4D printing reconfigurable, deployable and mechanically tunable metamaterials

Chen Yanga, Manish Boorugua, Andrew Doppa, Jie Rena, Raymond Martina, Daehoon Hana, Wonjoon Choib and Howon Lee*a
aDepartment of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, New Brunswick, NJ 08901, USA. E-mail: howon.lee@rutgers.edu
bSchool of Mechanical Engineering, Korea University, Seoul, Korea

Received 25th February 2019 , Accepted 19th March 2019

First published on 19th March 2019

The exotic properties of mechanical metamaterials emerge from the topology of micro-structural elements. Once manufactured, however, the metamaterials have fixed properties without the ability to adapt and adjust. Here, we present geometrically reconfigurable, functionally deployable, and mechanically tunable lightweight metamaterials created through four-dimensional (4D) printing. Using digital micro 3D printing with a shape memory polymer, dramatic and reversible changes in the stiffness, geometry, and functions of the metamaterials are achieved.

Conceptual insights

Since the spatial arrangement of micro-structural elements determines the properties of mechanical metamaterials, once manufactured, the geometry and properties of the metamaterials are irreversible with no ability to adapt and adjust. In this work, we employed a 4D printing approach to create geometrically reconfigurable, functionally deployable, and mechanically tunable lightweight metamaterials. Using a digital micro additive manufacturing technique and a thermo-responsive shape memory polymer which exhibits a dramatic change in elastic modulus, we created lightweight mechanical metamaterials whose effective stiffness can be varied over 100 times. Ultra-tunable shock absorption at impact loading was also demonstrated. Furthermore, they can be deformed substantially and mechanically programmed into an arbitrary geometry with the ability to fully recover the original shape on-demand. The micro-architected programmable materials created a new class of mechanical metamaterials with remarkable versatility and adaptability to environmental change or varying loading conditions. The 4D printed mechanical metamaterials may find a broad range of applications such as in tunable shock absorbing interfaces, morphing aerospace structures, soft robotics, and implantable biomedical microdevices.

Metamaterials are artificial materials engineered to have properties that may not be found in nature.1 Metamaterials offer exceptional opportunities for tailoring macroscopic physical properties including electromagnetic,2 acoustic,3 mechanical4,5 and thermal properties,6,7 through appropriate design and arrangement of their micro-structural elements. The mechanical metamaterials refer to cellular materials exhibiting unprecedented mechanical properties defined by the geometry of repeating unit cells. Recently, there have been exciting new studies in this area that have created new, previously inaccessible properties and have significantly expanded the available property spaces.8,9 These advances have been accelerated by the evolution of additive manufacturing, also referred to as three-dimensional (3D) printing, which breached the long-standing barrier for the physical production of otherwise unrealizable design concepts with highly ordered material architectures in 3D space. The examples range from high stiffness and strength at extremely low density4,10 to exotic physical properties that are not present in nature, such as negative Poisson's ratio,11 negative thermal expansion,6,12 ductility in ceramic materials,13 and fluid-like solids with near zero shear modulus.14 In particular, low-density materials with superior mechanical performance have attracted great interest in recent years for their wide range of applications including in structural components,15 energy absorption16 and biomaterials.17

The properties of mechanical metamaterials emerge from the 3D spatial arrangement of the micro-structural elements. Therefore, once manufactured, such properties are irreversible. However, incorporating a material with reversibly tunable properties in a metamaterial could offer the metamaterial flexibility and adaptability, leading to the ability to significantly modulate the mechanical performance in many applications. For example, the tunable stiffness can improve both comfort and safety in automobiles,18 create adaptive airplane wings to improve flight performance in aeronautics,19,20 lower damage caused by wind and earthquakes in civil engineering,21 or create appendages adaptable to different grasping and locomotion tasks in robotics.22 Cellular materials with tunable moduli have been demonstrated by coating wax on a 3D printed cubic lattice, but the property change was not reversible once the wax melted away.23 The programmable effective stiffness with a compressive pre-strain was achieved with the molded shape memory polymer (SMP) lattices, but only 2D lattices were demonstrated due to the limitation of the molding process.24,25 Recently, a 35% increase in effective stiffness was achieved by injection of magnetorheological (MR) fluids into a hollow lattice and applying a magnetic field; however, the increment of 35% is not significant.26

