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3D PRINTING AND ADDITIVE MANUFACTURING Volume 4, Number 3, 2017 ª Mary Ann Liebert, Inc. DOI: 10.1089/3dp.2017.0027
ORIGINAL ARTICLE
Large Shape Transforming 4D Auxetic Structures Marius Wagner, Tian Chen, and Kristina Shea
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Abstract
Three-dimensional (3D) printing of active materials is a rapidly growing research area over the last few years. Numerous works have shown potential to revolutionize the field of four-dimensional (4D) printing and active self-deploying structures. Conventional manufacturing technologies restrict the geometric complexity of active structures. 3D printing allows the fabrication of complex active structures with no assembly required. In this study, we propose active 3D printed auxetic meta-materials that are capable of achieving area changes up to 200%. With these meta-materials, we design geometrically complex active structures that can be programmed into versatile shapes and recover their original shape given an external stimulus. We simulate the proposed metamaterials based on thermoviscoelastic material properties obtained by experimental characterization. A reduced beam model is constructed to predict forces and deformations of complex active structures. Excellent correlation is found between finite element simulation and experimental data from a 3-point bending test. Rectilinear tiling of the proposed meta-materials achieves the desired shape transformation. To demonstrate versatile programming, a selected meta-material is tiled into a complex contour, programmed into an arbitrary shape, and recovers as predicted. Simulation results verify this behavior. Such programmability in conjunction with 3D printing may be further exploited for applications such as biomedical devices, civil structures, and aerospace. Keywords: 4D printing, shape memory polymers, auxetic meta-materials, deployable structures, shape configuration, self-assembly
Introduction
Rapid advancement in three-dimensional (3D) printing technologies has led to improvements, in part, to quality, achievable resolution, and printable materials. Recent studies present approaches in which enormous design freedom is combined with active materials for the fabrication of shape transforming structures. Active materials are capable of changing their properties or shape as a response to an external stimulus. When incorporated in structures, these materials allow controllable self-actuation without external mechanical input. Fabrication of active structures using 3D printing technologies allows for much more complex designs than what is feasible with conventional manufacturing. 3D printing using active materials has been termed fourdimensional (4D) printing,1 where time is the fourth dimension, and structural variations are programmed to respond to external stimuli like temperature and humidity, that is, swelling.
4D printing has large untapped potential in applications where configuration change cannot be manually achieved and where electromechanical actuation is not feasible, for example, in aerospace2 and in medical fields.3 In addition, 4D designs have the advantage of volume and support reduction.4 Most studies on 3D printing of active materials use stimuliresponsive shape changing polymers. These polymers can be divided into two subclasses, the programmable Shape Memory Polymers (SMPs)5–9 and the artificial hydrogels.9–11 The mechanism of shape change for these two types of polymers differs greatly. SMPs are deformed externally at high temperatures and stay in the deformed configuration if they are cooled below the activation temperature, which is also referred to as programming. Upon heating, actuation takes place and the original shape is recovered.12 Ge et al.5 proposed Printed Active Composites (PACs) fabricated from multimaterial 3D printing. The structures
Engineering Design and Computing Laboratory, Department of Mechanical and Process Engineering, Swiss Federal Institute of Technology Zurich, Zurich, Switzerland. Opposite page: Large shape transforming 4D auxetic structure: The auxetic structure transforms from the circular programmed state (top) to the intermediate (middle) and permanent ordered state (bottom) using a heat stimulus. Photo credit: Jung-Chew Tse, Marius Wagner.
