impact characterization of sandwich structures with an integrated orthogrid stiffened syntactic foam...

Composites Science and Technology 68 (2008) 2078–2084

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Composites Science and Technology

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Impact characterization of sandwich structures with an integrated orthogridstiffened syntactic foam core

Guoqiang Li a,b,*, Venkata Dinesh Muthyala a

a Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803, USAb Department of Mechanical Engineering, Southern University, Baton Rouge, LA 70813, USA

a r t i c l e i n f o

Article history:Received 4 January 2008Received in revised form 21 February 2008Accepted 13 March 2008Available online 28 March 2008

Keywords:A. SandwichB. ImpactC. Finite element analysisE. KnittingGrid

0266-3538/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.compscitech.2008.03.014

* Corresponding author. Address: Department of Misiana State University, Baton Rouge, LA 70803, USA. T225 5785924.

E-mail address: [email protected] (G. Li).

a b s t r a c t

This paper presents the manufacturing, testing, and modeling of a new composite sandwich structurewith a hybrid grid stiffened core. The hybrid core consists of a continuous fiber reinforced polymer ortho-grid skeleton that is filled in with light weight syntactic foam in the bays or cells. The grid skeleton wasmanufactured by a dry weaving process per the pin-guided filament winding technology. Low velocityimpact tests and compression after impact (CAI) tests were conducted to evaluate the impact responseand residual strength of the sandwich structure. C-scan and SEM observation were implemented to inves-tigate the impact damage. A finite element analysis using ANSYS was conducted to validate the compres-sion test results. It is found that this integrated core enhances impact energy transfer, energy absorption,and positive composite action, insures quasi-static response to impact, and has higher CAI strength.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Impact damage has been an epidemic problem for compositesandwich structures. In a composite sandwich structure, the skinis responsible for eroding and breaking projectiles, carrying bendingload, and protecting the core; the core is responsible for separatingand fixing the skins, resisting transverse shear, carrying in-planeload, and providing other functionalities like absorbing impact en-ergy, shielding radiation, and insulating heat transfer. Therefore,the versatility of sandwich construction comes from the core. Vari-ous types of core materials have been studied such as foam core(polymeric foam, metallic foam, ceramic foam, balsa wood, syntacticfoam, etc.) [1,2], truss, honeycomb and other web cores [3], 3-D inte-grated core [4,5], foam filled web core [5,6], laminated compositereinforced core [7], etc. While these core materials have been usedwith a certain success, they are limited in one way or another. Forexample, the brittle syntactic foam core absorbs impact energy pri-marily through macro length-scale damage, sacrificing residualstrength significantly [8–10]; and web cores lack of bonding withthe skin and also have impact windows [5,6].

Usually, the impact response of composite structures can be di-vided into boundary controlled and wave controlled [11], which

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can be further categorized into four types based on the impact in-duced stress wave transfer in the target [12–14]: (1) hypervelocityimpact response is dominated by dilatational waves with a veryshort impact duration and very small projectile mass; (2) highvelocity impact response is again dominated by dilatational wavesbut they are transversally reflected several times, which occurswith a little bit longer impact duration and larger impactor mass;(3) intermediate velocity impact response is dominated by flexuralwaves and shear waves with an intermediate impact duration andintermediate impactor mass; and (4) low velocity impact responseor quasi-static impact response is a boundary controlled impact re-sponse in which the flexural waves and shear waves have a suffi-cient time to come to and be reflected by the boundary manytimes. The quasi-static impact response usually results in less dam-age than other types of impact responses because it homogenizesthe stresses to make the peak load, deflection and strain more orless in phase. Therefore, it is critical to control the response of acomposite structure to impact in a quasi-static manner.

In order to achieve a boundary controlled impact response, wepropose to develop a new sandwich core, a grid skeleton that isfilled in by syntactic foam. We believe that this core is better in im-pact resistance and residual strength because (1) each cell or bay isa small panel with elastic boundary, leading it towards quasi-staticresponse; (2) the periodic grid skeleton, the primary load carryingcomponent with 2-D continuity, is responsible for transferring theimpact energy elastically and providing the in-plane strength andtransverse shear resistance; (3) the light-weight syntactic foamin the bay, the secondary load carrying component, is primarily

