cheng’s method needed to be improved to systematically calculate the material properties required by the finite 

element material model based on coupon level experimental 

results. The focus of this paper is to fill this need for quasiisotropic triaxial braided carbon-epoxy composites. However,

the methodology which will be presented is applicable to other 

triaxially braided fiber architectures or theoretically any textile 

composite architecture.

One application for triaxially-braided composite materials is 

for use in jet engine fan blade containment systems. To create 
NASA/TM—2012-217621 3

an optimum engine case design, the failure, damage, and 

deformation needs to be simulated with the use of commercial 

explicit finite element codes. A design tool is required to 

capture the structural effect of the braid and damage along fiber 

bundles while modeling the entire engine case. In order to 

balance these needs, a macro scale finite element simulation 

technique was developed employing an advanced continuum 

damage mechanics material model in the finite element code 

LS-DYNA (Ref. 12). For these aerospace applications, the 

model needed to accurately simulate the textile composite under 

both static loading and impact loading situations. The unique 

way the fiber architecture was incorporated into the finite 

element analysis will be discussed later. A triaxially-braided 

composite with a [+60°/0°/–60°] layup was investigated. The 

braided composites under consideration for this study have six 

plies through the thickness. In the braided composites, the 0° 

fibers have 24k filaments per tow, while the +60° and –60° 

fibers have 12k filaments per tow. A unit cell for a typical 

triaxially-braided fiber preform is shown in Figure 1(a). In 

Figure 1, 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 inplane. 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.

Approach

Previous research in modeling architecturally-dependent 

damage in braided composites was conducted by Cheng

(Ref. 11) and Littell (Ref. 13). Their analytical models

discretized the braided composite into a series of parallel shell 

elements. Each of these elements were modeled as laminated 

composites (Ref. 14). The use of layered shell elements 

allowed for architecturally-dependent damage to be modeled 

while maintaining computational efficiency. However, Littell

(Ref. 13) approached the analysis with a different method. He 

used a top-down method to back out stiffness and strength 

properties from experimental coupon level data. In addition, 

Littell attempted to approximate the ply shifting that has been 

observed in braided composites by his discretization method.

There were some difficulties implementing the discretization 

method, and the irregular damage patterns of the braided 

composites could not be captured. In the current study, to 

improve the simulation tool, a top-down approach for 

determining the strength properties was merged with a 

bottom-up approach for determining the stiffness properties.

In order to resolve discretization issues, independently 

homogenized shell elements were used, where each element is 

modeled as a smeared continuum with a set of homogenized 

stiffness and strength properties. Each subcell in the model is 

defined to have different homogenized properties, which 

allows for the simulation of architecturally-dependent damage.

In the top-down approach, all of the information needed to 

characterize the material strengths was taken from the global 

strengths obtained from macro-scale experimental quasi-static 

coupon tests. In the bottom-up approach, the information 

needed to characterize the material stiffness was taken from 

micro-scale fiber and matrix stiffness properties.

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).

As shown in Figure 1, the unit cell is divided into four parallel 

subcells. Next, each subcell is approximated to be a laminated 

composite composed of a stack of fiber tows at various 

orientations that are determined by the braid architecture

(Figure 1(c)). 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. 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. Li, et al. (Ref. 15)

have examined using more subcells with this type of analysis 

approach to more accurately simulate the fiber undulations 

which are present in the actual composite. However, increasing the number of subcells used to model the unit cell 

increases the computational cost of applying the methodology, 

especially when applied to realistic structural configurations.

Furthermore, each subcell could be broken up into several

elements, and preliminary investigation into mesh refinement 

has yielded equivalent results. Also, results to date have 

indicated that further discretization is not required to obtain 

acceptable results. Any pure matrix pockets present in the 

composite are not modeled explicitly, but are instead incorporated into the effective properties of each layer within the 

subcell, affecting the effective fiber volume ratio of each 

subcell. Xiao, et al. (Ref. 16) developed a similar model in 

which the pure resin pockets are explicitly modeled as layers 

of pure matrix. In the future, such an approach may be 

attempted for this method to determine whether the simulation 

results can be improved. 

Each subcell is modeled as an individual shell element in a 

finite element model. The unit cell thus consists of four shell 

elements. The assumption of using shell elements is justified 

since the length and width of typical structures composed of 

these materials are much greater than the thickness. Impact 

tests conducted by Littell (Ref. 13) noted that the out-of-plane 

deformation in flat panel impact tests was found to be 

relatively small in relation to the panel dimensions. In 

addition, the availability of appropriate constitutive models for 

composites using solid elements in transient finite element 

codes such as the commercial software LS-DYNA (Ref. 12)

are limited. Future efforts may involve developing an 

appropriate constitutive model suitable for use with solid 

elements. A full structure can be modeled by replicating this 

four element unit cell throughout the finite element mesh.
NASA/TM—2012-217621 4

Material Model

The finite element software used in the analysis is LSDYNA (Ref. 12). LS-DYNA is a commercially-available 

transient dynamic finite element solver, which contains 

contact algorithms for ballistic impact modeling (Ref. 12).

This solver also contains a number of material models for 

simulating composites. One of these is a laminated composite 

material model for composite shell elements derived from 

Matzenmiller’s (Ref. 17) method. Matzenmiller (Ref. 17)

developed a plane-stress constitutive model for anisotropic 

damage of fibrous composite materials with nonductile 

matrices. The method employed continuum damage mechanics theory in the material axis system to approximate damage 

initiation and ultimate material failure. Each element was 

assumed to be a laminated composite, and any nonlinearity 

was assumed to be due to damage mechanisms. The development of damage was completely dependent on the stress and 

strain states of the individual unidirectional lamina. Matzenmiller then adopted the Hashin failure criteria, which determined a failure envelope based on the five strength properties 

of the unidirectional lamina: longitudinal tension, longitudinal 

compression, transverse tension, transverse compression, and

shear strength (Ref. 18). The equations used in the LS-DYNA 

material model *Mat_58 reflect the Matzenmiller method and 

assumptions (Ref. 12).