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consist of a rubbery matrix reinforced by fibers made from SMP. The PACs can be printed flat and evolve into three dimensional shapes upon programming. By introduction of several SMPs with multiple activation temperatures, Yu et al.6 designed 3D printed structures that exhibit controllable sequential shape changes. Following this approach, Wu et al.7 developed PACs exhibiting two temperature dependent active shape changes using two tailored polymers. Ge et al.8 used projection microstereolithography for multimaterial printing of SMPs. This allows the manufacturing of parts with higher resolution and without support material. This represents an extension to most of the other studies using inkjet printing for manufacturing of active structures. Artificial hydrogels react to fluids in their environment by swelling. The shape change of hydrogels proceeds as long as the stimulus is applied. In a dry environment, the permanent shape is slowly recovered as the absorbed fluid evaporates.12 Raviv et al.10 showed that 3D printing of hydrogels in combination with flexible polymers can be used to design active structures that self-deploy when submerged in water. Different actuation principles such as linear extension and bending were proposed. Gladman et al.11 used 3D printed hydrogels reinforced by aligned cellulose fibrils to generate anisotropic swelling behavior of the printed strands. Different activated shapes were achieved by changing the strand orientation. By combination of swelling hydrogels with SMPs, Mao et al.9 developed structures that can reversibly change their shape when subjected to a hydrothermal cycle. The swollen hydrogel was used to program the SMPs. The programmed shape is fixed by cooling the SMP below the activation temperature. Upon heating to the SMP’s activation temperature, the permanent shape is recovered. Compared to hydrogels, SMPs have the advantage that they exhibit a clearly defined shape change. In contrast, hydrogels will continue swelling as long as the stimulus is applied until saturation. Shape change occurs at a much faster rate, several seconds, with SMPs compared to several minutes up to hours for hydrogels. The major drawback of SMPs is that they require manual programming. This process is often imprecise and causes failure in designs. In addition, the achievable shape change of PACs is limited to bending of the structures. Presently, fabrication of SMP and hydrogel designs requires multimaterial 3D printing. This functionality is currently still limited to a few expensive machines. We address these challenges by introducing SMP-based shape transforming auxetic meta-materials that can be tiled to form active structures. The versatility of the proposed metamaterials enables the tiled structures to be programmed into multiple shapes. These structures are programmed with greater accuracy, allowing both the permanent and the programmed states to be precisely defined. The resulting structures exhibit much larger multidimensional shape transformation than previous publications. With the performed material characterization and resulting constitutive models, we propose a simplified procedure to simulate the programming and recovery behavior with accuracy. To simplify the fabrication process, the proposed metamaterials consist of a single material. They can be fabricated with inexpensive inkjet printing processes using commer-
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cially available materials. This also broadens the potential for fabricating 4D designs for a variety of applications. Geometrically complex active structures are formed by these meta-materials. These structures can be programmed into versatile shapes and recover their original shape upon an external stimulus. The example of an ETH logo based structure being programmed into a circular shape is shown. The proposed auxetic meta-materials exhibit a carefully designed microstructure to enable negative Poisson’s ratio and a tunable stiffness.13 Designs with a negative Poisson’s ratio have the advantage that when deformed in compression or tension, the structure will shrink or expand in the transverse directions respectively. This is especially useful for SMP based structures since programming of large structures can be challenging if forces need to be applied consistently in all dimensions. To simulate the proposed designs, we first characterize the thermomechanical behavior of the SMP. We fit the resulting data to a linear viscoelastic model. A detailed finite element simulation of the smallest component of the designs is implemented. To efficiently model large active structures of complex geometries, we construct a reduced beam element that follows the same mechanical behavior. The computational effort is reduced while predicted forces and displacements remain accurate. Materials and Methods
