Due to its complex phase transformation behavior, a Shape Memory Polymer filled honeycomb composite has been proposed as an efficient material for skin on a morphing wing. This work develops a finite element model of the honeycomb composite that captures the material behavior while morphing through all geometric phases. To model the shape memory polymer filling, the simulation implements an experimentally calibrated user defined material subroutine in Abaqus, a commercially available finite element software. In order to validate the model, the modeled behavior is compared to experimentally determined behavior of shape memory polymers. The geometry and deformations of representative unit cells are then discussed

Russey, Brookelynn Gay

Texas A&M University

 MODELING SHAPE MEMORY POLYMER FILLED HONEYCOMB AS A 
COMPOSITE SKIN FOR A MORPHING WING 
 
 
An Undergraduate Research Scholars Thesis 
by 
BROOKELYNN RUSSEY 
 
 
Submitted to Honors and Undergraduate Research 
Texas A&M University 
in partial fulfillment of the requirements for the designation as an 
 
 
UNDERGRADUATE RESEARCH SCHOLAR 
 
 
Approved by 
Research Advisor:                   Dr. Dimitris Lagoudas 
 
 
May 2014 
 
 
Major: Aerospace Engineering  
  
TABLE OF CONTENTS 
Page 
ABSTRACT .................................................................................................................................... 1 
ACKNOWLEDGEMENTS ............................................................................................................ 2 
NOMENCLATURE ....................................................................................................................... 3 
CHAPTER 
 I             INTRODUCTION ................................................................................................. 4 
 II           METHODS............................................................................................................. 7 
Materials ................................................................................................................ 7 
Modeling Methods............................................................................................... 10 
           III          RESULTS ............................................................................................................ 14 
           IV          CONCLUSIONS ................................................................................................. 16 
REFERENCES ............................................................................................................................. 18 
 
1 
 
ABSTRACT 
Modeling Shape Memory Polymer Filled Honeycomb as a Composite Skin for a Morphing 
Wing. (May 2014) 
 
Brookelynn Russey 
Department of Aerospace Engineering 
Texas A&M University  
 
Research Advisor: Dr. Dimitris Lagoudas 
Department of Aerospace Engineering 
 
Due to its complex phase transformation behavior, a Shape Memory Polymer filled honeycomb 
composite has been proposed as an efficient material for skin on a morphing wing. This work 
develops a finite element model of the honeycomb composite that captures the material behavior 
while morphing through all geometric phases. To model the shape memory polymer filling, the 
simulation implements an experimentally calibrated user defined material subroutine in Abaqus, 
a commercially available finite element software. In order to validate the model, the modeled 
behavior is compared to experimentally determined behavior of shape memory polymers. The 
geometry and deformations of representative unit cells are then discussed.  
  
2 
 
ACKNOWLEDGEMENTS 
 
I would first like to thank the Shape Memory Alloy Research Team (SMART) under Dr. 
Dimitris Lagoudas for use of their resources and guidance. I would also like to thank the 
UMAT’s developer Dr. Brent Volk for teaching me to use it during previous research 
assistantships under the UMAT’s creator, Dr. Brent Volk. Finally, I would like to thank 
University of Dayton Research Institute and the Air Force Research Laboratory for collaborating 
to create a working model of the honeycomb structure.  
  
3 
 
NOMENCLATURE 
 
SMP    Shape Memory Polymer 
AFRL    Air Force Research Laboratory 
UMAT   User material subroutine  
2D    Two Dimensional  
3D    Three Dimensional  
GUI    Graphical user interface 
  
4 
 
CHAPTER I 
INTRODUCTION 
 
Morphing wings have recently been a focus in the aerospace industry because of their ability to 
obtain more efficient configurations for different mission profiles. Although the graceful flight of 
birds has inspired flight for centuries, the complex and fluid motion of bird wings are difficult to 
model and reproduce mechanically. However, recent discoveries of advanced materials and 
actuators and the increased capacity of computer models have allowed researchers to reconsider 
mimicking bird flight mechanics for small aircraft. A bird’s wing efficiently provides lift by 
changing shape in different stages of flight. Geometry factors such as twist, cross-section 
camber, and sweep are different for take-off, gliding, and landing. Modern aircraft already use 
geometry variation to increase efficiency for different mission profiles, but not to the degree of 
that bird flight utilizes [1]. Mechanical actuators can be heavy. Movement of heavy aircraft 
requires more fuel, so designers must conduct trade-off studies to determine maximum 
efficiency. However, if the geometry can be altered without heavy mechanical actuators, 
designers can use a larger range of geometry variations. Recently developed “smart” materials 
can change shape without mechanical actuations. Stimuli such as temperature change, magnetic 
field, and electricity alter the materials at a microstructural level.  
 