The required inputs for the *Mat_58 material model are 

based on material axis system properties. The properties 

required by this model are properties of the homogenized 

laminate (the equivalent properties of each element). A 

fundamental problem in the analysis of textile composites is 

that the lamina properties are not known and cannot be 

directly measured. To characterize the composite material the 

“Independently Homogenized Subcells” method was developed. This method back-calculates lamina properties from 

experimental results and computes a set of homogenized 

properties for each of the subcells listed in Figure 2: subcells 

‘A’, ‘B’, ‘C’, and ‘D’. The equivalent properties seen in Table 

1 were calculated employing the “Independently Homogenized Subcells” method. It should be noted that the “In Plane 

Poisson Ratio” required for the material model and listed in 

the table is ν21 not ν12. There are stress limiting parameters, 

which allow for the material to accumulate strain even after 

the maximum stress is reached in addition to these inputs in 

the *Mat_58 material model. These particular parameters will 

be discussed in greater detail later. There are several advantages for using this approach. The constitutive model that 

was utilized is a continuum damage mechanics model, an 

important quality for impact analysis. The experimental data 

required for characterizing strength comes solely from tests on 

the triaxially braided composite samples; no additional inputs 

are required. In addition, the model is computationally 

efficient, and can be employed to model large components. 

The stiffness and strength inputs for the material model are 

listed in Table 1. For the current system the material inputs 

required by the *Mat_58 model are material axis system 

strength and stiffness properties. Many of the properties needed 

for inputs in the material model are not directly measurable. An 

equivalent unidirectional laminate cannot be made and tested 

that represents the braided composite. The method of combining 

a top-down approach with a bottom-up approach to determine 

the required properties was formed to fill this need.

Figure 2.—Schematic of subcell discretization of six layer triaxial braided composite.
NASA/TM—2012-217621 5

TABLE 1.—CALCULATED MATERIAL PROPERTY VALUES 

USED FOR THE QUASI-STATIC COUPON SIMULATIONS 

Material T700 – PR520 T700 – E862 T700 – 5208 T700 – 3502

Material parameter name (MPa) (MPa) (MPa) (MPa)

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

Axial modulus (E11) 96580 8567 95367 6398 96403 8253 96224 7934

Transverse modulus (E22) 39577 38032 38276 31830 39393 37194 39204 36322

In plane shear modulus (G12) 17388 23618 16525 23066 17264 23537 17136 23455

In plane Poisson ratio (ν21) 0.127 1.427 0.127 1.634 0.127 1.454 0.127 1.482

Axial tensile failure strain (ε11T) 0.020 0.020 0.016 0.016 0.013 0.013 0.012 0.012

Axial compressive failure strain (ε11C) 0.019 0.019 0.012 0.012 0.005 0.005 0.010 0.010

Transverse tensile failure strain (ε22T) 0.054 0.017 0.043 0.013 0.036 0.011 0.033 0.010

Transverse compressive failure strain (ε22C) 0.015 0.009 0.010 0.006 0.007 0.005 0.009 0.005

In plane shear failure strain (ε12) 0.028 0.020 0.023 0.017 0.023 0.017 0.016 0.012

Axial tensile stress at failure (σ11T) 1925 171 1537 62 1290 103 1189 80

Axial compressive stress at failure (σ11C) 694 62 632 42 459 39 670 55

Transverse tensile stress at failure (σ22T) 1048 1048 800 800 696 696 634 634

Transverse compressive stress at failure (σ22C) 346 346 305 305 215 215 242 242

In plane shear stress at failure (σ12) 308 308 257 257 308 308 224 224

Determination of Material Properties

To accurately assign properties to the individual elements 

(subcells) in the finite element simulation, an analytical 

algorithm called “Independently Homogenized Subcells” was 

developed. This algorithm was developed to calculate material 

axis system inputs for *MAT_58 from the fiber and matrix 

stiffness properties, and the global quasi-isotropic coupon test 

strengths. The use of this type of algorithm to compute inputs 

for the finite element simulation facilitates the simulation of

architecturally-dependent damage by defining the various 

subcells of the model as having different mechanical properties. Subcells ‘A’ and ‘C’ have similar configurations only 

vertically inverted (Figure 2). Subcells ‘B’ and ‘D’ also have 

similar configurations only, again, vertically inverted.

Therefore, only two sets of properties must be calculated. One 

set of mechanical properties is calculated for subcells ‘A’ and 

‘C’, while another set is calculated for subcells ‘B’ and ‘D’.

These mechanical properties, calculated though rigorous 

micromechanical and composite laminate theories were 

adapted to characterize the material properties used in the 

braid architecture approach developed by Cheng (Ref. 11) and 

Littell (Ref. 14).

The next six sections contain a detailed account of the inner 

workings of the “Independently Homogenized Subcells” 

program. In Figure 3, the pseudocode is presented, and each 

subroutine is labeled. The following paragraphs explain the 

algorithms of the individual subroutines employed.

Inputs

The inputs needed for the “Independently Homogenized 

Subcells” program are indicated in Figure 3 by green ovals.