The goal of this study is the design and simulation of active structures. The study is conducted following the procedure in Figure 1. First, we characterize the thermomechanical properties of the 3D printed polymer. A linear viscoelastic constitutive model is then constructed using the experimental data. The simulation incorporating this constitutive model is validated by experiments with a three-point bending test. Following this, we design, simulate, fabricate, and test shape transforming active meta-materials. The shape memory cycle of the meta-materials is modeled using finite element simulations. With the force-displacement data from the simulation, we fit the artificial stiffness of beam elements such that they exhibit the same mechanical behavior. The reduced beam modeling approach allows for the simulation of large complex structures with low computational expense. Materials and fabrication
The active meta-materials are parametrically modeled and fabricated with a multimaterial inkjet 3D printer (Objet500 Connex3; Stratasys). In this process, a liquid polymer is jetted in thin layers and cured with UV light to fabricate complex structures. A dissolvable support material is used that allows for the manufacturing of more complex geometries. The designs are fabricated using the shape memory properties of VeroWhitePlus RGD835 (VW+), which is the same material that can be used on the most inexpensive, single material PolyJet printers. Thermomechanical characterization
The parameters required to model the thermomechanical behavior of the polymer are obtained by experimental characterization. Four sets of material related parameters are
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FIG. 1. Method procedure. (a) Experimental material characterization. (b) Constitutive model. (c) Finite-element simulation and validation by comparison to experiments. (d) Design of active structures. (e) Design simulation by reduced modeling approach and testing. tested: (1) the glass transition temperature Tg, (2) the fully relaxed modulus, (3) the coefficient of thermal expansion (CTE), and (4) frequency sweeps of the storage modulus at different temperatures. A dynamic mechanical analysis (DMA) (Mettler Toledo DMA 861) is used to measure the Tg of the polymer. For amorphous SMPs, the Tg is the activation temperature. In the experiment, the temperature is increased from -20C to 120C with a rate of 1C/min. A shear setup with a cylindrical specimen (/ = 4 mm, h = 2 mm) is used. The tests are performed by applying a sinusoidal displacement with a frequency of 3 Hz and an amplitude of 0.5 lm. The fully relaxed equilibrium modulus of VW+ is measured in a compression experiment using a Zwick Z020 universal testing machine equipped with a 2 kN load cell and a temperature chamber. To obtain the relaxed modulus, the experiment is performed at 80C with a rate of 5 mm/min. Cylindrical specimens (/ = 7 mm, h = 9 mm) are used. VW+’s CTE is measured using a Perkin Elmer DMA 7e. A cylindrical specimen (/ = 7 mm, h = 10 mm) is heated from 0C to 80C with a rate of 1C/min, and the thermal strain is measured. The DMA is used to measure the storage modulus over frequency at different constant temperatures. A shear setup and cuboid specimen with the dimensions 3.00 · 4.30 · 2.05 mm are used. The displacement frequency is swept from 100 Hz to 0.01 Hz with an amplitude of 0.5 lm. This procedure is repeated at 20C, 40C, 50C, 60C, 80C, and 100C. Linear viscoelastic constitutive theory
The time temperature superposition principle is applied to the measured shear storage modulus to obtain a continuous master curve using shift factors. The shift factors are approximated by the Williams-Landel-Ferry (WLF) equation (Eq. (1)).14 log10 aT ¼ log10
sðT Þ C1 ðT T0 Þ ¼ : sðT 0 Þ C 2 þ ðT T0 Þ
2 p
Z
1 0
G¢ G1 sin xt dx x
GðtÞ @ G¢ðxÞ þ 0:00782½G¢ð8xÞ G¢ð4xÞ 0:09990½G¢ð4xÞ G¢ð2xÞ þ 0:02000½G¢ð2xÞ G¢ðxÞ h x i 0:21600 G¢ðxÞ G¢ 2 h x xi 0:39700 G¢ G¢ 2 4 h x x i 0:11100 G¢ G¢ 8 16 h x x i G¢ 0:027600 G¢ 32 64 h x x i G¢ ... 0:00689 G¢ 128 256
(3)
Theoretically Equation (3) consists of an infinite number of terms. Each additional term will have the frequency and the coefficient divided by the factor of four compared to the predecessor term. In this study 11 terms are used since additional terms are found to have negligible improvement on the accuracy of the approximation. The relaxation modulus is approximated by means of a Prony series of the form, N
GðtÞ ¼ G1 þ + Gi e t=si
(4)
i¼1
(1)
The storage modulus master curve can be transformed into the relaxation modulus master curve by means of a Fourier transform (Eq. (2)),14 with G1 being the equilibrium modulus and G¢ being the storage modulus. G ðt Þ ¼ G 1 þ
In this study, the Fourier transform is approximated by Equation (3) according to the approach proposed by Schwarzl.15
(2)
In Equation (4), Gi is the stiffness of the nonequilibrium branches, and si is the relaxation time. For approximation of the experimental data, a Prony series with N = 19 nonequilibrium branches is used. Gi and si are determined by least square fitting. The behavior at different temperatures is modeled by multiplying the relaxation times of the reference temperature T0 by shift factors of the corresponding temperature (Eq. (5)).14