In this work, we report geometrically reconfigurable, functionally deployable, and mechanically tunable lightweight metamaterials created through 3D printing. We used a photo-crosslinkable and temperature-responsive SMP as a constituent material for the mechanical metamaterials. The SMPs are polymeric materials which have the ability to maintain a temporarily deformed shape (shape programming) and return to their original shape (shape recovery) upon appropriate stimulation such as heating. This shape memory effect has been extensively studied and widely used for smart structures in many engineering applications.27–31 3D printing with SMPs has played a central role in the emerging field of 4D printing32 (3D printing of shape-transforming structures), but the focus has predominantly been on geometrical transformations.33–39 Instead, here we exploit a substantial mechanical property transition between glassy and rubbery states of a SMP around its glass transition temperature (Tg) and apply it to mechanical metamaterials. By using a digital light processing (DLP) additive manufacturing technique, projection micro-stereolithography (PμSL), and a SMP, we developed lightweight mechanical metamaterials that can change their stiffness by over two orders of magnitude with the temperature between 30 °C and 90 °C. Using the ultra-tunable stiffness, dramatic modulation in shock absorption at an impact loading is achieved. Furthermore, the metamaterials can be significantly deformed and locked into an arbitrary geometry while maintaining the mechanical performance. The ability to fully recover the original shape and rigidity even after aggressive deformation renders the deployable metamaterials able to bear mechanical loads in various situations.

To fabricate 3D SMP metamaterials, we employed a high precision additive manufacturing technique, PμSL. PμSL is a stereolithography technique capable of rapidly producing a complex micro-structure through maskless projection with a digital dynamic mask.40–42 Various soft reconfigurable materials including responsive hydrogels and SMPs have been 3D printed using this versatile additive manufacturing method.43–46 A schematic of the PμSL process is shown in Fig. 1A. A 2D cross-sectional image extracted from a 3D computer-aided design (CAD) model is displayed on a digital micromirror device (DMDTM) that works as a dynamic virtual photomask. The ultraviolet (UV) light illuminated from a light emitting diode (LED) is reflected off the dynamic mask and then focused on the surface of the photocurable liquid polymer through a projection lens. Once a layer is photo-polymerized, a linear stage moves the sample down and the next layer is formed on top of the previous layer. A 3D micro-structure is built layer upon layer by repeating the process until all the layers are completed. The resolution of the digital dynamic mask is 1920 × 1080 and the projection area is 24 × 14 mm, making the nominal resolution of 13 μm. A layer thickness of 50 μm was used for all micro-structures, and a curing time of 5 s was chosen for each layer based on a curing depth test where the depth of the cured layer versus exposure energy was studied (ESI, Fig. S1).

image file: c9mh00302a-f1.tif
Fig. 1 4D printing of mechanical metamaterials. (A) Schematic diagram of the digital additive manufacturing process. (B) Photocurable shape memory polymer (SMP) consisting of acrylic acid (AA) as a monomer to form chains and bisphenol A ethoxylate dimethacrylate (BPA) as a crosslinker to form nodes. (C) Storage modulus, loss modulus and tan[thin space (1/6-em)]δ of the SMP. (D) A typical shape memory cycle of a SMP microlattice. Shape programing through heating, deformation and cooling, and shape recovery to its original shape upon heating. Scale bar is 2 mm.

A photocurable SMP precursor solution was prepared using acrylic acid (AA) as a monomer and bisphenol A ethoxylate dimethacrylate (Mn ∼ 1700) (BPA) as a crosslinker (see ESI for details). Upon photo-polymerization, a cross-linked polymer network is formed with AA as the chain and BPA as the nodes connecting the AA chains, as illustrated in Fig. 1B. While AA has a short side group and therefore a high Tg of 130 °C,47 BPA has a long pendant group and thus a low Tg of as low as −40 °C.45 It has been shown that the material characteristics of SMPs, such as Tg and glassy/rubbery moduli, can be tailored by using different ratios of monomer and crosslinker.29,48 The ratio between AA and BPA was determined by estimation from the Gordon–Taylor equation (see ESI for details of calculation). The thermomechanical properties of the SMP were then characterized by dynamic mechanical analysis (DMA) tests on both 3D printed and molded specimens (see ESI for details). The results from DMA tests on both specimens are shown in Fig. 1C. Note that the storage modulus of the SMP changes by more than two orders of magnitude from 3.0 GPa at 30 °C (glassy) to 6.4 MPa at 90 °C (rubbery). Tan[thin space (1/6-em)]δ indicates that the SMP has a Tg of 71 °C. The small discrepancies in DMA results between the 3D printed and the molded sample are attributed to the surface roughness caused by the layer-by-layer printing process and higher light intensity of 29 mW cm−2 used for 3D printing compared to 4.4 mW cm−2 of the UV oven used for molding (see ESI for details). The shape programming and shape recovery of a 3D printed SMP microlattice (and a schematic CAD model) are shown in Fig. 1D. A 3 × 3 × 1 octet-truss microlattice printed with the SMP was first heated to 80 °C (>Tg, the rubbery state) and then twisted at 90°. When the temperature was lowered to 25 °C (<Tg, the glassy state), the deformed shape was retained even after the removal of mechanical loading. Upon heating back to 80 °C, the original shape of the microlattice was completely recovered as the SMP underwent the glassy-rubbery transition.

