soft mechanical metamaterials with unusual swelling behavior … · posites can be designed to...

SC I ENCE ADVANCES | R E S EARCH ART I C L E

MATER IALS SC I ENCE

1Applied Mechanics Laboratory, Department of Engineering Mechanics, TsinghuaUniversity, Beijing 100084, P.R. China. 2Center for Mechanics and Materials and Centerfor Flexible Electronics Technology, Tsinghua University, Beijing 100084, P.R. China.3Institute of Advanced Structure Technology, Beijing Key Laboratory of LightweightMulti-Functional Composite Materials and Structures, Beijing Institute of Technology,Beijing 100081, P.R. China.*Corresponding author. Email: [email protected] (D.F.); [email protected] (Y.Z.)

Zhang et al., Sci. Adv. 2018;4 : eaar8535 8 June 2018

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Soft mechanical metamaterials with unusual swellingbehavior and tunable stress-strain curvesHang Zhang1, Xiaogang Guo1,2, Jun Wu1, Daining Fang3*, Yihui Zhang1,2*

Soft adaptablematerials that change their shapes, volumes, and properties in response to changes under ambientconditions have important applications in tissue engineering, soft robotics, biosensing, and flexible displays.Upon water absorption, most existing soft materials, such as hydrogels, show a positive volume change, correspond-ing to apositive swelling. By contrast, the negative swelling represents a relatively unusual phenomenon that does notexist inmost natural materials. The development ofmaterial systems capable of large or anisotropic negative swellingremains a challenge. We combine analytic modeling, finite element analyses, and experiments to design a type of softmechanical metamaterials that can achieve large effective negative swelling ratios and tunable stress-strain curves,with desired isotropic/anisotropic features. This material system exploits horseshoe-shaped composite microstructuresof hydrogel and passive materials as the building blocks, which extend into a periodic network, following the latticeconstructions. The building block structure leverages a sandwiched configuration to convert the hydraulic swelling de-formations of hydrogel intobendingdeformations, thereby resulting in an effective shrinkage (up to around−47% linearstrain) of the entire network. By introducing spatially heterogeneous designs, we demonstrated a range of unusual,anisotropic swelling responses, including those with expansion in one direction and, simultaneously, shrinkagealong the perpendicular direction. The design approach, as validated by experiments, allows the determination oftailored microstructure geometries to yield desired length/area changes. These design concepts expand the capa-bilities of existing soft materials and hold promising potential for applications in a diverse range of areas.

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INTRODUCTIONDevelopment of soft adaptable materials that change their propertiesand performances in response to changes under ambient conditions isof growing interest in recent years, due to their applications in tissueengineering (1, 2), soft robotics (3–6), biosensing (7, 8), and flexibledisplays (9–11). To design these soft responsive materials, variousactivematerials have been exploited, including hydrogels (12–16), shapememory polymers (17–20), and liquid crystal elastomers (21, 22). Theresulting composite systems are capable of responding to well-definedexternal stimuli such as ionic concentration, heat, pH, and light (23–29).In particular, the material systems that incorporate hydrogels as theactive components are very attractive due to the superior biocompatibil-ity and high level of swellability [for example, up to 1000-fold when im-mersed in certain solvents (30, 31)]. Their programmable large swellingscan be used in a diversity of environmentally responsive devices [forexample, microfluidic valves (32, 33) and artificial muscles (34, 35)]. Theexisting studies mainly focused on the positive swelling behavior (thatis, corresponding to a positive volume change during water absorption)as a means to achieve desired shape programming or other functional-ities. By contrast, the negative swelling behavior (that is, correspondingto a negative volume change during water absorption) represents a rela-tively unusual phenomenon that does not exist inmost natural mate-rials. This unusual behavior, similar to negative thermal expansion(36–44), can be used to systematically control the changes in length,area, and volume, in combination with the traditional positive swell-ing behavior. Capabilities of hydrogel-based systems for large revers-

ible expansion/shrinkage are also attractive for a variety of potentialapplications, such as drug delivery, biocompatible stents, molecularsieves, andmoisture/pH sensors. Despite its potential, the developmentof material systems that can achieve a large negative swelling remains achallenge, and very limited designs can be found in literature (45). In par-ticular, no strategy has been reported to achieve large, anisotropic, neg-ative swelling on demand.

Here, we introduced a class of soft mechanical metamaterials thatcan achieve large effective negative swelling ratios, with desired isotropic/anisotropic features. The design concepts incorporate horseshoe-shapedsandwichmicrostructures originally developed for stretchable electronics(46, 47) into periodic networks related to those proposed for lightweight,loading-bearing structures (48, 49). Inspired by Lakes and colleagues’seminar works on the designs that rely on bending bilayer bars to achievenegative thermal expansion (37, 43), the horseshoe-shaped sandwichmicrostructure designed herein can effectively convert a hydraulic swellingdeformation of hydrogel into a bending deformation and, thereby, ashrinkage or an amplified expansion of the entire network. Since thisnetwork design does not involve any instabilities, it is different fromthe design adopted by Liu et al. (45) that leverages buckling to enabletunable negative swelling ratios. During the shrinkage of the networkmetamaterial, the horseshoemicrostructure pattern is also able to makemore efficient use of the space without interacting with the neighboringmicrostructures, as compared to the arc pattern (similar to half of a si-nusoidal wave) that may appear during buckling. By using validateddesign tools based on the computational mechanics, these networkcomposites can yield a wide range of desired swelling responses, includ-ing some unusual behavior, such as a concurrent expansion along a di-rection and shrinkage along the perpendicular direction. A systematiccomparison to the existing soft materials illustrates the powerful capa-bility of the proposed design concepts. Furthermore, these network com-posites can be designed to offer a variety of tunable stress-strain curves,which has important utilities in deployable antennas and soft robotics toactively control their configurations and/or motions.