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responsible for absorbing impact energy through damage. If rub-berized foam is used [8–10], it can also extend the impact dura-tion; (4) the grid skeleton and the foam develop a positivecomposite action, i.e., the grid skeleton confines the foam toincrease its strength and the foam provides lateral support to resistrib local buckling and crippling. In addition, the foam also providesadditional in-plane shear strength for bi-grids such as orthogrid;and (5) the core and skin are fully bonded because the bay is fullyfilled, without the limitation of honeycomb core or truss core. It isworthy mentioning that the synergy between the grid skeleton andthe filled materials in the bay areas have been validated by statictesting of grid tube confined concrete cylinders [15] and analyticalmodeling of sandwich structures with hybrid grid core under a sta-tic bending load [16]. The microwave absorption capacity of simi-lar lattice structures has also been validated [17]. However, there iscurrently a lack of understanding of the impact response of thisnew sandwich structure. The objective of this study is thus to fab-ricate, test, and model the impact response and residual strength ofthis type of new sandwich structures.

Fig. 1. Schematic of weaving pattern.

2. Manufacturing and characterization

2.1. Raw materials

The materials used were glass fiber rovings by Saint Gobain,glass microspheres by Potters Industries, DER 332 epoxy resinand DEH24 curing agent by DOW Chemicals, and woven rovingfabric by Fiber Glast. From the manufacturers’ data sheets, theYoung’s modulus and Poisson’s ratio are, respectively, 75.2 GPaand 0.25 for E-glass fiber, 1.8 GPa and 0.37 for epoxy, and73.0 GPa and 0.22 for glass microballoon. The syntactic foam con-sisted of 60% by volume of microballoons and 40% by volume ofepoxy. The density of the cured syntactic foam was 0.5 g/cm3;the compressive strength was 13.5 MPa and the Young’s moduluswas 723 MPa per ASTM C365-94 standard.

A total of eight Groups of specimens were prepared. Group 1was a laminated composite as control. Groups 2–4 were the pro-posed sandwich structures with orthogrid reinforced syntacticfoam core. The bay areas of the orthogrid skeleton for Groups 2–4 were 12.7 mm � 12.7 mm, 25.4 mm � 25.4 mm, and 50.8 mm �50.8 mm, respectively. In order to have a common ground for com-parison, each Group has almost the same overall fiber volume frac-tion. Based on the fiber rovings available, the overall fiber volumefractions for Groups 1–4 were 11.0%, 10.3%, 11.1%, and 11.1%,respectively. The dimension of the specimens from each Groupwas also the same, which means almost the same amount of rawmaterials was used for the specimens from each Group. Therefore,the comparison of Group 1 with Groups 2–4 can directly show thedifference between the traditional laminated composite and theproposed sandwich composites. The comparison among Groups2–4 can directly reveal the effect of the bay area on the structuralperformance. In addition to the Group 1 as control, four otherGroups, Groups 5–8, were also manufactured to investigate thedevelopment of composite action. Group 5 was a grid core sand-wich without foam (bay area 25.4 mm by 25.4 mm); Group 6was a pure orthogrid skeleton without skin (bay area 25.4 mmby 25.4 mm); Group 7 was a sandwich with pure foam core; andGroup 8 was a pure foam without skin. This design can revealthe synergy between the grid skeleton and the skin, the foamand the skin, and the grid skeleton and the foam.

2.2. Manufacturing process

The procedure of fabricating the proposed sandwich structure issimilar to conventional sandwich structures using vacuum bagging

system. A special feature persists in the hybrid core. The grid skel-eton was created using a dry weaving process in which the glassfiber roving was woven without applying any resin during theweaving. In order to do this a wooden mold of 56 cm by 56 cmwas selected and steel pins were hammered in along the perimeterof the mold, with the spacing determined by the bay area. The dryglass fiber rovings were woven around these pins in a pattern sche-matically shown in Fig. 1. Syntactic foam was then prepared andpoured into the grid preform. The whole system, with the bottomand top skins, were secured by a vacuum system for a period of24 h at room temperature for curing. The thickness of the curedpanels was constant for each Group, 12.7 mm, to facilitate the im-pact tests and compression after impact tests. After curing the pa-nel was removed from the mold and the panel was cut to152.4 mm � 152.4 mm specimens using a precision cutter. Theadvantage of this dry-weaving process is that it insures that thegrid skeleton, the foam in the bay areas, and the skins are co-cured,and thus an integrated sandwich structure is formed. It is believedthat this insures a higher interfacial bonding strength than pouringfresh foam into a cured grid skeleton [17]. In order to fabricate theGroup 1 panel, six layers of glass fabric were used and 1/5 of thetotal foam was placed in between each layer and then the wholesetup was secured under vacuum for 24 h for curing. Because thesame amount of foam and fiber was used, the cured thickness ofthe laminates was also 12.7 mm. The Groups 5–8 were fabricatedusing a similar process. After curing, specimens of 152.4 mm �152.4 mm were cut using the same precision cutter.

