CHARACTERIZATION OF DROP-STITCH CONSTITUENT MATERIALS AND INFLATED PANEL RESPONSE

Drop-stitch inflatable structures are of increasing significance in aerospace, naval, and military applications. The advantages of dropstitch inflatable structures are high strength to weight ratios, rapid deployment capabilities and ease of storage. The sti↵ness of the structure increases with inflation pressure and is dependent on the material properties of the panel skin. The objective of this research was to characterize the constituent material properties and mechanical response of drop-stitch inflatable panels subjected to various load conditions. This research aimed to characterize the nonlinear elastic response of drop-stitch inflatable panels by using a new material system in comparison to previous studies. These characterizations included three dimensional digital image correlation, uniaxial and biaxial loading, and panel inflation and bending experiments. Material properties of the drop-stitch inflatable panel skin were experimentally determined across multiple experiments utilizing three dimensional-digital image correlation. In addition, three dimensional digital image correlation was used to characterize panel skin surface displacements and strains in a way not done before in previous drop-stitch structure research. The results of this research found that relevant material properties of the dropstitch inflatable panel were able to be experimentally determined through multiple di↵erent experiments, however these material property values are extremely sensitive to load conditions. Further research is required to accurately predict the structural behavior from constituent characterization data.


Drop-stitch inflatable structures
Drop-stitch technology has an advantage to traditional air-inflated structures

Drop-stitch inflatable structure applications
As stated previously, drop-stitch technology can be found in a variety of fields such as aero-space, military, commercial and marine to name a few. Figure 3: Navatek Inflatable Boat Ramp [3] Pictured above in Figure 3 is an inflatable boat ramp from Navatek LLC, a company that specializes in drop-stitch inflatable structures. This example is used in a marine application to assist in retrieval when out at sea. When inflated, the ramp can be dropped down o↵ the edge of a vehicle to act as a bridge between the water and vehicle, and when deflated, can be easily pulled back and stored in the vehicle. Figure 4: Sierra Nevada Corporation Inflatable Space Habitat [4] Pictured above in Figure 4 is an inflatable space habitat prototype that the Sierra Nevada Corporation fabricated as a prototype for NASA in 2019. The large scale drop-stitch inflatable habitat is compact enough to fit inside an 18-foot rocket fairing but then able to expand to 27 feet in diameter and 27 feet long when deployed and inflated by astronauts in space to use.

Motivation
The challenge in accurately predicting the behaviour of inflatable drop-stitch fabric structures has been due to the complex loading arrangement due to the panels being internally pressurized with air. The panel skin properties in the axial and transverse directions also prove challenging to determine. In a study of air inflated drop-stitch panels being subjected to bending loads it was determined in addition to overall panel sti↵ness, the panel skin properties in the axial and transverse directions also have an apparent dependence on inflation pressure [11] Using classical beam theory is the most simple approach to predict the behaviour of a drop-stitch inflatable structure under a four-point loading configuration. Classical beam theory assumes that the cross-sections of the beam remain planar and normal to the mid plane. Classical beam theory also assumes that there is no shear component to the deformation [12].
Air-inflated structures sti↵en with increasing pressure and are sensitive to changes in volume produced by transverse shearing deformations of their cross sections. Because classical beam theory requires that plane sections remain planar and normal to the mid plane it neglects transverse shearing deformations. Because of this shear deformable beam theory provides an alternative representation of panel behaviour [11]. For long, slender beams, the shear deformation is very small and can be neglected.
Pressure dependent skin properties are typically determined through correlation with inflated panel bending data. In previous research these skin properties have been experimentally determined through stress vs strain curves from uniaxial or biaxial testing machines. This research aims to utilize three dimensional digital image correlation to characterize the material properties under biaxial load conditions designed to simulate stresses induced during bending of inflated drop-stitch panels.

Objective of research
The primary objective of this research is to characterize the constituent mate- and four-point bend tests. In addition to these tests, skin samples were taken from this panel to conduct uniaxial and biaxial skin material tensile testing. All testing utilized three dimensional digital image correlation to provide displacement and strain field data for analysis.

Thesis overview
The purpose of this thesis is to analyze the response of the assumed orthotropic panel skin material and its constituent components utilizing three-dimensional digital image correlation characterizations of uniaxial and biaxial tensile testing, inflation testing and four-point bend testing.
Chapter 2 will review published literature and previous work done on modeling air-inflated structures and their constituent materials.
Chapter 3 will explain the theory behind this research. This chapter will discuss digital image correlation, mechanics of laminated composites, skin stresses due to inflation and four-point bending. In addition, chapter three will also discuss the preparation, setup and execution of the experiments performed in this research.
Chapter 4 will present the results from the experiments performed in chapter 3 utilizing the theoretical methods and equations also presented earlier in chapter 3. These results will consist of material property calculations in addition to three dimension displacement and strain fields of tensile testing, inflation testing, and four point bend testing of the new material system.
Chapter 5 provides a summary and discussion of the findings from this research, as well as a discussion of the potential topics for future research and experimentation.