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si ðT Þ ¼ a T si ðT0 Þ
(5)
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Implementation of finite element simulation
For modeling of the shape memory effect of 3D printed polymers, Ge et al.8 and Mao et al.9 use finite element simulations with subroutines to predict the shape changing kinematics, as well as the force produced by the structures. Bodaghi et al.16 implemented an anisotropic material model subroutine for finite element simulations taking the characteristic layered microstructure of parts manufactured by additive manufacturing into account. Others use simpler reduced order models to predict the kinematics of the shape changes.10,11 Finite element simulations allow the accurate modeling of shape changing kinematics and actuation forces. The drawbacks are that the simulations presented so far require the implementation of constitutive models in subroutines. The modeling of large structures using finite element method is computationally expensive. Existing reduced models on the other hand are not capable of accurately predicting the temperature-dependent recovery kinematics and actuation forces.10,11 Thus we model the 3D printed SMP using conventionally available finite element software. Following a similar approach by Diani et al.17 for modeling of the shape memory behavior, the Prony series equation in shear and the WLF equation implemented viscoelastic material model in Abaqus (Dassault Systems) are utilized. In addition, in the fully relaxed state, the elastic behavior and the Poisson’s ratio are specified. Nearly incompressible behavior is assumed ¼ 0:5 and K ðT Þ ¼ 1. This assumption is valid since all deformations occur at temperatures above the Tg at which the polymer is in a rubbery state and exhibits a Poisson’s ratio close to 0.5. For modeling of the thermal strain, a temperature-dependent expansion coefficient is used. The model consists of C3D8RH hybrid brick elements that allow for simulation of incompressible behavior. Validation of model accuracy
To validate the accuracy of the finite element simulation, a shape memory cycle in a three point bending experiment is tested on a Perkin Elmer DMA 7e. In the first experiment, a free recovery test is performed, and a cuboid specimen with the dimensions 25 · 5 · 1.5 mm is used. The specimen is held for 5 min at 80C. Then the beam is deformed by a instantaneous programming force of 750 mN. After holding
the specimen for 3 min, the temperature is reduced to 0C with a rate of 10C/min. Then the specimen is held at 0C for 1 min with the programming force applied and for 1 min after removal of the programming force. The recovery of the original shape is initiated by heating the specimen to 80C at a rate of 20C/min and holding at 80C for 10 min. In the second experiment, the constrained recovery is tested. We use a specimen of the dimensions 25 · 5 · 2 mm and a programming force of 1200 mN. Instead of removing the force in the recovery step, 700 mN are applied to constrain the recovery of the SMP beam. The other experimental parameters are identical to those of the free recovery experiment. The data from the three point bending experiment is compared to Abaqus simulations of the same experiments using the temperature-dependent viscoelastic material model. The temperature of the experiment measured at the thermocouple is used as input for the specimen temperature in the finite element simulation. Design of active structures
We propose active auxetic meta-materials that can be programmed by large deformations exhibiting a negative Poisson’s ratio and recover their original shape upon external stimulus. The design of the auxetic meta-materials is shown in Figure 2a–c. Figure 2a depicts a compressible reentrant honeycomb. The geometry is designed to allow area changes of up to 160%. The reentrant honeycomb structure in Figure 2b can be stretched in the programming step and will shrink in the recovery step. The area of the structure can be reduced by 200%. Figure 2c shows an anti-tetrachiral honeycomb structure, which can be compressed and expands its area by 50% in the recovery step. The negative Poisson’s ratio is achieved though the internal rotation of the micro-structure. To evaluate the shape transforming capabilities of the meta-materials, they are programmed in water at 80C. The programmed shape is fixed by cooling in a water bath of a temperature of 5C. The original shape is recovered by submerging in 80C water. The proposed meta-materials can be tiled into active structures with arbitrary complex geometries. As an example, the logo of ETH is tiled with auxetic reentrant honeycomb unit cells (Figure 3). We demonstrate precise shape transformation by imposing a circular programmed state. This is indicated by the red circle. Using a heat stimulus, the structure is transformed from circular shape into the letters.
FIG. 2. CAD models of active auxetic structures: (a) reentrant honeycomb expansion,18 (b) reentrant honeycomb shrinkage, (c) anti-tetrachiral honeycomb expansion.19 All dimensions are stated in mm.