2.3. Burn-out test

While the overall fiber volume fraction in each Group was al-most the same, the fiber volume fraction was not the same in eachstructural component (rib, node, skin). A burn-out test was con-ducted per ASTM D2584 standard. The volume fractions of glass fi-ber in the rib, node and skin were 36%, 72%, and 51%, respectively,

Compressive Strain (mm/mm)

0.000 0.005 0.010 0.015 0.020 0.025

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Group 5Group 6Group 7Group 8Group 3

Fig. 2. Compressive stress–strain behavior of Groups 3, and 5–8.

2080 G. Li, V.D. Muthyala / Composites Science and Technology 68 (2008) 2078–2084

for Group 2 specimens; they were 38%, 77%, and 51%, respectively,for Groups 3 and 4 specimens. For Group 1, the fiber volume frac-tion of each lamina is 34%.

2.4. Determination of elastic properties

Once the fiber volume fraction was obtained, tensile testcoupons per ASTM D3039 standard were prepared using the samefiber volume fraction as the lamina, rib, node, and skin. The longi-tudinal modulus, transverse modulus, and major Poisson’s ratioare, respectively, 13.6 GPa, 1.8 GPa, and 0.27 for the Group 1 lam-ina, 14.4 GPa, 1.9 GPa, and 0.27 for the Group 2 rib, 27.9 GPa,5.4 GPa, and 0.26 for the Group 2 node, and 20.0 GPa, 2.8 GPa,and 0.26 for the Group 2 skin. The elastic properties for each cor-responding component in Groups 3 and 4 are the same due tothe same fiber volume fraction. The respective longitudinal modu-lus, transverse modulus, and major Poisson’s ratio are 15.4 GPa,2.0 GPa, and 0.27 for the rib, 30.1 GPa, 6.8 GPa, and 0.26 for thenode, and 20.0 GPa, 2.8 GPa, and 0.26 for the skin.

2.5. Impact testing

Instron Dynatup 8250 HV Impact testing machine was used forcarrying out this test. Energy and load traces were acquired by theintegrated data acquisition system. The initiation energy and prop-agation energy were calculated using these data. Impact energy cor-responding to the maximum impact force is defined as initiationenergy. Propagation energy is defined as the difference betweenthe maximum impact energy and the initiation energy. These defini-tions have been used previously [8–10]. It has been suggested thatthe initiation energy is basically a measurement of the capacity forthe target to transfer energy elastically and a higher initiation en-ergy usually means a higher load carrying capacity; on the otherhand, the propagation energy represents the energy absorbed bythe target for creating and propagating gross damage.

Three velocities and two hammer weights were used for con-ducting the impact tests. Specimens were tested at velocities of2 m/s, 3 m/s, and 4 m/s using a hammer weight of 22.7 kg and4 m/s using a hammer weight of 40.0 kg. The tup nose was ahemi-sphere with a diameter of 12.7 mm. For Groups 2–4, eachGroup was tested at three locations (bay, rib, and node) that sur-rounded the center of the specimen. For Group 1, the impact wasat the center of the specimen. The specimens were squares witha side length of 152.4 mm and thickness of 12.7 mm. At least threeeffective specimens were tested for each parameter considered.

2.6. Ultrasonic and SEM inspection

Ultrasonic inspection was performed on all specimens over a152.4 mm � 152.4 mm area using a 1 MHz transducer both beforeand after they were impact tested. An UltraPac inspection machinefrom Physical Acoustics Laboratory was used in conjunction withUltraWin software to acquire the C-scan images and identify dam-ages. Scanning electron microscope (SEM) observation of microlength-scale damage was conducted using the Hitachi S-3600NSEM.