These inputs were the fiber volume ratios of the subcells, fiber

Figure 3.—Independently homogenized subcells pseudocode.

and resin stiffness properties, lamina orientations, and global 

strengths of the composite. For this study, the average fiber 

volume ratio for each subcell and the fiber volume ratio for 

individual plies within each subcell, were determined based on 

high-fidelity finite element models of triaxially-braided 

composites developed by Li, et al. (Ref. 15). In this model, 

various dimensions for the unit cell and the fiber tows were 

taken from optical micrographs, and a finite element model with 
NASA/TM—2012-217621 6

average dimensions was constructed. To compute the required 

finite element ratios for the “Independently Homogenized 

Subcell” program, the finite element mesh of Li, et al. (Ref. 15)

was virtually divided into subcells and layers within the subcell 

(including the fiber tow and resin rich regions). The percentage 

of elements of a given material type (fiber tow or matrix) within 

each subcell and subcell layer was then computed. Given an 

assumed fiber volume fraction within the fiber tow, and 

knowing an overall fiber volume ratio for the composite, 

average fiber volume ratios for each subcell and the individual 

layers within each subcell (assuming that the subcell layer 

consists of the fiber tow and pure resin regions) were computed.

Other approaches have been developed by Liu, et al. (Ref. 19)

and Xiao, et al. (Ref. 16) in which the unit cell geometry and 

dimensions as measured by micrographs are explicitly used to 

determine the required subcell and layer fiber volume ratios 

within the unit cell. These approaches will be applied in the 

future to the current method to see if improved geometry and 

fiber volume ratio values can be obtained. Through Li’s virtual 

experiments, volume fractions of the axial plies in subcells ‘A’ 

and ‘C’ were identified as 0.80, and the volume fractions of 

the bias plies in all subcells were identified as 0.50 (Ref. 15).

The fiber and matrix constituent stiffness properties were 

given by the composite manufacturer (Ref. 13) (Table 2). The 

lamina orientations are listed in Figure 2. The global strengths 

were obtained from the quasi-static coupon test properties 

(Table 3) (Ref. 13).

Stiffness Properties

The first step was to utilize Goldberg’s Slice Model (Ref. 

20) to create effective unidirectional lamina stiffness matrices 

for the composite laminates employed to represent each 

subcell. This model is a micromechanics model developed for 

use in calculating effective composite properties (Ref. 20).

This method was employed due to its simplicity and accuracy.

The Slice Model calculates effective unidirectional ply 

properties from the fiber volume fraction, and the fiber and 

matrix stiffness properties. This model was employed to 

determine the stiffness of a single ply within a subcell. The 

calculation for the stiffness of a single ply was performed for 

the ‘A’ and ‘C’ subcells, and the ‘B’ and ‘D’ subcells 

independently.

Classical lamination theory (CLT) (Ref. 21) was then 

employed to compute the overall effective laminate stiffness 

matrices for each subcell. The effective stiffness matrices of 

the unidirectional laminae calculated in the previous process 

were utilized for the calculations. Only in-plane loads were 

assumed to be applied. Therefore, the moment curvature 

relations of classical laminate theory were neglected. In-plane 

normal-shear couplings were neglected as well, because the 

subcells were approximated as balanced laminates. In 

addition, tension-bending coupling was neglected even though 

the composite layups were anti-symmetric, because no out-ofplane bending was observed in testing when in-plane strains 

were applied. Further, in the global braided material, the 

composite was approximately symmetric, which resulted in 

the elimination of the tension-bending coupling. From the 

calculated laminate stiffness matrices, the overall stiffness 

matrix, moduli, and Poisson’s ratio for each subcell were then 

computed assuming orthotropic material behavior. As 

previously noted, in the actual triaxially-braided composite, 

the zero degree fiber bundles contained twice as many fibers 

as the bias fiber bundles. To account for this, in subcells ‘A’ 

and ‘C’, the zero degree laminae were given twice the 

thickness of the bias laminae in the composite stiffness matrix 

calculations. These effective stiffness properties were then 

applied as the stiffness inputs for the finite element model.

TABLE 2.—CONSTITUENT PROPERTIES 

E11,

GPa

E22,

GPa ν12

G12,

GPa

T700 (fiber) 230.00 15.00 0.20 27.00

PR520 (resin) 4.00 4.00 0.36 1.47

E-862 (resin) 2.70 2.70 0.36 1.47

5208 (resin) 3.80 3.80 0.36 1.47

3502 (resin) 3.60 3.60 0.36 1.47

TABLE 3.—GLOBAL STRESS VALUES USED IN CALCULATIONS

(MPa) T700/PR520 T700/E862 T700/5208 T700/3502

Global stress at failure (axial tension) 1048 800 696 634

Global stress at failure (transverse tension) 1048 800 696 634

Global stress at failure (axial compression) 378 337 249 363

Global stress at failure (transverse compression) 346 305 215 217

Global stress at failure (shear) 308 257 308 224

Stress at pt. of nonlinearity (axial tension) 1048 495 650 524

Global strain-at-failure (axial compression) 0.019 0.012 0.005 0.010

Global strain-at-failure (transverse compression) 0.012 0.008 0.006 0.007

Global strain-at-failure (shear) 0.024 0.020 0.020 0.014
NASA/TM—2012-217621 7

Strength Properties—Axial Tension

The third subroutine in the “Independently Homogenized 

Subcells” program identified the global strengths needed to 

back-calculate the subcell strengths and then computed those 

properties. These properties can be seen in Table 3. The global

strength properties were utilized to run the “Subcell Calculations.” The global stresses, the effective laminate stiffness 

properties from the previous step, and various uniform stressstrain assumptions between subcells were employed to 

calculate homogenized strengths for each subcell. Because 

these subcells have equivalent properties the same material 

was characterized for both ‘A’ and ‘C’. This was also the case 

for subcells ‘B’ and ‘D’. Therefore, there were only two 

independent materials to characterize. Separate subroutines of 

the “Subcell Calculations” were run for axial, transverse, and 

shear loading cases.

