Shape Adaptive Structures by 4D Printing

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This paper introduces a 4D printing method to program shape memory polymers .... temperature, T. As it can be seen, the large storage modulus in glassy phase ...
Proceedings of the ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems SMASIS2017 September 18-20, 2017, Snowbird, UT, USA

SMASIS2017-3773 SHAPE ADAPTIVE STRUCTURES BY 4D PRINTING G. F. Hu, A. R. Damanpack, M. Bodaghi, and W. H. Liao Smart Materials and Structures Laboratory Department of Mechanical and Automation Engineering The Chinese University of Hong Kong Shatin, N.T., Hong Kong, China

ABSTRACT This paper introduces a 4D printing method to program shape memory polymers (SMPs) during fabrication process. Fused deposition modeling is employed to program SMPs during depositing the material. This approach is implemented to fabricate complicated polymeric structures by self-bending features without need of any post-programming. Experiments are conducted to demonstrate feasibility of one-dimensional (1D)-to 2D and 2D-to-3D self-bending. It is shown that 4D printed plate structures can transform into 3D curved shell structures by simply heating. A 3D macroscopic constitutive model is developed to predict thermo-mechanical behaviors of the printed SMPs. Governing equations are also established to simulate programming mechanism during printing process and shape change of self-bending structures. In this respect, a finite element formulation is developed considering von-Kármán geometric non-linearity and solved by implementing iterative Newton-Raphson scheme. The accuracy of the computational approach is checked with experimental results. It is shown that the structural-material model is capable of replicating the main features observed in the experiments.

primitive structures made of hydrophilic polymers and rigid materials that could perform self-folding when dipped in water. Recently, Ding et al. [4] printed self-folding composite structures consisting of shape memory polymers (SMPs) and elastomeric materials by inducing compressive strains during photo-polymerization of PolyJet process. In all research work done in the 4D printing field, as discussed above, no post-programming process has been carried out on the printed objects after fabrication stage. It may be due to simple shape change and/or function expected from the design. However, some efforts have been conducted to program smart materials after printing procedure. For instance, using PolyJet printing technology, Wu et al. [5] printed SMP composite structures in trestle, helix, insect and hook shapes. After programming the structures and adding pre-stain, they could do self-assembling and disassembling. By printing various SMP fibers into a flexible matrix, Bodaghi et al. [6] designed an actuator unit, stent and metamaterial lattice. After a post-thermomechanical programming, they could expand and then recover their original shapes automatically upon heating. In many engineering applications, it is very difficult to program the printed structures after printing stage. This paper presents a 4D printing method to program SMP materials during fabrication process. Fused deposition modeling (FDM) as a filament-based printing method is utilized to program SMPs during material deposition. The approach is applied to fabricate 1D and 2D structures pre-strained during fabrication, and then transform to 2D and 3D structures by simply heating via freestrain recovery. It is experimentally shown that printed 1D ribbons and 2D plates can be shifted to 2D curved ribbons and doubly-curved shells upon heating by releasing pre-strain induced in the fabrication stage. In order to predict the induced pre-strain and simulate structural shape-change during activation, a material-structural model is developed. In this respect, a 3D macroscopic constitutive SMP model is developed

INTRODUCTION Additive manufacturing technology (AM) is an advanced manufacturing technology used for fabricating geometrically complex and materially heterogeneous objects. As traditional AM, also known as three-dimensional (3D) printing, grows, creeping up in the context is 4D printing [1]. 4D printing combines intelligent materials with AM techniques to offer a streamlined path from idea to reality with performance-driven functionality programed directly into the materials. In the recent years, the feasibility of 4D printing for some active materials have been demonstrated with opening questions and challenges. For instance, using PolyJet multi-material 3D printing technology, Tibbits and his colleagues [2, 3] printed

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and embedded into a finite element (FE) formulation considering von-Kármán geometric non-linearity. Governing equations of equilibrium with material and geometrical non-linearities are then solved by iterative Newton-Raphson approach. The excellent accuracy of the developed formulation and solution is verified through comparative studies with experiments. MATERIALS AND METHODS Conceptual design Thermal-responsive SMP materials with shape memory effects (SMEs) are employed for actuation purpose. SMPs are capable of returning from deformed shape to original one upon heating beyond the glass transition temperature, Tg . The shape memory cycle in SMPs generally consists of a high-temperature shape programming stage followed by a shape recovery upon heating as shown in Figure 1. The material initially in a low temperature, Tl , is first heated above the transition temperature range, T  Th  Tg (a  b) . It is then stretched to gain a