2.7. Compression after impact test

The testing was conducted using a MTS 810 machine and thefixture used was a ‘‘Boeing compression after impact compressiontest fixture”. The size of the specimen was 152.4 mm long,101.6 mm wide, and 12.7 mm thick. In order to obtain the101.6 mm wide specimen from the impact tested square speci-mens, the impact damaged 152.4 mm wide specimens were ma-chined by removing 25.4 mm from each side of the specimens. At

least three effective specimens were tested for each parameterconsidered. A strain controlled testing mode was used during thetesting and the loading rate was 5.0 mm/min.

3. Results and discussion

3.1. Development of composite action

Fig. 2 shows the typical compressive stress–strain curves ofGroups 3, 5–8 without impact damage. Group 3 is selected forcomparison because it has the same bay area as Groups 5 and 6.It is clear that the skin increases the peak stress of the orthogridbut reduces its ductility; see Groups 5 and 6. For the foam, the skinincreases both its strength and ductility; see Groups 7 and 8. The-oretically, Group 3, the proposed sandwich, is a combination ofgrid core sandwich (Group 5) and pure foam (Group 8) or a combi-nation of foam core sandwich (Group 7) and pure grid skeleton(Group 6). From Fig. 2, the peak stress of Group 3 (47.2 MPa), ishigher than the sum of the peak stress of the Group 5 (37.3 MPa)and Group 8 (5.8 MPa), which is 43.1 MPa; similarly, the peakstress of Group 3 (47.2 MPa) is also higher than the sum of the peakstress of Group 6 (25.1 MPa) and Group 7 (13.8 MPa), which is38.9 MPa. Therefore, the composite action between the grid skele-ton and the foam within the bay areas is positive.

3.2. Impact test results and discussion

Typical load and energy traces are shown in Fig. 3 for a Group 2specimen impacted at bay with an impact velocity of 4 m/s and ahammer weight of 40.0 kg. The initiation energy, propagation en-ergy, and peak impact force using a 22.7 kg hammer weight onthe four Groups of specimens (Groups 1–4) are shown in Figs. 4–7 , respectively. The impact test results for Groups 1–4 using avelocity of 4 m/s and a hammer weight of 40.0 kg are shown inFig. 8 (it is noted that for Group 1 the impact was at the centerof the specimen although the legend for impact at bay is used).The error bar in Figs. 4–8 represents the standard deviation ofthe test results.

From Figs. 4–8, the following observations can be made: (1)Groups 2–4 generally have higher initiation energy and lowerpropagation energy as compared with the control Group (Group1), when the impact was at the ribs and nodes. With the highestincident energy level (Fig. 8), the proposed sandwich structures(Groups 2–4) show a higher impact load, higher initiation energy,and lower propagation energy than those of Group 1, except forthe Group 4 impacted at the bay. In particular, the Group 2 showsa consistent improvement over Group 1 in terms of impact re-

Fig. 3. Typical impact force and energy traces.

Impact Velocity (m/s)

2 3 4

Ene

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(J),

Loa

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N)

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Initiation Energy (J)Propagation Energy (J)Maximum Load (kN)

Fig. 4. Impact test results of Group 1 specimens with hammer weight of 22.7 kg.


2 3 4

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180Bay Initiation Energy (J)Bay Propagation Energy (J)Bay Maximum Load (kN)Node Initiation Energy (J)Node Propagation Energy (J)Node Maximum Load (kN)Rib Initiation Energy (J)Rib Propagation Energy (J)Rib Maximum Load (kN)



2 3 4

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Initiation Energy with impact at bayPropagation Energy with impact at bayLoad with impact at bayInitiation Energy with impact at nodePropagation Energy with impact at nodeLoad with impact at nodeInitiation Energy with impact at ribPropagation Energy with impact at ribLoad with impact at rib

Fig. 8. Impact test results of each Group of specimens with an impact velocity of4 m/s and hammer weight of 40.0 kg.


sponse. Therefore, it can be concluded that the proposed sandwichstructure can be designed to perform better than traditional lami-nated composite although almost the same amount of fiber andfoam are used. (2) The effect of the bay area on the impact responseis significant. Basically, Group 2 performed better than Group 3 and4 with few exceptions. This is understandable because the Group 2has the smallest bay or cell area. Compared with Groups 3 and 4,


each cell in Group 2 is more likely to respond to impact quasi-stat-ically because of the short distance between the point of impactand the cell boundary. This leads to higher initiation energy, highermaximum impact force, and lower propagation energy. (3) Simi-larly, the effect of the impact location is obvious. The bay has thelowest initiation energy and highest propagation energy. The nodeis to the opposite of the bay. The response of the rib is usually in-between the node and the bay. This is understandable because thenode has the highest fiber volume fraction and the bay has no anyfiber reinforcement, suggesting that the node has the higheststrength and stiffness and highest capacity to transfer energyelastically.