 The skin on the morphing wing must satisfy two constraints: the in-plane stiffness must be low 
enough to easily manipulate the shape of the skin and the out-of-plane stiffness must be high 
enough to avoid deformation due to aerodynamic loads. While smart materials can satisfy the 
first constraint, they cannot satisfy the second without sacrificing morphing capabilities. One 
5 
 
solution proposed involves the use of a honeycomb configuration. The honeycomb provides high 
stiffness along the plane of the honeycomb wall, while the filling material defines the in-plane 
stiffness [2]. 
 
Shape memory polymers (SMP), the proposed smart material filler, cure into an initial shape 
called the parent configuration. While the temperature of the SMP is above its glass transition 
temperature, the SMP is in the rubbery phase. The material properties of the SMP in the rubbery 
phase include a high elastic modulus and low stiffness, and the SMP can be easily manipulated 
into a secondary shape. If the SMP is held in the secondary shape while being cooled to below 
the glass transition temperature, the secondary shape can be maintained without applied force. 
The SMP then has a new set of material properties that include a low elastic modulus and high 
stiffness in a second state called the glassy phase. Upon reheating to above the glass transition 
temperature, the SMP returns to the rubbery phase and the parent configuration. This cycle, 
shown in Figure 1, can be repeated numerous times with different secondary shapes, allowing 
wing configurations for several mission profiles [3, 4, 5] . 
 
Figure 1: Phases of the shape memory cycle  
 
Initial Shape – 
rubbery phase 
Deform – rubbery 
phase 
Cool to glassy 
phase then 
remove loads 
Reheat to rubbery 
phase to retrieve 
the initial shape 
6 
 
Modeling the honeycomb composite requires understanding of the material in three phases: the 
rubbery phase, the glassy phase, and the transition phase between the two. During the transition 
phase, the material properties vary non-linearly with the temperature change. While models of 
the composite have been created for the rubbery phase and the glassy phase, few models attempt 
to incorporate the transition phase [6]. To fully model and optimize a morphing skin, all phases 
must be incorporated and analyzed.  
 
A finite element model of all three phases is possible with the experimentally calibrated user 
material subroutine (UMAT) described in Volk et al. When the UMAT is implemented in 
Abaqus, a commercially available finite element software, a simulation of an SMP structure in 
the transition phase from glassy to rubbery can be produced. 
 
Initially, the finite element model first included a single unit cell of the honeycomb structure to 
determine the computation requirements for a simple structure. Once the simple unit cell model 
is functional, a multi-cell skin will be modeled. Select cells will be heated and cooled through a 
phase cycle to morph the shape of the skin. Simulation results will be compared to experimental 
results. After the model is validated by experimental results, the skin will be optimized for a 
given wing configuration. 
 
  
7 
 
CHAPTER II 
METHODS 
2.1 Materials 
 
2.1.1 Shape Memory Polymer  
 
The shape memory polymer used for this study is a thermally crosslinked polyurethane. The 
polymer, as adapted from [7], is composed of the monomers 1,6-hexamethylene diisocyanate 
(HDI), N,N,N0,N0-tetrakis(2-hydroxypropy)ethylenediamine (HPED), and triethanolamine 
(TEA) [10]. This material is used, because it’s highly crosslinked microstructure supports large 
deformation recoveries of 400% with enough strength to manipulate the aluminum honeycomb 
walls. The material has also been used in several demonstrations of applications of the SMP 
UMAT with Abaqus, and the computation methods in the UMAT were optimized using this 
material. A list of the material properties used for the model is seen in  The subscripts r and g 
denotes a property present only in the glass or rubbery phase. The Shear modulus, Lamé 
constant, and coefficient of thermal expansion are G, λ, and α respectively. The final eight 
material properties represent the recovery behavior of the SMP from the deformed glassy phase 
to the parent rubbery phase. The temperatures at the beginning and end of the transformation 
phase are θmin and θmax. The variable A is the temperature at the inflection point and is also called 
the glass transition temperature. The scaling factor B is shown in  
 
 ( )  
    (
      
 
)     (
   
 
) 
    (
      
 
)     (
      
 
)
                                         Eq. 1 
8 
 
where ϕ is the glassy volume fraction as a measure of temperature. The glassy volume fraction is 
a measure of a fraction of the glassy phase scaled to 1. A visual of this relationship is seen in 
Figure 2. For this SMP the recovery behavior, a perfect hyperbolic tangent curve does not 
represent the behavior as well as a combination of two hyperbolic tangent curves. NormFact 
scales the first curve, and θswitch is the temperature at which the first curve transfers to the second 
curve. The variables A2 and B2 are the inflection point and the scaling factor for the second curve 
[3,4,5].  
 