Figure 1. Stress-strain-temperature diagram displaying thermo-mechanical programming of SMPs and the free-strain recovery.

maximum strain,  m (b  c) . The material is fixed to maintain the deformed shape and cooled to temperatures lower than Tg (c  d ) . By releasing the constraint, thermo-elastic strain is

(a)

recovered while a pre-strain is kept in the material,  p ( d  e) . The pre-strain may be released by heating above Tg , that is called free-strain recovery (e  b) . Finally, thermal strain can be removed by cooling down to Tl (b  a) . In the FDM printing method as a layer-by-layer process, the nozzle is first heated to melt the filament. The material is heated above its Tg and then extruded onto the build platform or adjacent existing layers. The extrusion head moves over the build platform horizontally while the extruded material is partially stretched. The thin printed layer of the polymer bonds with platform or existing layers beneath it, cools and finally solidifies. This process is very similar to thermo-mechanical programming procedure, previously stated above and depicted in Figure 1, and completes by removing the printed object from the platform. It brings the idea that the FDM printing process may be employed for thermo-mechanical programming of SMPs. Therefore, in the current research, the FDM printing of SMP filaments is proposed to fabricate flat 2D structures pre-strained during fabrication so as to transform to 3D complicated structures by simply heating via free-strain recovery. An FDM-based 3D printer (FlashForge New Creator Pro) is used for fabrication. Polyurethane-based SMP filaments are employed to print mechanical objects. They have a glass

(b)

Figure 2. SMP phase transformation based on the DMA test: (a) storage modulus, (b) tan (δ).

transition temperature of 60 0C . Temperatures of build platform

A sample with a dimension of 1 5 10 mm is first printed and then tested using a DMA analyzer (NETZSCH, DMA 242). The investigation is performed in an axial tensile mode with frequency of force oscillation 1 Hz and heating ramp rate

and nozzle are set as 24 and 200 0C while chamber temperature is 24 0C .A dynamic mechanical analysis (DMA) is performed to determine temperature-dependent material properties of the 3D printed objects.

5 0C / min ranging from -20 to 85 0C . The ratio of applied

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dynamic stress to static stress is about 1.5. Figure 2 illustrates the phase transformation behaviors of the polyurethane-based SMP in terms of storage modulus, E S , and tan ( ) as functions of temperature, T. As it can be seen, the large storage modulus in glassy phase reduces drastically at rubbery phase. The temperature corresponding to the peak of the tan ( ) graph is assumed to be the glass transition temperature. It is read as Tg  60 C .

(a) after printing

(b) after heating-cooling speed (mm s 1 ) 30 40

Figure 3. Configurations of the ribbons printed with various building speeds: (a) after printing; (b) after heating-cooling process.

2D self-bending As it can be found from SME mechanism shown in Figure 1, the pre-strain value directly depends on the mechanical forcing stage. This force is provided by the movement of the nozzle head during printing process. Therefore, the pre-strain value may be affected by the building speed. This postulation is investigated by printing some SMP ribbon samples with different building speeds. 8 ribbons with dimension of 1 315 mm (thicknesswidth-length) are printed with various building speeds of 30

3D self-bending The method of programming during printing process can be employed for complicated shape change and/or function. In this study, it is used to design self-bending flat 2D structures that can convert to complicated 3D structures by simply heating. Curvedshaped structures have widely been used as practical structural elements in many fields. It is worth noting that these 3D curved structures can be printed by traditional 3D FDM printing directly. However, on the basis of FDM printing concept, mechanical properties/strengths of 3D hollow structures would not be as good as 3D solid structures when they are printed in a flat shape. It is because they may need some supports that affect printing quality and mechanical properties/strengths of the object. Besides better mechanical properties, transporting flat structures, specially to remote locations, is easier than spatial structures. In this section, it is wished to print 2D flat circular/square plates that can transform to 3D conical and doubly-curved shell structures by simply heating. Two flat plates in circular and

and 40 mm s 1 . The printing direction is considered to be along the ribbon length. A printed ribbon is displayed in Figure 3a. In order to activate the printed SMP ribbons, they are put into hot water with a prescribed temperature of 90 C that is much higher than Tg  60 C . The configuration of samples after cooling and drying is presented in Figure 3b. As it can be seen, the straight ribbons can bend into curved ribbons with different curvatures. This is a demonstration of 1D to 2D shape-shifting by self-bending mechanism. The outer arc length of curved beams is measured averagely and its difference with the length before heating, called l , is listed in Table 1. It is found that, the final length is less than initial length of the printed ribbons so that shrinkage values are positive. Shorter length and curved shape imply that not only the printed SMPs are programed and pre-strained during printing process but also the pre-strain varies through the thickness direction having an increasing trend. The pre-strain difference leads a strain recovery mismatch that enables the overall shape to be changed toward the upper layer. This phenomenon can be associated to different conditions of the programming during the printing process. As it can be seen in Table 1, the building speed increases the shrinkage value so that the printed 15 mm-SMP ribbon can experience length change of 2.7 mm at the lower layer for the building speed