Two sets of microlattices were designed and printed with the SMP to study their tunable mechanical behavior. Depending on the topology of a unit cell and how it carries a mechanical load, the cellular materials are grouped into two distinctive classes; stretching-dominated and bending-dominated.49 A stretching-dominated microlattice bears load through tension and compression of struts, while a bending-dominated microlattice bears load through bending of struts. When the relative stiffness of the lightweight cellular materials scales with their relative density as Erelρnrel, the bending-dominated lattices have a quadratic relationship (n = 2) whereas the stretching-dominated materials have a linear scaling (n = 1), which is mechanically more efficient (see ESI for details). The relative stiffness Erel and relative density ρrel are effective stiffness and effective density normalized by its bulk property, i.e. Erel = Eeff/E0 and ρrel = ρeff/ρ0, where E0 and ρ0 are stiffness and density of the constituent material, respectively. 3D printed with an SMP, the load-bearing behavior of the microlattices is determined by the unique thermomechanical properties of the SMP as well as the unit cell topology. In this work, octet-truss (OT) and tetrakaidecahedron (also known as Kelvin foam, KF) unit cells were chosen as representative unit cell topologies for stretching- and bending-dominated microlattices, respectively, as shown in Fig. 2. Four microlattices of each group were designed to have various relative densities and printed with the SMP using PμSL (see ESI for details). The samples in each group were named as OT1 ∼ OT4 and KF1 ∼ KF4, respectively.

image file: c9mh00302a-f2.tif
Fig. 2 Thermally tunable mechanical property. The stress–strain curves of (A) OT4 and (B) KF4 at five temperatures. Effective Young's modulus versus relative density of (C) OT and (D) KF microlattices on a logarithmic scale. Moduli of both OT and KF drop significantly from 30 °C to 90 °C. A linear relationship with a scaling factor of 1.2 for OT and a quadratic relationship with a scaling factor of 2.2 for KF are maintained at all temperatures. The stress–strain curves of 2 consecutive compression cycles of (E) OT2 and (F) KF2 at 30 °C and 90 °C. Scale bars in the top images of the printed microlattices are 2 mm.

To characterize the thermally tunable mechanical properties, compression tests were conducted on the printed SMP microlattices at different temperatures. Fig. 2A and B show stress–strain curves of OT4 and KF4 at 30 °C, 45 °C, 60 °C, 75 °C, and 90 °C (see ESI for the stress–strain curves for all samples). Notably, the stiffness of both microlattices dropped significantly as the temperature increased from 30 °C to 90 °C because the SMP undergoes a dramatic change in stiffness within the range of test temperatures around its Tg of 71 °C. At 30 °C, the elastic modulus obtained from the stress–strain curve was 11.6 MPa for OT4 and 7.1 MPa for KF4. At 90 °C, in contrast, they were only 0.083 MPa for OT4 and 0.042 MPa for KF4, showing more than 100 times decrease in stiffness for both cases. The stiffness was fully recovered when the temperature dropped back to 30 °C, demonstrating that the mechanical performance can be reversibly tunable. Similarly, a large modulation in stiffness was observed in all other microlattices (ESI, Fig. S4). Effective elastic moduli of all the microlattices at each temperature were plotted over relative density on a logarithmic scale in Fig. 2C and D. Not only did each sample exhibit two decades of stiffness change with temperature, but a topology-specific scaling law between the modulus and relative density was also preserved at each temperature. The scaling exponents of OT and KF microlattices were found to be about 1.2 and 2.2, respectively, which are in good agreement with the theoretical values (n = 1 for OT, n = 2 for KF). Furthermore, each group of OT and KF microlattices retained their own stretching- and bending-dominated behavior consistently throughout all temperatures while their effective moduli shifted by a factor of 100. Also noted is that the OT always outperformed KF at the same relative density, and the superior mechanical properties of OT become more prominent as the relative density decreases due to the favorable linear scaling factor of n = 1.