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conditions imposed. Using this, applied displacement and the resulting reaction force of both the programming and the recovery step are recorded. A linear stiffness of a fictitious beam element is fit to the force-displacement data. From these beam elements, we assemble large complex structures which then are simulated with low computational expense. This is demonstrated for the example of auxetic reentrant honeycomb structures and the ETH structure. Results Material characterization
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FIG. 3. ETH logo assembled from auxetic reentrant honeycomb meta-materials. The red circle represents contour of the programmed shape. Two ABS printed half rings are used to program the design. All dimensions are stated in mm. Modeling of active structures
We propose a reduced simulation approach for modeling of complex active structures. The detailed finite element simulation using hybrid brick elements and the thermoviscoelastic material model are performed for a quarter unit cell of the meta-material shown in Figure 2a with symmetry
Figure 4a shows the resulting tanðdÞ (solid line), the storage modulus (dashed line), and the loss modulus (dotted line) of VW+ from the DMA experiment. The peak indicates a Tg of 60C and a wide transition region between *40C and 80C. Thus we use 80C as the programming temperature and fix the deformation of the SMP by cooling to 5C. As shown in Figure 4b, for the relaxed modulus a mostly linear relationship between stress and strain can be observed up to a compressive strain of 15%. The results of the thermal strain measurements are shown in Figure 4c. Above the Tg a CTE of 2:42 · 10 4 C 1 and below the Tg a CTE of 1:60 · 10 4 C 1 are measured. Figure 4d depicts the shear storage modulus data of the frequency sweeps and the master curve constructed from the experimental data using a
FIG. 4. Thermomechanical material characterization of VW+. DMA shear setup, tangent delta over temperature, Tg approximately at 60C (solid line), shear storage modulus (dashed line), shear loss modulus (dotted line) (a). Uniaxial compression test at 80C (b). Thermal strain experiment (c). Shear storage modulus from DMA frequency sweeps in shear setup and master curve with a reference temperature of 40C (d). Transformation to the shear relaxation modulus (dots) and Prony series approximation (solid line) (e). Shift factors (dots) and WLF equation (solid line) (f). DMA, dynamic mechanical analysis; WLF, Williams-Landel-Ferry.
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reference temperature of 40C. The transformed shear relaxation master curve and the Prony series fit are shown in Figure 4e. It is found that the 19-branch Prony series very accurately approximates the experimental data, with a root mean square deviation of 0.528 MPa. The WLF approximation of the shift factors is shown in Figure 4f. For temperatures higher than the reference temperature of 40C, the shift factors are approximated very accurately. At lower temperatures, overestimation of the shift factors occurs.
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into the four steps of the shape memory cycle (step 1: programming, step 2: cooling, step 3: unloading, and step 4: recovery). The programming of the SMP beam is simulated accurately in both experiments. In the cooling step, the experiments show a larger thermal strain than the simulated three point bending beam. There is a slight delay between the experimental and the simulated recovery (arrows in Fig. 5). Overall, excellent correlation between the experiment and the simulation is found.
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Validation of model accuracy
The results of the comparison between experimental and simulated shape memory cycle with free (Fig. 5a, b) and constrained (Fig. 5c, d) recovery are shown in Figure 5. Graphs (Fig. 5a) and (Fig. 5c) show the temperature (dashed line) and force (solid line) of the respective shape memory cycle. Graphs (Fig. 5b) and (Fig. 5d) compare the resulting beam deflections in the experiment (solid line) and the simulations (dotted line). The time axes are divided
Evaluation of active structures
The shape transformation of the designed active structures is evaluated (Fig. 6). The rate of the shape transformation depends on the temperature in the recovery step. All structures recovered their permanent shape in less than 10 s in the experiments at *80C. Figure 6a depicts the shape transformation of the expanding auxetic reentrant honeycomb structure. An increase in area of more than 150% is realized. The shape transformation of the shrinking auxetic reentrant honeycomb structure is shown in Figure 6b, with an area reduction of *200%. Figure 6c shows the shape transformation of the anti-tetrachiral honeycomb structure with an area increase of 62%. Modeling of active structures
The modeling approach is illustrated in Figure 7. As shown in Figure 7a, the complete shape memory cycle using nonlinear analysis and the viscoelastic material model is simulated on a volume finite element model of the meta-material. The characteristic curve shown in Figure 7b is used to construct a linear stiffness (red line) approximating the force displacement behavior. This reduced beam model is used to simulate a simple tiling of the reentrant honeycomb structure under compression (Fig. 7c). Using this simplification, the computation time can be reduced from up to 24 h to several minutes. Using the same model, the lettering ‘‘ETH’’ assembled from reentrant honeycomb meta-materials is programmed into circular shape. When subjected to a heat stimulus the permanent shape is recovered (Fig. 8). Discussion
FIG. 5. Comparison between three point bending free (a, b) and constrained (c, d) recovery experiment and simulation. (a, c) Solid line force, dashed line temperature. (b, d) Displacement solid line experiment, dotted line simulation. Arrows in (b) and (d) indicate the discrepancy between simulation and experiment as a result of heat conduction.