CHAPTER 2
Literature review

Inflatable structures
A general understanding of the inflation and loading mechanics of inflatable structures is described in technical reports titled "Air-Inflated Fabric Structures"   [1] and "Technology and Mechanics Overview of Air-Inflated Fabric Structures"   [13]. Both emphasize that the sti↵ness of the structure is largely dependent on the inflation pressure. As the inflation pressure increases, the skin and fabric layers become stressed and in turn, sti↵en the structure. Once external loads are applied to the inflated structure, these loads superpose stress with the inflation stresses already present.
This superposition causes a redistribution of stress along the inflated structure. The redistribution of stress is a natural mechanical response of the structure to balance the load being applied and maintain it's state of static equilibrium.
Depending on inflatable structure geometry and loading configuration, the redistribution of stresses can either increase or decrease the tension in the structure skin. If the stresses from the applied external load(s) su ciently reduce inflation induced stresses, meaning the tension in the skin approaches zero, the onset of wrinkling is expected to occur within the structure. Wrinkling decreases the structure's load carrying capability and leads to a loss in overall sti↵nes and eventually collapse of the structure.
In order to better model di↵erent inflatable structure geometries and various   To provide material property inputs to the finite element analysis model, uniaxial and biaxial tensile tests were conducted to experimentally determine the elastic modulus in the longitudinal (axial) direction of the air beam and also the shear modulus of the skin material. The findings of this study from comparisons of experimental and simulated four-point bend tests were that the structure's volume change will be larger at higher inflation pressures because the beam is sti↵er at higher pressures and will require a larger load to deflect the beam. This higher external load creates larger shearing forces in the beam. Furthermore, this research found that air compressibility causes a nonlinear sti↵ening e↵ect in the bending behavior of inflatable structures. As the air volume decreases due to deformations from external loads causing transverse shearing, wrinkling, and section collapse, the internal air pressure will increase. If air compressibility is appreciable, a gas law was suggested to be incorporated in the bending analysis.

Inflatable panel beam models
Although classical beam theory is one of the most simple methods of modeling the behaviour of drop-stitch inflatable panels, the results of "Bending Tests of Inflatable Drop-stitch Panels" (Falls and Waters, 2011) [15] suggest that shear deformation in these inflated structures is present during bending. The accuracy of the model was tested for panels between 250mm and 1000mm (  A secondary aim was to validate assumptions and analytical theories that were derived in previous research [16].  In order for the software to e ciently correlate points during the image series of the deformation, the test specimen must be prepared with a random patterning of ideally contrasting regions to it's surface. An initial reference photo of the the patterned surface of the test object prior to external loading and deformation is captured and the software applies a gray scale numerical value to each pixel in the field of view of this reference photo in order to correlate points between the following deformed photos. The DIC software groups these gray scale valued pixels into facets to form a virtual grid on the test object surface as shown below in figure 8. The correlation to follow pixels between the reference and deformed photos is then performed by looking for facets with corresponding gray scale value arrangements as shown in 9. Lastly, by using a correlation algorithm to track the displacement of facets on the surface of the test object as it deforms in the image sequence due to loading, the DIC software generates displacement and strain fields which can then be used for further data analysis.
This research was interested in capturing potential out of plane deformations, so three-dimensional digital image correlation utilizing two cameras was performed.
In contrast to two-dimensional digital image correlation, three-dimensional digital image correlation can track non planer movements in relation to the cameras. This is due to the pattern being viewed by both cameras and triangulating the position of the facets in a virtual three dimensional coordinate system. Figure 10: Three dimensional digital image correlation using two cameras [7] This requires a calibration process of the camera setup to inform the DIC software where the cameras are in relation to one another in this virtual space. The digital image correlation software, camera setups and calibration process specific to the testing performed in the research will be discussed in detail later in the chapter in section 3.2.