Inherited from their constituent SMP, the tunable mechanical metamaterials are also capable of retaining a significantly deformed temporary shape and returning to their original geometry. The shape-fixity ratio and shape-recovery ratio are two criteria to quantitatively characterize the performance of the shape memory effect. The shape-fixity ratio quantifies the ability of the SMP to fix the mechanically deformed or programmed geometry after the removal of mechanical stress, whereas the shape-recovery ratio measures the ability of the SMP to recover its initial or permanent shape.50 We performed compression tests on OT2 and KF2 at 30 °C and 90 °C, respectively, to measure the shape-fixity and shape-recovery ratios of the printed SMP microlattices (see ESI for details). During the first compression by 85% at 30 °C, both SMP microlattices showed a mechanical behavior usually found in typical lattices; linear elastic deformation, buckling, and densification.51 When unloaded, however, they stayed compressed without much elastic recovery and the shape was programmed in this state. As the second cycle of 85% compression was applied, a strain at which the compression stage made the first contact to the sample was measured to determine the shape-fixity ratio. The shape-fixity ratio at 30 °C was 71.4% for OT2 and 70.7% for KF2, respectively. In this test, a shape fixity of 71% was achieved with a fixing temperature of 30 °C and holding time of only a few seconds (Movie S1, ESI). The shape fixity can be improved if needed, by increasing the holding time or temperature during programming.52 When the temperature was raised to 90 °C, both microlattices fully recovered their original shapes, which therefore corresponds to a shape-recovery ratio of 100% for both cases. Note that the loading and unloading curves almost overlap at 90 °C, whereas huge hysteresis occurred at 30 °C in both samples. Interplay between the thermomechanical properties of SMP and structural mechanics allows a microlattice to exhibit completely different mechanical behaviors as needed. The high shape-fixity ratio and shape-recovery ratio with a large strain can be utilized to create highly programmable and deployable structures.

The tunable mechanical performance of the SMP renders the metamaterials uniquely able to alter shock absorption during an impact loading. We performed an impact test on a SMP microlattice at 30 °C and 90 °C, as illustrated in Fig. 3A. A KF microlattice with a relative density of 18.7% was placed on a rigid steel plate inside a temperature oven. An impact loading was given to the sample by dropping a metal ball on the sample at 30 °C and 90 °C, while acceleration was measured at the bottom of the rigid substrate (ESI, Fig. S5A). As clearly shown in the time-lapsed images during the impact in Fig. 3B, the deformation of the microlattice during the impact was remarkably different due to the large difference of elastic modulus. Therefore, the amount of energy absorbed in the microlattice through elastic deformation during the impact was significantly different. With the rigid effective modulus of 20.2 MPa at 30 °C (ESI, Fig. S5B), the microlattice only deformed minutely during the impact and only a small amount of energy was absorbed. As a result, a large peak acceleration of 598 m s−2 was transmitted to the substrate, as shown in Fig. 3C. In contrast, with the effective modulus shifted dramatically down to 0.17 MPa at 90 °C (ESI, Fig. S5B), the microlattice collapsed significantly upon the same impact. Therefore, a large amount of energy was absorbed in the microlattice during the impact loading, leaving only a small fraction of the energy transmitted to the substrate. As a result, a remarkably reduced peak acceleration of 14.7 m s−2 was measured at the substrate. With the tunable mechanical metamaterial, a smart lightweight protective material can be created which can adapt to varying loading conditions by switching between a rigid protective mode and a compliant shock absorbing mode on-demand.

image file: c9mh00302a-f3.tif
Fig. 3 Thermally tunable, reconfigurable, and deployable microlattices. (A) Schematic drawing of the impact test platform. (B) Time-lapsed images of the KF sample during an impact loading at 30 °C and 90 °C. Scale bars are 3 mm. (C) Acceleration measured at the substrate at 30 °C and 90 °C. (D) Reconfigurable OT microlattice. (i) The sample is in its original shape and bears a load, (ii) the sample is programmed to a different geometry and bears the same load, (iii) the sample returns to its original shape upon heating, (iv) the sample is reprogrammed to a bent configuration and still bears the same load, and (v) the sample returns to its original shape again upon heating. Scale bar is 5 mm. (E) Deployable KF microlattice. (i) The sample in its original shape (the overall thickness is larger than the inner diameter of the channel) is placed in the left compartment and bears a load, (ii) the sample is programmed to have a smaller diameter and navigates through the curved channel to move to the right compartment, (iii) the sample comes out of the channel and regains the load-bearing capability in the right compartment. Scale bar is 20 mm.