To calculate the axial tension strength in the subcells, both 

the stress at failure and the stress at the point where the stressstrain curve becomes nonlinear were used. For three out of the 

four materials, at a particular stress level, significant stiffness 

degradation occurred, reflected in the stress-strain curves 

becoming nonlinear. For example, as shown in Figure 4, for 

the T700/3502 material, this stiffness degradation (pointof-nonlinearity) occurs at a stress level of 524 MPa. The 

point where the stress-strain curve becomes nonlinear was 

identified by Littell (Ref. 13) as being correlated to the stress 

level where there is a significant amount of bias fiber bundle 

splitting (local matrix microcracking) and out of plane 

deformation. This phenomenon was simulated in the analysis 

model by assuming that failure in subcells ‘B’ and ‘D’ 

occurred at the global stress level where the stress-strain curve 

became nonlinear given that these subcells contain bias fibers 

only. Therefore, the stress at the point of nonlinearity was 

used to compute the strength for subcells ‘B’ and ‘D’. For 

subcells ‘A’ and ‘C’, the axial strength in the subcells was 

calculated employing the ultimate axial tension failure stress.

To account for the fact that the overall composite does not 

fail even after subcells ‘B’ and ‘D’ reach their maximum stress, 

the “stress limiting parameter” available in the *MAT_58 

material model was used. By setting this parameter to “1” for 

the case of axial tension in subcells “B” and “D”, the subcells 

could continue to accumulate strain even after the maximum 

stress in the subcells was reached. Catastrophic failure occurs 

experimentally in the axial tension test specimen only when the 

axial fibers break (Ref. 13), which is represented in the current 

model as resulting in failure in subcells ‘A’ and ‘C’. A visualization of how the SLIMT1 parameter changes the simulation 

results is shown in Figure 5. It can be seen in the figure that the 

subcells ‘B’ and ‘D’ continue to elongate until the subcells ‘A’ 

and ‘C’ fail, resulting in all of the subcells failing at the same 

axial tensile strain.

Figure 4.—Axial tension experimental coupon test for the T700/3502 material which 

demonstrates stiffness degradation.
NASA/TM—2012-217621 8

Figure 5.—Illustration of the SLIMT1 (Stress Limiting Parameter in Axial Tension).

The global strength from the axial tension coupon test 

where significant stiffness degradation occurs (point-ofnonlinearity), was used to calculate the axial tension strength 

in subcells ‘B’ and ‘D’. Using mechanics of materials theory 

and appropriate uniform stress and uniform strain assumptions, the following equations were derived to compute the 

partitioned subcell stress. The axial tension stress in subcells 

‘A’ and ‘C’ at the point-of-nonlinearity (PON) was calculated 

using Equation (1). The axial tension strength in subcells ‘B’ 

and ‘D’ was then calculated using Equation (2)

σ11A(pon) = σ11(pon) /(0.5 (1 + S11A/S11B)) (1)

σ11B = S11A/S11B σ11A(pon) (2)

The axial tension failure strength of subcells ‘A’ and ‘C’ 

were computed using the axial tension failure stress for the 

overall composite and the failure strength of subcells ‘B’ and 

‘D’ by using Equation (3)

σ11A = 2 (σ11 – 0.5 σ11B) (3)

This equation is based on the assumption that the failure of 

subcells ‘A’ and ‘C’ results in the ultimate axial tensile failure 

of the composite and that at this point the stress in subcells ‘B’ 

and ‘D’ remain at their computed maximum value. The axial

tension failure strain for both subcells ‘A’ and ‘C’ and 

subcells ‘B’ and ‘D’ were assumed to be equal to the global 

axial tension failure strain obtained from the experiments, as 

shown in Equations (4) and (5).

ε11A = ε11 (4)

ε11B = ε11A (5)

To calculate the axial compression strength in the subcells, 

expressions similar to Equation (1) and (2) were used. The 

global composite axial compressive failure stress was used in 

the computations due to the assumption that all of the subcells 

failed at the global composite axial compressive failure strain.

The axial compressive failure strains were set equal to the 

global axial compression failure strains obtained from

experiments.

Strength Properties—Transverse Tension

As discussed by Littell (Ref. 13), triaxially-braided composite transverse tensile tests conducted on straight-sided 

coupons may not yield results that are truly representative of 

the actual material response. Specifically, the transverse 

tension tests yielded ultimate strengths much lower than the 

expected values. More discussion about the transverse tension 

coupon tests can be found in Reference 13. For this reason, the 

experimental test results in transverse tension were not used in 

this method. The calculations were instead based on the 

ultimate stress obtained from the axial tension coupon test.

The transverse tension failure stress was assumed to be equal 

to the axial tension failure stress due to the theoretical quasiisotropy of the materials. Using mechanics of materials theory 

the following equations were derived to calculate the partitioned subcell stresses. The transverse tension strengths for the 

individual subcells were then set equal to the global assumed 

transverse tension strength, as shown in Equations (6) and (7).