Mechanics of laminated composites
The testing performed in this research was designed based on the assumption that the skin material of the drop-stitch panel was an orthotropic continuous fiber-reinforced laminate. Assumed characteristics of continuous fiber reinforced laminates are [17]: 1. The material is constructed of one or more layers, each comprised of fibers that are all uniformly parallel and continuous across the material.
2. The material is in a state of plane stress, i-e., the stresses and strains in the through-the-thickness direction are ignored.
3. The thickness is much smaller than the length and width of the laminate.
A material is considered to be isotropic when it has identical property values in all directions. A material is considered to be orthotropic when material properties exhibit three mutually-orthogonal symmetry planes. Orthotropic materials are a subset of anisotropic materials, a group of materials whose material properties change when measured from di↵erent directions [12].
It's assumed for the drop-stitch inflatable structure tested in this research that the panel skin is orthotropic, having di↵erent material properties in the warp (axial) and weft (transverse) directions.
Hooke's law for an isotropic material under plane stress load conditions is given by where and ✏ are taken to be the stress and strain in the load direction. For an orthotropic material under uniaxial loading in the warp or weft directions, the stress strain relations are given by The warp (axial) direction will be notated with a subscript 1 while the weft (transverse) direction will be notated with a subscript 2, reducing equation 3 to Strains in the axial and transverse directions are related through Poisson's ratio.
Poisson's ratio associated with lateral contraction in the weft direction due to loading in the warp direction is given by while Poisson's ratio associated with lateral contraction in the warp direction due to loading in the weft direction is given by The strains in the axial and transverse directions can now be related and written as the strain in the direction of an applied force minus the contraction of Poisson's e↵ect.
Substituting equations 4 into equations 7 yields Equation 8 can be rearranged to solve for axial and transverse moduli, giving the result and Equating equations 9 and 10 gives equation 11.
Rearranging equation 11 gives expressions for the elastic modulus of an orthotropic laminated composite in the warp (axial) and weft (transerse) directions. were recorded by the load frame and later converted to stresses 1 and 2 , strains ✏ 1 and ✏ 2 were measured from digital image correlation, and the Poisson's ratios ⌫ 12 and ⌫ 21 were calculated from uniaxial testing using equations 5 and 6.
Shear stresses and strains are related by an in-plane shear modulus, G 12 through the relation ASTM 3518 [8] which was adopted from the work of Rosen [18] previously, describes a method of determining the shear modulus of a composite through uniaxial tensile testing of a 45 o↵set sample. The sample described is shown in Figure 11. tively. Under these load conditions, the shear modulus associated shear parallel to the fiber directions can be shown to be given by where the constants given by S are: Inverting the compliance matrix gives stress as a function of strain as shown in equation 17.
where the constants given by Q are:

Inflation stress
Using the same approach as Alich [6], thin pressure vessel theory can be applied to drop-stitch inflatable panels to calculate the stresses in the panel's skin due to inflation. By considering equilibrium between the inflation pressure and the stresses in the panel skin leads to the relation Equation 20 states the product of internal inflation pressure multiplied by the cross sectional area of the internal cavity of the panel must equal the stress in the panel skin multiplied by the cross sectional area of the panel skin. Figure 12 shows the axial and transverse areas and applicable dimensions.

Four-point bending
The reason four point bending is the preferred loading configuration for testing inflatable drop-stitch panels is because four-point bending generates a region at the mid span of the panel of pure bending and no shear transverse stress which occurs locally under the loading pins. This is shown in the shear and moment diagrams of a conventional structure in figure 13 [11]. The panel skin is pre-tensioned due to inflation, and these stresses superpose with bending stresses as the panel deflects [6]. This is shown in the bending stress diagram in figure 14. According to Roylance [19], if the relation between the applied load and the deflection of a beam bending experiment is known, it's possible to determine elastic modulus from the measurement. A sti↵ness measured this way is called the flexural modulus.

For a beam under a symmetrical four-point bending load, the deflection any-
where along the span of the beam is given by equation 24 ...
where x is the position along the span of the beam, F is the total applied load, L is the distance between supports, a is the distance from the support to the load, E is the flexural modulus in the axial direction and I is the moment of inertia.
Using a similar approach to Smith [16], the moment of inertia of the axial cross-sectional area of the drop-stitch inflatable panel used in this research can be calculated using the parallel axis theorem. Figure The moment of inertia of the top/bottom rectangle is given by equation 26 which is the approximated moment of inertia of the panel cross section.
Knowing that the maximum experimental deflection of the drop-stitch inflatable panel was 3 inches, equation 24 can be used with the corresponding total applied load measured by the test frame load cell to determine apparent material property values from the four-point bending tests.

Experimental preparation and setup 3.2.1 Drop-stitch inflatable panel build
As stated previously, this research aims to characterize the nonlinear elastic response of drop-stitch panels by using a new material system in comparison to previous studies. These experiments evaluated a commercial PVC panel as show in Figure 16.   Table 1 summarizes the panel's build characteristics with common textile industry measurements of drop-stitch inflatable structures.