Table 1. The subscripts r and g denotes a property present only in the glass or rubbery phase. The 
Shear modulus, Lamé constant, and coefficient of thermal expansion are G, λ, and α respectively. 
The final eight material properties represent the recovery behavior of the SMP from the 
deformed glassy phase to the parent rubbery phase. The temperatures at the beginning and end of 
the transformation phase are θmin and θmax. The variable A is the temperature at the inflection 
point and is also called the glass transition temperature. The scaling factor B is shown in  
 
 ( )  
    (
      
 
)     (
   
 
) 
    (
      
 
)     (
      
 
)
                                         Eq. 1 
where ϕ is the glassy volume fraction as a measure of temperature. The glassy volume fraction is 
a measure of a fraction of the glassy phase scaled to 1. A visual of this relationship is seen in 
Figure 2. For this SMP the recovery behavior, a perfect hyperbolic tangent curve does not 
represent the behavior as well as a combination of two hyperbolic tangent curves. NormFact 
scales the first curve, and θswitch is the temperature at which the first curve transfers to the second 
9 
 
curve. The variables A2 and B2 are the inflection point and the scaling factor for the second curve 
[3,4,5].  
 
Table 1: Material Properties of the SMP entered into the UMAT 
Property  
Gr (MPa) 8.5 
λr (MPa) 4200 
αr (°C
-1
) 2.1E-04 
Gg (MPa) 650 
λg (MPa) 2600 
αg (°C
-1
) 7.8E-05 
θmin (K) 320 
θmax (K) 360 
A (K) 350 
B 3.1 
NormFact 0.93 
θswitch (K) 340 
A2 (K) 510 
B2 18 
 
 
 
Figure 2: The transition phase as described by the glassy volume fraction. Θmin and Θmax denote the initial and 
final temperatures, respectively, of the transition between the glassy and rubbery phase. The glassy volume 
fraction is a measure of the fraction of glassy phase present out of 1.  
10 
 
 
2.1.2 Aluminum 
 
The honeycomb walls in the model are composed of aluminum alloy 3003 and were constructed 
to mimic the honeycomb structure as purchasable from McMaster-Carr. In the model, the elastic 
modulus is 210 GPa and the Poisson’s ratio is 0.33 [2].   
 
 
Figure 3: Empty aluminum honeycomb compressed in-plane. 
2.2 Modeling Methods 
 
The material properties are inserted into Abaqus to be used as parameters in a user material 
subroutine (UMAT). The UMAT overrides the simple finite element models for elastic materials 
and replaces it with a user defined model of the material’s behavior. Abaqus is a commercially 
available finite element software with a graphic user interface (GUI). The interface was used to 
create unit cell models to determine appropriate geometry and strain limitations for individual 
cells. The unit cell models are split into three different types: SMP only, SMP/aluminum 
composite, and SMP/aluminum composite with periodic boundary conditions.  
11 
 
 
The SMP only unit cell models the only the hexagonal shape of the SMP filling.  A boundary 
condition is applied to the bottom face that restricts displacement in all directions, and a shear 
load is applied to the top surface in the x-direction as shown in Figure 4. The SMP/aluminum 
composite had similar boundary conditions and loading. The geometry is shown in Figure 5. The 
final unit cell model is a 1 element thick 3D model of a representative unit of the honeycomb 
structure. Periodic boundary conditions are then applied to represent the interactions from the 
neighboring cells. The mesh of elements was created by cutting the unit cell into simple 
geometries to use the structured meshing module. Structured meshing reduces computation costs 
of the model.  A screenshot of the Abaqus GUI is shown in Figure 6 with the elements of the unit 
cell model visible. The unit cell split into simple geometry is shown in Figure 7.  
\ 
 
Figure 4: SMP unit cell with shearing load 
Initial Shape  Deformed  
Shearing Load 
12 
 
 
Figure 5: SMP/aluminum composite unit cell 
 
 
Figure 6: Abaqus GUI with unit cell model. 
 
13 
 
 
Figure 7: The unit cell split into simple geometries to create a mesh.  
  
14 
 
CHAPTER III 
RESULTS 
 
A successful simulation of the shape memory effect was accomplished with the model of the 
SMP only unit cell. The stress gradient at the end of each step is shown in Figure 8. The 
geometric deformation was reduced until the simulation converged, however the simulation took 
3 days of computation time to complete. All deformation is recovered upon reheating, but 
residual stress is still present after fully reheating to the initial shape in the rubbery phase. 
Deformations in compression were also attempted, but the crosslinked microstructure of the 
SMP resists this type of deformation during the cooling phase. 
 