3.3. Ultrasonic inspection results and discussion

Fig. 9a–d shows typical C-scan images before and immediatelyafter impact when subjected to an impact velocity of 4 m/s andhammer weight of 22.7 kg. Each image represents a scanned areaof 152.4 mm by 152.4 mm. Pulse-echo transmission method wasused to capture the signal and the color of the image changed withthe strength of the signal received by the transducer. The red re-gion depicts the area with foam and the blue region shows thepresence of glass fiber. Red color represents an excess of 80% ofthe signal returning to the receiver, whereas blue color indicatesthat 50–80% of the signal is being received and green color indi-cates that less than 50% of the signal is being received. Therefore,the change of the color indicates a certain type of damage. FromFig. 9, the damage of the Groups 2–4 specimens is localized, whilethe damage in Group 1 is extended to the whole specimen. This canbe further validated by visual observation; see Fig. 10a–c for Group3 specimens subjected to an impact velocity of 4 m/s and hammerweight of 40.0 kg. The reason for the localized damage is that thedamage in Groups 2–4 is difficult to propagate into neighboringbays due to the lattice arrangement of the grid skeleton and theconfinement of the foam in the bay by the grid skeleton. On theother hand, the damage in Group 1, especially delamination, caneasily propagate along the lamina interface to the whole panel.Of course, the nature of the damage is of paramount importance.Fig. 11a shows the damage in a rib which is directly under impact.It is clear that the damage is in micro length-scale, i.e., fiber frac-

Fig. 9. Pre and post-impact C-Scan im

ture and fiber pull-out. Although the rib can also be consideredas a laminated rod, no delamination, which is a typical macro-scopic damage in laminated composite, is found in the rib.Fig. 11b shows the SEM observation of the damage in the foamwithin the bay directly under impact incident. Obviously, themechanism for absorbing impact energy is through micro length-scale damage like microballoon crushing and matrix microcrack-ing. The damage in micro length-scale serves to absorb impact en-ergy without significantly sacrificing residual load carryingcapacity. Therefore, it is expected that the localized damage inGroups 2–4 specimens may lead to a higher residual strength thanthat of the Group 1 specimen.

3.4. Compression after impact (CAI) test results and discussion

The initial and CAI peak stresses for each Group are summarizedin Fig. 12 when they were impacted by a hammer weight of 27.2 kgand impact velocity of 2 m/s, 3 m/s, and 4 m/s, respectively (it isnoted that the impact was at the center for the Group 1 specimensalthough the legends of bay, rib, and node were also used). Whenthe hammer weight was 40.0 kg and the impact velocity was4.0 m/s, the residual peak stress for each Group is shown in Fig. 13.

From Figs. 12 and 13, the following observations can be made:(1) When the impact was at the rib or node, the residual strength ofGroups 2–4 is usually higher than that of Group 1. At the highestincident energy level investigated (Fig. 13), Groups 2–4 consis-tently have a higher residual strength than the control Group(Group 1), regardless of the impact location. (2) The effect of thebay area is significant. The lower the bay area is, the higher thecapacity to retain the load carrying capacity becomes. This is inagreement with the impact test results that grid core with a smal-ler bay area usually has a higher tolerance to impact damage (low-er propagation energy). However, it seems that an optimal bay areaexists. This is because the sandwich with a zero bay area (Group 1)has a lower impact tolerance and lower capacity to retain its loadcarrying capacity than the Group 2 sandwich. (3) The impact loca-tion is crucial. Just like the impact response, the node is the stron-gest in retaining the load carrying capacity, followed by the rib,with the bay the weakest. (4) The propagation energy alone cannotbe used to estimate the residual strength. It must be used along

age for each Group of specimens.

Fig. 10. Visual inspection of impact damage.

Fig. 11. Microscopic damage in (a) rib and (b) foam.

Group No.

1 2 3 4

Pea

k S

tres

s (M

Pa)

0

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40

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Without impactImpact of 2m/s at bayImpact of 2m/s at nodeImpact of 2m/s at ribImpact of 3m/s at bayImpact of 3m/s at nodeImpact of 3m/s at ribImpact of 4m/s at bayImpact of 4m/s at nodeImpact of 4m/s at rib

Fig. 12. Peak CAI stress for each Group after an impact with a hammer weight of27.2 kg.