Using the shape programming and shape recovery attributes of a 3D printed SMP microlattice, we created a reconfigurable, high-stiffness mechanical metamaterial as shown in Fig. 3D. An OT microlattice with a relative density of 8% was printed and attached to a rigid substrate. In the original configuration, this highly stiff lightweight structure provided a stable support for a loading of 300 times its own weight with a small deformation of only 0.4% (microlattice: 0.8 g, load: 24 g) (Fig. 3D-i). After we reprogrammed the geometry by squeezing it in the middle at high temperature and subsequently cooling it, the structure also successfully sustained the same loading (Fig. 3D-ii). Upon heating, the original state was completely restored (Fig. 3D-iii). Next, more aggressive deformation was applied by bending the microlattice by 90° at high temperature and cooling it to reprogram this new configuration. The same high load was also very well maintained without failure in the reconfigured state (Fig. 3D-iv). Again, the original shape was completely recovered by heating (Fig. 3D-v). It should be noted that a deformed geometry is locked at room temperature, so no additional energy is needed to maintain its temporary shape. We also printed a KF microlattice with a relative density of 6.3% (Fig. 3E-i). The diagonal length of the cross-section was 8.3 mm. After being reprogrammed to a much thinner diameter, it was able to easily navigate through a narrow and curved channel (ID: 6.35 mm) which it would not be able to pass through with its initial geometry (Fig. 3E-ii). Furthermore, the microlattice regained its structural property upon shape recovery and became fully functional to again withstand a mechanical loading (Fig. 3E-iii). These demonstrations show that the mechanical metamaterials can be transformed into various configurations and be deployable upon heating while maintaining superior mechanical performance.

Since the tunability of the metamaterials emerges from the temperature-responsive viscoelastic behavior of the SMP, the response time of the tunable metamaterials is determined by the time needed to reach a thermal equilibrium and the time for viscoelastic relaxation of the SMP. For the mechanical property modulation without shape reconfiguration, the response time is simply determined by thermal equilibrium. On the other hand, for shape reconfiguration where a large deformation is involved, viscoelastic relaxation time needs to be also considered. Using a linear viscoelastic model and time-temperature superposition principle, viscoelastic relaxation time for different thermal conditions can be obtained (details in ESI).52 Furthermore, by incorporating the modulus of the SMP obtained from the viscoelastic model, modified effective modulus microlattice models of OT and KF (eqn (18) and (19) in ESI, respectively) were obtained to capture the thermo-temporal mechanical tunability of the metamaterials. Details of viscoelastic modeling and analysis are discussed in the ESI. It is worth noting that the thermal equilibrium time is proportional to the strut radius because the characteristic time scale of heat transfer scales linearly with the characteristic length scale,53 whereas viscoelastic relaxation time is independent of dimension since it arises from the intrinsic material property of the SMP (details in ESI).


In summary, we demonstrated geometrically reconfigurable, functionally deployable, and mechanically tunable lightweight metamaterials using 4D printing. Within a range of temperatures from 30 °C to 90 °C, the effective stiffness of the printed lattices changed by over two orders of magnitude. The characteristic scaling laws for stretching- and bending-dominated unit cell topology were still preserved during this dramatic material property change. The tunable impact-absorption capability, reconfigurability, and deployability of the lightweight SMP microlattices were also demonstrated. Our lightweight SMP microlattices have unprecedented capability of mechanical adaptation to unpredictable circumstances such as varying external loading and geometrically complex environments. The reconfigurable and tunable mechanical metamaterials may find a broad range of applications such as tunable shock absorbing interfaces, morphing aerospace structures, and minimally invasive biomedical devices.

Conflicts of interest

There are no conflicts to declare.


This work was supported by Rutgers University through the School of Engineering and the Department of Mechanical and Aerospace Engineering, Defense Acquisition Program Administration and Agency for Defense Development (UD150032GD), and Haythornthwaite Foundation Research Ignition Grant. R. M. acknowledges support from Rutgers University Mechanical and Aerospace Engineering and New Jersey Space Grant Consortium (RUMAE-NJSGC) Summer Research Cluster. The authors would like to thank Professor Edward DeMauro for the permission to use the high-speed camera and Professor Ashutosh Goel for the permission to use the FTIR.

Notes and references

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Electronic supplementary information (ESI) available. See DOI: 10.1039/c9mh00302a

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