(a)

(b)

(c)

uzm=15.9 mm (d)

(e)

of 40 mm s 1 . Table 1. The shrinkage value of the lower layer of the ribbons printed in various building speeds after heating-cooling stage.

uzm=21.0 mm

S ( mm s1 ) l (mm )

30 1.8

Figure 4. Configurations of self-bending structures with circular (a, b) and square (c, d, e) bases after printing (a, c) and after heating-cooling stage (b, d, e). Part e is a bottom view of part d.

40 2.7

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where  g and  r are volume fractions of the glassy and rubbery

square shapes are printed as shown in Figure 4a and 4c. The infill pattern is in curved and straight schemes along lateral sides of the circular and square plates, respectively. Printing starts from

phases satisfying  g   r  1 . Henceforth, subscripts “g” and

outer edge to inner part having 40 mm s 1 speed. The plates have 1 mm thickness with 40 mm diameter/length

“r” signify the glassy and rubbery phases, respectively. ε g and

( H p  1mm, Dop  40 mm, Lp  40 mm) where the superscript p

respectively. εt represents the thermal strain as

ε r denote elastic strain in the glassy and rubbery phases,

means the geometric parameters after printing. For the actuation,

T

Tr

αe (T ) dT in

which α e is effective thermal expansion that follows the rule of mixture as α r  (α g  α r ) g (T ) . Finally, εi is related to an

they are put in hot water with a temperature of 90 0C . Figure 4b, 4d and 4e illustrates the configurations of the printed circular and square plates after heating-cooling process. The maximum value of transverse displacement, uzm, that is equal to structure height is also included in this figure and following Figure 5. As the flat plates absorb the heat, they start to bend leading to 3D curved shells with various curvatures. The circular plate exhibits an automatic pattern switch to a conical shell with a straight hypotenuse. The conical shell has outer diameter of

inelastic phase transformation strain. As a generally well-known assumption, it is considered that volume fractions of glassy and rubbery parts are only functions of temperature during phase change. In this study, the following trigonometric function is considered to interpolate DMA data previously displayed in Figure 2 in a smooth manner. It is formulated as:

Dohc  31.4 mm and a total height of H hc  15.9 mm after

g  

heating-cooling stage. The opening angle of the cone known as vertex angle defined as   2 atan(Dohc / 2H ) is calculated as

tanh(aTg  bT )  tanh(aTg  bTh )

(2)

tanh(aTg  bTh )  tanh(aTg  bTl )

where a and b are chosen to fit experimental DMA curve. In a cooling process when the temperature is decreased, the rubbery phase transforms gradually to the glassy phase and the strain is stored in the SMP material. On the other hand, during heating process, the stored strain is released gradually. Therefore, the inelastic strain vector can be expressed in a rate form as [6]:

  89 .3 . In conjunction with the deformation mechanism, 3D printed circular fibers are actuated and try to recover their initial shape. In this respect, they are supposed to shrink in the length direction and expand in the transverse direction. Since circular fibers are closed and construct a full structure, relaxing the prestrain provides compressive stresses that trigger out-of-plane buckling to induce deformations. The pre-strain is also distributed through the thickness direction and may produce some bending moments. Thus, the final deformation mainly would be due to global bending and compressive buckling process throughout the entire structures. Regarding to shape change of the flat plate with square base, Figure 4d and 4e reveal that the structure bends up and looks like a doubly-curved shell. Its maximum transverse displacement becomes uzm=21.0 mm. As it can be seen, the shell has different curvatures near and away from the apex. While its hypotenuse is fully straight near the apex, it becomes curve far away the apex. It is also seen that corners even bend into the shell. This feature can be useful for designing 3D grippers to catch external objects.

 g  ε εi    g i  ε  g r

T  0

(3)

T  0

where a superposed dot denotes differentiation with respect to time. As it can be found from equation (3), the strain release is independent of the strain state in the heating path. By considering Helmholtz free energy density functions, satisfying the second law of thermodynamics and implementing backward Euler integration technique for flow rule (3), SMP stress-strain constitutive equation can be derived as:

Formulation This section aims at developing constitutive model and computational simulation to realize SMP programming in processing stage and thermo-mechanical features of the printed SMPs during activation and phase transformation. A macroscopic constitutive model introduced in Refs. [6, 7] is briefly described here for phase transformation of SMPs based on the continuum thermodynamics of irreversible processes. Considering the fact that the printed structures may experience small strains and moderately large rotations, the total strain vector, ε , can be additively written as:

ε   g ε g  (1   g )εr  εt  εi



(4)

σ  Cei (ε  εt   εiq )

where parameters C ei and  are defined in cooling and heating stages as: C ei  C e ( I   g ( g I  ( S r1C e ) 1 ) 1 ),   1 for T  0 C ei  C e ,  

g  gq

for T  0

(5)

in which

(1)

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Ce  ( Sr   g ( S g  Sr )) 1 ;  g   g   gq

where  and  denote tensile and shear strains, respectively. Also, the comma symbol in the subscript indicates partial differentiation with respect to the following coordinate. Next, a Ritz-based FE formulation is established to solve the present problem dealing with thermo-mechanical features of 3D printed SMP structures. In this respect, a 3D 20-node serendipity hexahedron element [8] is employed to discretize the volumetric domain. The 8 corner nodes are augmented with 12 side nodes mounted at the midpoints of the sides. Taking 3 degrees of freedom per node, i.e., displacements in three directions, the element has 20  3  60 degrees of freedom. Following standard FE method, governing equations of the 3D printed SMP objects can be derived as:

(6)

and S  C 1 denotes the compliance matrix. Also, the superscript q indicates quantities at previous time step. By knowing ε iq and

 gq

from the previous step and  g as a

known temperature-dependent function, εi can be obtained via the following equations.

εi  ( I   g S r C e ) 1 (εiq   g S r C e (ε  εt )) εi 

g q εi  gq

for T  0 for T  0

(7)

Kw  ft  fi q  f m

In order to derive the governing equations of equilibrium and associated boundary conditions of the 3D printed SMP structures, the principle of minimum total potential energy is implemented. The virtual strain energy can be expressed as:

U   εT Cei (ε  εt   εiq ) dV

where K denotes non-linear element stiffness due to geometric non-linearity, w is vector of generalized nodal displacements while ft , fi q and f m are force vectors induced by temperature change, SMP phase transformation and mechanical loadings. Equations (11) is a set of non-linear algebraic equations in terms

(8)

V

of unknown mechanical nodal variables, w , and nodal εiq ’s that are distributed within all elements and known through equations (7) for cooling and heating processes. An iterative approach such as Newton-Raphson method [8] is implemented to solve nonlinear algebraic equations (11).

where  indicates the variational symbol and V is the volume of the 3D printed SMP object. It should be noted that temperature q T and inelastic strain εi are variable through the volume. In this work, the temperature is assumed to be constant while Gauss-Legendre numerical integration rule is utilized to evaluate

Comparative studies First of all, the material parameters of a, b, Tl and Th introduced in (2) need to be calibrated based on the DMA results presented in Figure 2. a and b are set as 0.15 and 0.145 while the glass transition ranges, Tl and Th are selected as 20 and 100 ºC, respectively. Next, the computational tool is used to determine distribution of SMPs through the thickness of ribbons printed with different speeds. To this end, the configuration of samples presented in Figure 3 after printing and heating-cooling processes are considered as inputs for FE simulations. The output results in terms of pre-strain value at lower, middle and upper layers of the samples fabricated with various building speeds are given in Table 2. As it can be seen, the pre-strain has minimum, middle and maximum values at lower, middle and upper layers,

volumetric integral by discretizing εiq . The virtual external work done by concentrated generalized force vector P in moving through its respective virtual displacement vector, u , can be formulated as:

 Px  u x      W  u P , u  u y  , P  Py  P  u   z  z

(9)

T

in which Pi and ui (i  x, y, z) are concentrated forces and displacements along x, y and z directions. In order to describe deformation of the 3D printed structures, the von-Kármán concept adopted for small strains and moderately large rotations is considered. Accordingly, non-linear kinematic relations can be expressed as:

   x   u x , x  12 u z2, x     1 2   y   u y, y  2 uz, y    z   u z , z  12 u z2, z ε    yz  u y , z  u z , y  u z , yu z , z   xz   u x , z  u z , x  u z , xu z , z       xy  u x , y  u y , x  u z , xu z , y 