σ22A = σ22 (6)

σ22B = σ22 (7)

The transverse tension failure strain for subcells ‘B’ and ‘D’ 

was calculated using Equation (8). Because of the orientation 

of the zero-degree ply fiber bundles, these bundles experience 

large transverse elongation during transverse tension testing 

due to axial fiber splitting and local matrix micro cracking

(Ref. 13). Based on these mechanisms, it is postulated that the 

zero-degree ply bundles carry almost no load at the point 

where the overall composite fails in transverse tension. To 

incorporate this effect into the finite element simulation, the 

compliance matrix of the zero-degree ply bundles was 

adjusted by setting the transverse elastic modulus of the zero 

degree layers in subcells ‘A’ and ‘C’ to fifty percent of the 

nominal value as shown in Equation (9). Using this value, a 

modified compliance matrix was assembled as shown in

Equation (10) (Ref. 21). The transverse tension failure strain 

for subcells ‘A’ and ‘C’ was then calculated using this 

modified compliance matrix. This failure strain for subcells 

‘A’ and ‘C’ was calculated using Equation (11).
NASA/TM—2012-217621 9

Figure 6.—Image of the unit cell in transverse tension. 

ε22B = S12B (S12A – S12B)/(S11A + S11B) σ22 + S22B σ22 (8)

S22A = 2 (1/E22A) (9)

[ ]





























−

−

=

12

11 22

12

11

12

11

mod

1 0 0

0 2

0 1

G

E E

v

E

v

E

S (10)

ε22A = S12A (S12B – S12A)/(S11A + S11B) σ22 + S22A σ22 (11)

Strength Properties—Compression and Shear

Transverse compression and shear strengths for the subcells 

were assigned to the subcells in the same way as for the 

transverse tension strength, with the subcell strengths being set 

equal to the global composite failure stress. The subcell failure 

strains were calculated as follows. For the cases of transverse 

compression, axial compression, and in-plane shear, examinations of the optical strain data obtained during tests conducted 

by Littell (Ref. 13) indicated that the strain field was uniform 

throughout the gage section. Therefore, all four of the subcells 

were assumed to fail simultaneously. Because of the highly 

nonlinear characteristics of the experimental transverse 

compression, axial compression, and in-plane shear curves, 

the subcell failure strains of these curves were computed based 

on the experimental global composite failure strain data, 

specifically the values indicated in Table 3. The transverse 

compression and shear failure strains for each subcell were 

computed by multiplying the global composite failure strains

by a scale factor determined by applying uniform strain and 

stress assumptions and mechanics of materials theory. In these 

calculations the actual ratios of the failure strains in the 

subcells are assumed to be equivalent to the ratios of the 

failure strains in each subcell computed using the failure 

stresses and elasticity theory.

The “Independently Homogenized Subcells” method is a 

rigorous and repeatable approach. This method was developed 

based on accepted theoretical algorithms and methods, and can 

easily be adapted to calculate material inputs for any woven or 

braided composite.

Quasi-Static Coupon Simulations

A series of simulations was conducted to evaluate the 

analysis methods described above and to check the correlation 

of the computed stiffness and strength input parameters.

Specifically, quasi-static axial and transverse coupon level 

tensile tests and quasi-static axial and transverse compression 

tests on four representative triaxially-braided composites were 

simulated. The materials were composed of a two-dimensional 

triaxially-braided preform and a 177 °C 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, CYCCOM PR 520 (Cytec 

Industries, Inc.), a one-part toughened resin was used. Cytec’s 

5208 resin and Hexcel’s 3520 resin were used for the remaining two material systems. 

For the composites under consideration, six layers of a 

[+60°/0°/–60°] braided preform were stacked on top of one 

another. The axial fibers were 24k flattened tows while the 

bias fibers were 12k flattened tows. Again, the differing sizes 

of the fiber bundles were accounted for within the subcell 

discretization by making the layers with axial fibers twice as 

thick as the layers with bias fibers in subcells A and C. The 

global fiber volume fraction for all of the triaxially-braided 

composites was determined to be approximately 56 percent.

The experimental tests were conducted by Littell, et al.

(Ref. 14), where full details of the experimental procedures 

can be found. Displacement-controlled tests were conducted.

A minimum of five tests were conducted in each direction for 

each material system. In the figures to follow, the test results 

plotted are representative of specific tests which yielded 

results near the average. As mentioned earlier, future efforts 

will involve determining a more statistically based “mean 

results curve” for the various tests that were conducted.

For the analytical simulations, to compute the stiffness 

properties for each subcell, first the fiber volume ratio in each 

layer of each subcell was computed using the methods 

described above. By using the specified procedures, the fiber 

volume ratio of the axial layers in subcells A and C were 

determined to be 0.80, and the fiber volume ratio of the layers 

with bias fibers in all of the subcells was determined to be 

0.50. The specified micromechanics methods and classical 

laminate theory were then applied to compute the effective 

stiffness properties for each subcell. In applying the micromechanics analysis methods, the stiffness properties for the fiber 

and matrix given in Table 2 (and taken from Littell (Ref. 13)) 

were applied. The applied constituent properties were obtained 

from a combination of manufacturer’s data and representative 

values for carbon fibers obtained through various micromechanics analysis methods. The computed stiffness properties 

for each subcell for all of the material systems studied are 

listed in Table 1. Note that the Poisson’s ratio listed is the 
NASA/TM—2012-217621 10

transverse Poisson’s ratio, ν21, which is required for the LSDYNA material model, which explains the large Poisson’s 

ratio values shown in the table. Also, note that the given 

properties are the smeared homogeneous properties for each 

subcell. One consequence of this approximation is that the 

transverse modulus is much higher than the longitudinal 

modulus for subcells B and D due to the bias fiber-dominated 

layup of these subcells. As already mentioned, these values are 

average values taken from representative tests conducted by 

Littell (Ref. 13) for each material. Future efforts will involve 

conducting a detailed statistical study of the global composite

coupon results in order to obtain statistically-significant mean 

and extreme values to use in the analysis.