In this study, we present auxetic meta-materials that undergo large shape transformations in area of up to 200%. This broadens the applications of the existing 3D printed active structures. Testing of the active structures showed that the intended shape transformation is realized. The proposed meta-materials can be assembled into complex active structures. This is demonstrated with the example of the ETH logo assembled from auxetic reentrant honeycomb unit cells. In this study, we show that the thermoviscoelastic equations implemented in Abaqus can be used to model the nonlinear time and temperature-dependent shape memory behavior of 3D printed structures with excellent accuracy. Compared to other studies,8,9 the implementation of a material subroutine is not required. This simplifies both material characterization and the finite element modeling process, as well as allowing the simulation to be performed by a nonexpert.
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FIG. 6. Shape transformation of active structures. Left column: programmed state, middle column: intermediate state, right column: permanent state. Active auxetic structures: reentrant honeycomb expansion (a), reentrant honeycomb shrinkage (b), anti-tetrachiral honeycomb expansion (c). Scale bars represent 10 mm.
FIG. 7. Brick finite-element model of quarter reentrant honeycomb unit cell (a). Force-displacement curve (b). Reduced order finite-element model of rectilinear tiling of the reentrant honeycomb (c).
The three-point bending experiments show higher thermal strain in the cooling step than the finite element simulations. This can be possibly attributed to superposition of thermal strain and an entropy elastic behavior of the polymer above the Tg . With decreasing temperature, the modulus decreases, leading to increasing beam deflection. The delay between simulated and experimental recovery (arrows in Fig. 5b, d) occurs due to heat conduction. Time is required for the temperature measured at the thermocouple to reach the inside of the specimen. In simulation, no heat conduction is taken into account, and the temperature measured at the thermocouple is directly used as input. This hypothesis is underlined by the fact that this effect is more pronounced in the constrained recovery experiment in which a specimen with a higher thickness is used. In addition the accuracy can be improved by accounting for the anisotropic properties of 3D printed parts. We develop efficient numerical simulation models that correctly predict the mechanical properties of complex structures during programming and recovery. With the efficient reduced beam simulation model, we are able to simulate the complex designs composed with the proposed meta-materials. The advantages, physical accuracy of volume finite element models, can be combined with the low computational expense of models like spring mass representations. Since the behavior of the active structures is nonlinear, an accurate prediction can be obtained if the deformations in the reduced beam model do not differ too greatly from the deformations in the finite element simulation of the brick model. Further inaccuracies are introduced when simulating a complex design, for example, the structure in Figure 8. We observe discrepancies
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FIG. 8. Shape transformation of ETH logo assembled from reentrant honeycomb. Scale bar represents 20 mm. The corresponding reduced model simulation is shown below. The programming phase is solved as a dynamic explicit problem. between simulation and the physical specimen during the intermediate state. This is due to friction between the specimen and the glass surface and the difficulty in simulating beam-to-beam contact. Nonetheless, the simulation indicates whether the structures can be programmed, recover, and the magnitude of force needed for programming. The active structures developed in this work undergo large shape transformation. This invariably leads to changes in mechanical properties such as stiffness,13 Poisson’s ratio, vibration damping, and energy absorption. This will be exploited in future studies to design structures that are capable of adapting their mechanical properties to their environment in a controlled manner. Conclusion
We 3D print SMPs to fabricate active meta-materials using a single material. The meta-materials we propose can achieve area changes of up to 200% within a programming and recovery cycle. This property is inherited in complex designs that are formed with these meta-materials. These designs can be programmed into versatile shapes and recover their original state when subjected to temperatures above the SMP’s activation temperature. For simulation of the meta-materials, we adapt a viscoelastic constitutive model with data from thermoviscoelastic material characterization experiments. The accuracy of the model is shown with a three-point bending test. To reduce computational effort, a reduced beam model is constructed to predict forces and deformations of complex active structures. To demonstrate that the metamaterials can conform to a given boundary, a letter based structure is fabricated and programmed into a circular shape. Simulation results confirm the behavior. Acknowledgments
The authors acknowledge Dr. Kirill Feldman of the Soft Material Laboratory at ETH Zurich and Dr. Joanna Wong of the Laboratory of Composite Material and Adaptive Structures at ETH Zurich for supporting this research by performing material characterization experiments.
Author Disclosure Statement
No competing financial interests exist. References
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Address correspondence to: Tian Chen Engineering Design and Computing Laboratory Department of Mechanical and Process Engineering Swiss Federal Institute of Technology Zurich Tannenstrasse 3, CLA F34.2 Zurich 8092 Switzerland E-mail:
[email protected] 