(11)

Table 2. Predictions for pre-strain (%) induced in lower, middle and upper layers of the SMP ribbon printed with various building speeds. (10)

5

S (mm s 1 )

lower layer

30 40

13 15

middle layers 18 22

upper layer 23 29

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CONCLUSIONS The main objective of the paper was to propose a 4D printing approach to program SMP materials and structures during fabrication process. It suggested a new paradigm in utilizing FDM printing technology to program SMP materials during deposition stage. The technique was applied to print polymeric structures by self-bending features without need of any postprogramming. It was experimentally shown that the printed structures were programmed and could be shifted from 1D to 2D and 2D to 3D upon heating above the glass transition temperature. In order to realize programming mechanism during fabrication and shape-shifting during activation, an FE formulation coupled with a 3D macroscopic constitutive model for SMPs were developed. Governing equations of equilibrium were derived based on the von-Kármán geometric non-linearity and solved by iterative Newton-Raphson method. Capabilities of the material-structural formulation were examined through comparative study with experimental results. It was found that the computational tool was able to accurately estimate the prestrain induced in the fabrication and simulate 1D-to-2D and 2Dto-3D self-bending.

respectively. When the SMP ribbon is activated by raising the temperature, the pre-strain causes bending deformation due to its asymmetric distribution through the thickness direction, see Figure 3b. From the results presented in Table 2, the pre-strain at middle layers seem to be an average value of those at upper and lower layers. Furthermore, an increase with the building speed is in accordance with experimental observation. These pre-strain values will serve as benchmark data for following simulations. The experimental results presented in Figure 4 for selfbending plates are replicated by means of the developed FEM. To this end, initial geometric parameters and pre-strain distribution through-the-thickness for 40 mms1 building speed selected from Table 2 are given in FEM. Figure 5 presents configurations of the printed circular and square plates before and after heating-cooling stages. Color bar in this figure shows transverse displacement to maximum transverse displacement, uzm. The vertex angle for conical shell is calculated as   88 .8 that is 0.56 % less than experimental value. Also, the FEM model estimates maximum transverse displacement for doublycurved shell equal to 20.6 mm that is 1.9 % less than experimental measurement. From a topological point of view, comparing results in Figures 4 and 5 reveal an excellent agreement between FE simulations and experimental results validating the accuracy of theoretical model and solution methodology. In this respect, the FE method can even successfully replicate negative curvature of the doubly-curved shell. (a)

(b)

(c)

uzm=15.9 mm (d)

ACKNOWLEDGMENTS The work described in this paper was supported by the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK 14202016) and The Chinese University of Hong Kong (Project ID: 3132823). REFERENCES [1] Choi, J., Kwon, O.C., Jo, W., Lee, H.J., and Moon, M.W., 2015 “4D printing technology: a review,” 3D Print. Add. Manufactur., 2, pp. 159-167. [2] Tibbits, S., 2014 “4D printing: multi-material shape change,” Architect Des., 84, pp. 116-121. [3] Raviv, D., Zhao, W., McKnelly, C., Papadopoulou, A., Kadambi, A., Shi, B., Hirsch, S., Dikovsky, D., Zyracki, M., Olguin, C., Raskar, R., and Tibbits, S., 2014 “Active printed materials for complex self-evolving deformations,” Sci Rep., 4, 7422. [4] Ding, Z., Yuan, C., Peng, X., Wang, T., Qi, H.J., and Dunn, M.L., 2017 “Direct 4D printing via active composite materials,” Sci. Adv., 3, e1602890. [5] Wu, J., Yuan, C., Ding, Z., Isakov, M., Mao, Y., Wang, T., Dunn, M.L., and Qi, H.J., 2016 “Multi-shape active composites by 3D printing of digital shape memory polymers,” Sci Rep., 6, 24224. [6] Bodaghi, M., Damanpack, A.R., and Liao, W.H., 2016 “Self-expanding/shrinking structures by 4D printing,” Smart Mater. Struct., 25, 105034. [7] Kim, J.H., Kang, T.J., and Yu, W.R., 2010 “Thermomechanical constitutive modeling of shape memory polyurethanes using a phenomenological approach,” Int. J. Plast., 26, pp. 204-18. [8] Reddy, J.N., 2004 “An introduction to nonlinear finite element analysis,” New York: Oxford University Press In.

(e)

uzm=20.6 mm Figure 5. FE simulations of experimental results presented in Figure 4. Color bar shows transverse displacement to maximum transverse displacement.

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