The axial and transverse tension simulations, seen in 

Figure 7, were developed to mimic experimental coupon tests.

For these static simulations, the nodes at the very top were 

fixed. Displacement in the static simulations was applied to 

the nodes at the bottom in the direction of the loading arrows.

The dimensions of both axial tension and transverse tension 

simulations are 30.48-cm (12.00-in.) by 3.58-cm (1.40-in).

The axial tension simulation is composed of 480 elements, 8 

across and 60 long. The transverse tension simulation is 

composed of 476 elements, seven across and 68 long. The 

stress-strain curves for these simulations were defined by 

averaging the elemental stresses and strains for the bottom six 

rows of elements in each model.

To calibrate the material properties for the composites 

examined in this study, simulations of the axial tension and 

transverse tension coupon tests were carried out and results 

from the axial tension simulations were compared with 

experimental data from quasi-static coupon tests conducted by 

Littell (Ref. 13). The material properties used in the analyses 

are shown in Table 1.

Figure 8 to Figure 15 display the results of the simulations 

for each of the materials examined in this study, and comparisons of the coupon simulation results (red) with the experimental coupon stress-strain curves (blue) are shown for the 

axial tension analyses. Figure 8, Figure 10, Figure 12, and 

Figure 14 contain the axial tension curves for the composite 

materials T700/PR520, T700/E862, T700/5208, and 

T700/3502, respectively. The computed axial tension values 

for the T700/PR520 composite compare well with the 

experimental axial tension test curve as shown in Figure 8.

Overall the simulation is slightly stiffer and fails at a slightly 

lower stress than the experiment shows, however, the area 

under the curve is similar. Therefore, the amount of energy 

absorption compares very well the experiment and this is an 

important aspect for impact simulation. The computed axial 

tension values for the T700/E862 composite also compares 

well with the experimental axial tension test curve as shown in 

Figure 10. Again for the T700/E862 composite the simulation 

is slightly stiffer and weaker than the experimental results, but 

the area under the curve is equivalent. The nonlinearity of the 

stress-strain curve is also captured by the simulation. The 

computed axial tension composite coupon response for the 

T700/5208 material also compares well with the experimental 

axial tension test curve as shown in Figure 12. The simulation 

does not capture the stiffening observed in the experiment, but 

that may be an artifact of the experimental results. The

computed axial tension coupon response for the T700/3502 

composite also compares well with the experimental axial 

tension test curve as shown in Figure 14. Again for the 

T700/3502 material the simulation is slightly stiffer and 

weaker, the area under the curve is nearly equivalent, and the 

nonlinearity is captured in the simulation.

Figure 7.—Finite element models of axial tension (left) and 

transverse tension (right) tests (Ref. 2).

Figure 8.—Axial tension experimental versus computed 

response for T700/PR520 composite coupon test.
NASA/TM—2012-217621 11

Figure 9.—Transverse tension experimental versus computed

response for T700/PR520 composite coupon test.

Figure 10.—Axial tension experimental versus computed 

response for T700/E862 composite coupon test.

Figure 11.—Transverse tension experimental versus computed 

response for T700/E862 composite coupon test.

The transverse tension experimental results were not used in 

the material property calculations because composite transverse 

tensile tests conducted on straight-sided coupons may not yield 

results that are truly representative of the actual material 

strength response. As can be seen in the figures the initial 

stiffness of the axial and transverse experimental curves are the 

same, the transverse tension results become nonlinear at a much 

lower stress than the axial tension results. Theoretically, due to 

the quasi-isotropic material properties these curves should be 

much more similar. There has been some investigation in how 

the premature failure near the fiber bundles that terminate at 

free edges can contribute to the overall nonlinearity noted in the 

resulting curves. More discussion about the transverse tension 

coupon tests can be found in Reference 13. Because the goal is 

to capture in situ properties of large composite structures, these 

edge effects are not included in the simulations. Therefore, only 

the initial stiffness can be reasonably compared with the 

experimental test, while the experimental strength and stiffness 

are much lower than those of the simulations. Following the 

trends observed in the axial tensile results, the computed 

transverse tension T700/PR520 composite coupon simulation 

resulted in the highest strength of the transverse coupon 

simulations as shown in Figure 9. This result is expected 

because the properties (Table 3) for this material were the 

highest of the four. The computed transverse tension T700/E862 

composite coupon simulation resulted in the second highest

strength of the transverse coupon simulations after the 

T700/PR520 simulation as shown in Figure 11. This result 

correlates well quantitatively with the input properties. As 

shown in Figure 12, for the T700/5208 material the computed 

transverse tension composite coupon simulation results in the 

third highest strength of the four materials and, as shown in 

Figure 15, the computed transverse tension T700/3502 composite coupon simulation yields the lowest transverse tension 

strength of the four materials. Overall, for all four materials the 

ultimate transverse tension strengths obtained in the simulations 

are slightly lower than the axial tension strengths, which 

correlated well with the expected material behavior. The 

simulated curves also display a significant amount of nonlinearity, which also correlates well with the expected material 

response.