 
Figure 8: Successfully modeled shape memory cycle of the SMP only unit cell 
 
The model of the SMP/aluminum composite unit cell shown in Figure 5 can only produce 
simulations for limited deformations as well. The aluminum further restricts recoverable strain 
by requiring the recovery force of the reheated SMP to overcome any plastic deformation in the 
aluminum. Since the elastic modulus of the aluminum is 5 orders of magnitude greater than that 
of the SMP in the rubbery phase and 3 orders of magnitude greater than that of the SMP in the 
High Stress Low Stress 
Initial Shape  Deformed  Cooled  Load Removed  Reheated 
Shearing Load 
15 
 
glassy phase, a very thin aluminum honeycomb wall was selected. The final configuration has an 
aluminum wall that is 3 orders of magnitude thinner than the SMP honeycomb. This allows for 
slight deformations in the wall without preventing full recovery of the SMP upon reheating. The 
periodic boundary conditions were originally written for elements incompatible with the SMP 
UMAT. A new compatible version is currently in progress.    
16 
 
CHAPTER IV 
CONCLUSIONS 
 
The SMP unit cell results show a modeling limitation that does not exist physically. It is shown 
experimentally that an SMP can deform up to 400% and fully recover this deformation upon 
reheating. However, the SMP only unit cell could only deform up to 10% in the simulation and 
required 3 days to converge. The simulation is computationally expensive; however modern 
parallelization methods could improve performance. The language in which the UMAT is 
written Fortran is an older language that is less compatible with modern parallelization methods, 
but further improvements can be made. Further modeling  of SMP composites is very limited by 
the high computation time and may not be very useful for complex models at the UMAT’s 
current state.  
 
The geometry and possible deformations of a unit cell is limited in several ways. Deformations 
in compression would be limited to a fraction of the deformations in tension and shear. The 
aluminum walls must be at least 3 orders of magnitude thinner than the SMP filling to avoid 
unrecoverable plastic deformation in the aluminum. Plane strain problems involving 1 element 
thick models have shown to produce greater deformations than thicker models. Currently, 
simulations with thinner unit cells and greater deformations are being attempted.  
 
In order to use the SMP UMAT, the recovery behavior must be observed experimentally and a 
hyperbolic tangent function must be fit to the experimental data. Currently, this process has only 
17 
 
been completed for a few types of SMP. To ensure proper material selection, more types of SMP 
should be explored and modeled for an optimized design.    
18 
 
REFERENCES  
[1]  J. Valasek, Morphing Aerospace Vehicles and Structures, 2nd ed., Chichester, England: 
hovoken: John Wiley & Sons, 2012.  
 
[2]  R. V. Beblo, J. P. Puttman, N. E. DeLeon, J. J. Joo and G. W. Reich, "SMP Filled 
Honeycomb as a Reconfigurable Skin: Model and Experimental Validation," in The 
International Conference on Composite Materials, Montreal, 2013.  
 
[3]  B. Volk, D. Lagoudas and Y.-C. Chen, "Analysis of the finite deformation response of shape 
memory polymers: II. 1D calibration and numerical implementation of a finite deformation, 
thermoelastic model," Smart Materials and Structures, vol. 19, no. 7, 2010.  
 
[4]  B. Volk, D. Lagoudas, Y.-C. Chen and K. Whitley, "Analysis of the finite deformation 
response of shape memory polymers: I. Thermomechanical characterization," Smart 
Materials and Structures, vol. 19, no. 7, 2010.  
 
[5]  B. Volk, D. Lagoudas and D. Maitland, "Characterizing and modeling the free recovery and 
constrained recovery behavior of a polyurethane shape memory polymer," Smart Materials 
and Structures, vol. 20, no. 9, 2011.  
 
[6]  J. Puttman, R. Beblo, J. Joo, B. Smyers and G. Reich, "Design of a Morphing Skin by 
Optimizing a Honeycomb Structure with a Two-phase Material Infill," in Smart Materials, 
Adaptive Structures, and Intelligent Systems, Stone Mountain, 2012.  
 
[7] T. S. Wilson, J. P. Bearinger, J. L. Herberg, J. E. Marion, W. Wright, C. L. Evans and D. J. 
Maitland, "Shape Memory Polymers Based on Uniform Aliphatic Urethane Networks," J. 
Appl. Poly. Sci., vol. 106, pp. 540-551, 2007. 
 
 
 


English

Modeling Shape Memory Polymer fill Honeycomb as a Composite Skin for a Morphing Wing

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Modeling Shape Memory Polymer fill Honeycomb as a Composite Skin for a Morphing Wing

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