Digital image correlation
In order to utilize three dimensional DIC to analyze experimental loading of the drop-stitch panel and it's constituent materials, the surfaces of these test samples needed to be prepared with proper patterning for accurate facet tracking through a series of images. In order to achieve maximum contrast between the outer PVC skin layer of the panel and the pattern, a white base coat was applied using spray paint as shown below in Figure 21.   The size of these speckles was produced by holding the spray paint nozzle partially down and sputtering the spray paint as opposed to the normal mist produced when the nozzle is held fully down.

Figure 23: Panel four-point bend test speckle pattern
An identical speckling process to that described for the drop-stitch panel was used to prepare the other test samples of this research for digital image correlation. Figure 24 shows both uniaxial and biaxial tensile testing samples prepared for digital image correlation. Notice that the speckle pattern on these samples are much finer than that of the panel shown previously. This is because the field of view for tensile testing was much smaller and closer compared to that of four point bend testing the drop-stitch panel. In order to still achieve three to five speckles in a single facet this fine speckle pattern was applied by misting the black spray paint over the white base coat.  Once the surfaces were prepared, the cameras were setup in order to achieve the desired field of view for each test. It was key to make sure the the measuring volume was also lit using external light sources to aid in the contrast between the base coat and pattern. The focus and aperture settings of the cameras were then adjusted appropriately.

Uniaxial tensile testing
In previous research performed by Cavallaro [11] and Smith [16], uniaxial ten-   The x direction was always taken to be the width of the sample, the y direction was always taken to be the length of sample and the z direction was then defined normal to the surface of the sample. Table 2 shows the directional notation used for the uniaxial tensile testing. Axialf ibers T ransversef ibers The 45 o↵set sample followed the same coordinate system orientation as the axial and transverse samples having the x axis be the width of the sample, the y axis be the length and the z axis be out of plane however both the x and y axis contained 45 o↵set fibers from the axial and transverse directions, in addition to the z axis still being out of plane.

Biaxial tensile testing
Previous research has indicated that uniaxial testing isn't su cient to characterize the drop-stitch panel skin material properties. Ideally biaxial tensile testing should be performed with a ratio of biaxial tension stresses matching the ratio of biaxial tension stresses produced in the actual structure from inflation. This ratio is given by equation 29 [11]. Table 3 shows the biaxial inflation stresses and corresponding biaxial stress ratio for the drop-stitch panel used in this research.

Inflation testing
In addition to replicating the biaxial inflation stresses in the drop-stitch panel skin using a biaxial load frame, a digital image correlation analysis of a panel inflation was performed on a local region of the panel skin. Figure 34 shows the placement of the local region on the drop-stitch panel.

Figure 34: Inflation testing local region
The panel was inflated incrementally from 0.5 psi to 15 psi in 0.5 psi increments. As shown in figure 35, the x axis was defined to be the transverse direction of the panel, the y axis was defined to be the axial direction of the panel and the z axis was defined to be normal to the panel.            Table 4 gives the elastic moduli of the panel skin. These moduli are the initial slopes of the uniaxial stress strain curves in figure 47.
Previous research has indicated that uniaxial tensile tests are not su cient to to fully characterize the behaviour of the drop-stitch inflatable panel skin. Since inflated panel skins are subjected to biaxial loading, it is expected that biaxial tensile tests are expected to provide an improved simulation of in-service load conditions. Figure 47 shows the uniaxial response for loading in the warp and weft directions and will be used for comparison purposes later in the chapter.
Uniaxial tensile testing also provides a measure of Poisson's ratio. Figure 48 shows the DIC measured negative transverse strains plotted against axial strains measured during uniaxial tension in the warp direction, and Figure 49 shows the DIC measured negative transverse strains plotted against axial strains measured during uniaxial tension in the weft direction. The slopes of these curves can be interpreted as the Poisson ratio's ⌫ 12 and ⌫ 21 , respectively, and are tabulated in Table 5.                  Table 9 gives the sti↵ness values of the above four-point bending tests and the measured load at the maximum programmed 3 inch deflection.      Table 9 gives the sti↵ness values of the above four-point bending tests and the measured load at the maximum programmed 3 inch deflection.    can be used with the loading configuration dimensions given in figure 36 to solve for an e↵ective axial elastic modulus under four-point bending. Table 10 gives the calculated modulus values at the tested inflation pressures.

Conclusions
The results presented in this study illustrate that the material properties of the drop-stitch inflatable panel skin are more complicated than traditional struc-

Recommendations for future research
Modeling drop-stitch inflatable structures is a very complex topic due to their unique nature. In addition to providing characterizations not seen before in inflatable drop-stitch structure research utilizing three-dimensional digital image correlation, this research also highlighted areas of focus for future work.