Axial and transverse compression simulations were carried 

out for the T700/PR520 and T700/E-862 materials using the 

same basic geometry and boundary conditions as shown in 

Figure 7 (only with compression loading as opposed to tensile 

loading). The simulated results were compared to experimental 

values obtained from quasi-static compression testing conducted 

by Littell (Ref. 13). The axial compression simulations 

compared well with experimental coupon testing results. These 

can be seen in Figure 16 and Figure 18. The transverse 

compression simulations also compared well with experimental 

coupon testing results. The comparison of the transverse 

compression simulations with the experimental results can be 

seen in Figure 17 and Figure 19. Both the stiffness and strength 

correlate well for both examined materials for the cases of both 

axial and transverse compression. 
NASA/TM—2012-217621 12

Figure 12.—Axial tension experimental versus computed 

response for T700/5208 composite coupon test.

Figure 13.—Transverse tension experimental versus computed 

response for T700/5208 composite coupon test.

Figure 14.—Axial tension experimental versus computed 

response for T700/3502 composite coupon test.

Figure 15.—Transverse tension experimental versus computed 

response for T700/3502 composite coupon test.

Figure 16.—Axial compression experimental versus computed 

response for T700/PR520 composite coupon test.

Figure 17.—Transverse compression experimental versus 

computed response for T700/PR520 composite coupon test.
NASA/TM—2012-217621 13

Figure 18.—Axial compression experimental versus computed 

response for T700/E862 composite coupon test.

Figure 19.—Transverse compression experimental versus 

computed response for T700/E862 composite coupon test.

Integration Point Study

To examine the predictive capability of the analysis approach, impact tests conducted by Pereira, et al. (Ref. 21) were 

simulated. Since all of the characterization was conducted 

based on results from the quasi-static coupon tests, the impact 

simulations discussed in this section of the report are truly 

predictive. The impact tests, which were conducted in the 

NASA Glenn Research Center Ballistic Impact Laboratory, 

utilized a single-stage compressed gas gun to propel an 

aluminum 2024 projectile into 0.305- by 0.305- by 0.0032-m 

composite panels composed of six layers of the T700/E862 

composite. The other materials have not been tested at the 

current time. The composite panel was held in a circular 

fixture with an aperture of 0.254 m. The projectile was a thinwalled hollow cylinder with a nominal mass of 50 gm and a 

front face with a compound radius. The overall length of the 

projectile was 0.0495 m, the wall thickness was 0.00076 m 

and the nominal diameter was 0.05067 cm. Tests were 

performed over a range of impact velocities to determine the 

velocity for the 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 to 

175 m/s. The threshold velocity for penetration was determined to be between 161 and 168 m/s.

First, the number of integration points was analyzed for the 

quasi-static coupon simulations. These simulations were 

conducted with the number of through-thickness integration 

points ranging from 2 to 8. There was no difference between 

any of the quasi-static coupon simulations. This was determined to be due to the lack of out-of-plane deformation in the 

quasi-static coupon simulation (which reflects the test results).

After this, the number of integration points was analyzed for 

the impact simulations (described in the next section of this 

report). For the impact simulations the number of throughthickness integration points was started at 2 and then increased 

until the solutions converged. There was no difference 

between the impact simulations using 12 and 13 integration 

points. Therefore, 12 integration points through-the-thickness 

were then used for all the simulations used in this analysis. All 

quasi-static and impact simulation results reported in this 

paper were run using 12 integration points which amounts to 2 

integration points per braid layer.

Impact Predictions

After the material properties for each of the composites 

examined in this study were determined using the “Independently Homogenized Subcells” program and correlated 

using quasi-static coupon tests, simulation of impact tests 

conducted by Pereira, et al. (Ref. 22) were conducted. The high 

velocity impact tests were performed using a hollow hemispherical projectile (Ref. 22). Only one of the material systems

examined in this paper, T700/E862, has undergone impact 

testing. The set-up for the impact simulation can be seen in 

Figure 20. The composite mesh simulated in the impact analysis 

had dimensions and constraints replicating those of the 

experiments. The panels were 30.5- by 30.5-cm (1- by 1-ft) 

squares with clamped boundaries in 25.4 cm (10 in.) diameter 

circles centered in the panels. The nodes in the circular 

boundary had all six degrees of freedom constrained. The panels 

were made up of 810 unit cells; 15 unit cells across and 54 unit 

cells vertically. Because there were four elements in a unit cell, 

the panel had 2700 elements, and 2805 nodes. The projectile 

was modeled as a linear elastic material to accurately account 

for energy absorption due to elastic deformation of the projectile. This was assumed due to the negligible amount of plastic 

deformation seen in the projectiles during testing. The density 

and stiffness of the projectile in the simulation were measured 

from the aluminum used in the experimental testing. The 

contact card employed was the LS-DYNA contact 

“*Contact_Automatic_ Single_Surface” (Ref. 12).
NASA/TM—2012-217621 14

Figure 21 displays a comparison between the impact simulation and the experimental impact test. The black and white 

image is test specimen after impact. The black and white 

textured surface is painted on prior to testing to create a grid 

that is used in the digital image mapping process. There are 

two predictions to point out in Figure 21. The first notable 

item is the prediction of penetration velocity. The simulation 

predicted penetration of the projectile at 160 m/s (525 ft/s) 

which was slightly below the experimental threshold velocity 

range of 162 to 171 m/s (530-560 ft/s). The discrepancy in 

velocities is within 1 percent and therefore fairly reasonable.

The second item of note is the simulation’s prediction of the 

damage pattern. There are a few limitations when comparing 

the simulations with experimental impact results. First, the 

experimental image displayed in Figure 21 is the image of 

panel post-testing. Because of this, it is difficult to assess the 

mode of initial failure and failure propagation in the experimental impact data. Second, there is a great deal of scatter in 

the data, as with most high velocity impact testing, and 

therefore the failure patterns differ greatly from test to test 

even though the ballistic limit has been identified within a 

reasonably tight range. In the experimental impact test 

specimen, the composite failure area appears to be shaped like 

an oval with more damage along the axial fibers (Figure 21).