Group No.

1 2 3 4

Pea

k S

tres

s (M

Pa)

0

5

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15

20

25

Impact on BayImpact on NodeImpact on Rib

Fig. 13. Peak CAI stress for each Group of specimens after impact with a velocity of4 m/s and a hammer weight of 40.0 kg.


with the nature of the damage (micro length-scale or macrolength-scale). Although the propagation energy of Group 4 is high-er than that of Group 1 when the impact is at bay (Fig. 8), the resid-ual strength of Group 4 is still higher than that of Group 1; seeFig. 13. The reason for this is that a good portion of the damagein the syntactic foam in Group 4 is in micro length-scale insteadof macro length-scale such as delamination in Group 1; see Fig. 11.

4. Finite element modeling

Finite element modeling (FEM) of the sandwich structures wasconducted using ANSYS version 11.0 software package. In this

study SOLID45 element was used for 3-D modeling of the solidstructures. In order to closely replicate the actual compression testfixture in the FEM, boundary conditions were specified as: The bot-tom face of the specimen was fully constrained; the three transla-tions along the two sides of the specimen were fixed; and on thetop surface of the specimen a compressive pressure was applied.Convergence analysis was performed to insure accuracy of the re-sults obtained from FEM. A converged mesh size, 3 mm, was usedthroughout the modeling.

Using the material properties from coupon tests, the compres-sive stress–strain curves of each Group from both FEM and testingare shown in Fig. 14. It is clear that the linear elastic FEM results

Strain (mm/mm)

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Str

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Group 1 (Test)Group 2 (Test)Group 3 (Test)Group 4 (Test)Group 4 (FEM)Group 3 (FEM) Group 2 (FEM)Group 1 (FEM)

Fig. 14. Comparison of test results with FEM.


are very close to the test results for Groups 1, 3, and 4. For Group 2,there is a considerable deviation between the modeling and thetest results. The FEM overestimates the stiffness (slope of thestress–strain curve) of the Group 2 specimens. A possible reasonis that the ribs in Group 2 are very thin (1.2 mm), leading to an as-pect ratio for each rib about 12.7 mm/1.2 mm = 10.6. Although theribs are laterally supported by the syntactic foam, which simulatesan elastic foundation, it cannot be avoided that higher mode localbuckling of the ribs may be possible for such slender ribs. As a re-sult, the stiffness and strength of the Group 2 are lower than thoseof linear elastic analysis. In order to consider the possible localbuckling of the slender ribs, a large deformation non-linear buck-ling analysis is needed.

5. Conclusions

Based on the testing and modeling of the novel sandwich struc-tures, the following conclusions are obtained:

� A new type of integrated sandwich structure with an orthogridstiffened syntactic foam core was proposed, fabricated, tested,and modeled.

� With almost the same amount of fiber and foam, the proposedsandwich structure usually has a higher initiation energy, lowerpropagation energy, and higher CAI strength than the tradi-tional laminated composites, regardless of the impact location.This tendency becomes more pronounced as the incidentenergy increases.

� The better performance of the proposed sandwich structure interms of impact response and CAI strength lies in the positivecomposite action between the grid skeleton and the foam, thesmall cell size which leads each bay towards a quasi-staticimpact response, and the localized and micro length-scaledamage.

� The impact resistance changes spatially. The node is the stron-gest in impact resistance, followed by the rib; the bay is theweakest in resisting impact.

� The bay area has a significant effect on the impact response andresidual strength. For the three groups of sandwiches studied,Group 2, i.e., the Group with the smallest bay area, has the bestperformance.

� The linear elastic analysis using ANSYS agrees well with thetest results for Groups 3 and 4. A considerable deviationoccurs for Group 2 due to the possible higher mode localbuckling of the slender ribs in this Group. A large deformationnon-linear analysis is needed for modeling this type of sand-wich structures.

Acknowledgement

This study is based upon work supported by the US Army Re-search Office under Grant number W911NF-05-1-0510 and byNASA/EPSCoR under Grant number (NASA/LEQSF (2007-10)-Phase3-01. Useful discussion with Dr. J.Q. Cheng at Louisiana StateUniversity is also acknowledged.

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