The simulation provides more detail on the initiation and 

propagation of damage. The initial area where failure propagates through all six layers of composite occurs in the lower 

left corner of the impact zone. From this point the failure 

begins to propagate, first along the bias fibers and then 

vertically along the axial fibers and finally horizontally. The 

projectile continues to damage the composite by folding back 

petals of the fractured region. The macro-scale simulation 

cannot capture fiber bundle splintering, but it can be interpreted as one of the physical mechanisms simulated by the 

petaling. The overall damage pattern in the experiment is 

slightly more elongated than the damage pattern seen in the 

simulation. However, it is safe to say that the simulation 

damage pattern is far closer to the experimental than a typical 

homogenized damage pattern where a perfect cross is formed.

It is possible the difference could be due, again, to the use of 

quasi-static properties. There may be some anisotropic 

stiffening due to rate effects.

Figure 20.—Finite element mesh for impact simulations.

Figure 21.—Simulated (left) and experimental (right) damage patterns for T700/E862 composite in impact (Ref. 20).
NASA/TM—2012-217621 15

Figure 22.—Simulated damage patterns 

for T700/5208 composite in impact.

High velocity impact simulations were conducted for the 

other three materials by using the same simulation setup. Here 

they are only examined qualitatively as there is no experimental data currently available to compare with directly. The 

T700/PR520 material had a ballistic limit of 240 m/s (775 ft/s) 

as seen in Figure 22. This was higher than the ballistic limit 

noted in the T700/E862 material simulation. The damage in 

the T700/PR520 simulation formed in a completely different 

way than the damage in the previous simulation. The damage 

initiated at the bottom center of the impact zone and propagated, first in both horizontal directions, and second upwards 

along the edges of the zone vertically cutting out a door-like 

flap of the composite plate. The initiation of vertical damage 

on the right side of the impact zone can be seen in the time 

step displayed in Figure 23. The T700/5208 material had a 

ballistic limit of 110 m/s (350 ft/s) as seen in Figure 23. This 

was the lowest ballistic limit of the examined materials and 

may be due to the low compression properties used in the 

“Independently Homogenized Subcells” program. In this 

simulation the failure initiated in the center of the impact zone 

and first propagated along the +60 bias fibers. The material 

continued to fail vertically and horizontally. The three petals 

that fold back during failure can be seen in Figure 23. The 

T700/3502 material had a ballistic limit of 150 m/s (500 ft/s) 

as seen in Figure 24. Damage propagation, again, occurred in 

a different way than the previous simulations. Damage in this 

simulation initiated in the center right of the impact zone and 

quickly propagated along the bias fibers both above and below 

the damaged area. While damage propagated in the horizontal 

direction, a new area of damage initiated in the center of the 

impact zone. This resulted in the damage of nearly all material 

in the impact zone. Because of this, no petaling occurred. This 

result differed from all the simulations with the other materials. The varying predicted damage patterns of the different 

materials show that material and architecturally-dependent 

damage mechanisms have been captured by the method. These 

simulations are also purely predictive because there has been 

no correlation on the impact level.

Figure 23.—Simulated damage patterns 

for T700/PR520 composite in impact.

Figure 24.—Simulated damage patterns 

for T700/3502 composite in impact.

Conclusion

A macro level finite element-based approach has been 

developed that allows for the simulation of the response of a 

triaxially-braided composite in a manner that 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. Quasi-static tension and 

compression tests on four representative composite materials 

were simulated, and the correlation between the analysis 

results and the experimental tests was reasonably good.

Representative flat-panel impact tests were also simulated 

using the analysis model. Since the input material parameters 

were correlated based on the coupon level tests, these 

simulations were purely predictive. For the one material 

system where experimental data was available, the predicted 

ballistic limit was only slightly below the experimental value.

The predicted impact damage patterns followed the details of 
NASA/TM—2012-217621 16

the braided architecture, and were similar to the experimental 

damage patterns. The predicted impact damage patterns for the 

four material systems examined in this study were significantly different, indicating that the analysis method could capture 

the effects of differing material strengths on the impact 

damage in the material. Overall, the analysis method appears 

promising in its ability to simulate the architecturallydependent impact damage in braided polymer matrix composites. Future efforts will involve incorporating the effects of 

strain rate into the model, modifying the method to allow for 

more general textile composite geometries, as well as 

investigating in more detail the capability of the model to 

simulate impact events, particularly before final penetration 

occurs.

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Polymer and 2D Triaxially Braided Composites”, Ph.D. 

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Braided Composite Materials”, Ph.D. Dissertation. University of Akron. Akron, Ohio. 2008.

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Braided Composites under Tensile Loading”, Journal of 

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4. TITLE AND SUBTITLE

Macro Scale Independently Homogenized Subcells for Modeling Braided Composites 

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6. AUTHOR(S)

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14. ABSTRACT

An analytical method has been developed to analyze the impact response of triaxially braided carbon fiber composites, including the 

penetration velocity and impact damage patterns. 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. Currently, 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. To determine the stiffness and

strength properties required for the constitutive model, a top-down approach for determining the strength properties is merged with a 

bottom-up approach for determining the stiffness properties. The top-down portion uses global strengths obtained from macro-scale coupon 

level testing to characterize the material strengths for each subcell. The bottom-up portion uses micro-scale fiber and matrix stiffness 

properties to characterize the material stiffness for each subcell. Simulations of quasi-static coupon level tests for several representative 

composites are conducted along with impact simulations. 

15. SUBJECT TERMS

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

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