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RESULTSFigure 1 presents a schematic illustration of the design strategy andfabricated samples. Here, the material system is constructed in a pe-riodic two-dimensional (2D) triangular lattice configuration, inwhich the filamentary, horseshoe composite microstructures of hy-drogel and passive materials serve as the building blocks. This type ofreconfigurable, network composite material can be fabricated usingthe techniques ofmultimaterial 3Dprinting (seeMaterials andMethodsfor details), similar to the concepts of 4D printing (50–52). Thehorseshoe-shaped microstructure consists of two identical circulararcs, with an arc angle of q and a radius of r, as shown in Fig. 1B. Eacharc segment has a sandwich structure (see fig. S1A for more details) ofa supporting layer (a digital polymeric material, ~65 MPa; RGD8530,Stratasys; in blue; width W1), an active layer (a hydrogel, ~0.2 MPa;SUP705, Stratasys; in red; widthW3), and an encapsulation layer (anelastomer, ~0.5 MPa; TangoBlackPlus, Stratasys; in green; widthW2). Here, a thin encapsulation layer (90 mm in width) serves to main-tain a well-bonded interface of the hydrogel layer and the supportinglayer during the swelling and deswelling processes. Small holes ar-ranged on top of the encapsulation layer allow water (or other solutions)to flow in and out, similar to the design adopted by Mao et al. (19, 20).The horseshoe-shaped sandwich microstructure can be representedmainly by four nondimensional parameters, including the arc angleq, width ratio W2/W1, normalized width W1/r, and length ratio (s/rq)of the active layer to the supporting layer, as long as the width of theencapsulation layer is fixed in the design. By tuning these designparameters, the middle of the hydrogel layer can be well separatedfrom the neutral mechanical plane of the sandwich structure suchthat the hydraulic swelling deformations of hydrogel can be con-verted into the bending deformations. Additional details of a specificexample that illustrate this mechanism appear in fig. S2. Both an effec-tive shrinkage and expansion of the entire network material are pos-sible with this mechanism, depending on the magnitude of the arcangle and the placement of the active layer relative to the supportinglayer (fig. S1B).

Figure 1 (C and D) demonstrates a representative network com-posite material that can achieve a reversible negative swelling, with afractional area change up to ~70% (and a relative length change upto ~45%). This design adopts a straight microstructure (q = 0°) suchthat the bending deformations can induce a relatively large change ofthe end-to-end distance. When the network material is immersed inwater, the hydration process begins to expand the hydrogel layer. Be-cause of an offset (~420 mm) of the neutral mechanical plane with re-spect to the middle of the hydrogel layer, a considerable bendingdeformation is evident, reshaping the straight microstructure intothe horseshoe geometry and resulting in shrinkage of the networkmaterial. As the hydration proceeds, this level of shrinkage increasesuntil the hydration time reaches ~45min, at which point the horseshoemicrostructures begin to contact each other. As the saturated networkmaterial is put in a drying oven maintained at 75°C, the hydrogel de-swells gradually due to the water evaporation. After dehydration for~35 min, the network material recovers almost completely. Figure 1Dpresents the effective strain components (ex-swelling and ey-swelling) of thenetwork material that quantify the shrinking deformations duringthe processes of hydration and dehydration. The slight deviation be-tween the responses of ex-swelling and ey-swelling results mainly fromthe PolyJet 3D printing techniques that cause slightly differentmechanical properties between the microstructures aligned hori-zontally and those aligned diagonally. After dehydration for ~40 min,


the residual strain is below ~5%, indicating relatively good revers-ibility, consistent with the results on a single straight microstruc-ture (fig. S2). Quantitative mechanics modeling based on the finiteelement analyses (FEA; see Materials and Methods for details) al-lows the prediction of the deformed configurations at different stagesof hydration and dehydration, as shown in Fig. 1C. The detailedstrain distribution and deformations of a representative unit cell ofthe network material are shown in fig. S3. The high strains occurmainly at the hydrogel layer and the encapsulation layer, while themaximum strains of the supporting layer are typically below ~3%,thereby ensuring the integrity of the lattice network. Quantitativeagreements of the computational and experimental results can be ob-served (Fig. 1, C and D), suggesting the FEA-based modeling as aneffective tool to guide the microstructure design for achieving desiredswelling ratios.

Because of the capability of altering the microstructure geome-tries (Fig. 1C), the mechanical properties of the network materialcan be tuned continuously by controlling the time of water absorption.As an example, Fig. 1 (E and F) presents the stress-strain curves of theabove design after water absorption for different times. Without anywater absorption, the network material, consisting of straight micro-structures, undergoes stretching-dominated deformations under a uni-axial stretching, leading to a relatively linear stress-strain response. Afterwater absorption (for example, for 45 min), the network material withreshaped horseshoemicrostructures undergoes bending-dominated de-formations at the initial stage of uniaxial stretching, as shown in Fig. 1Gand fig. S4. The stress thereby increases slowly with increasing strainduring this stage. As the horseshoe shapes begin to reach full ex-tension (~65% strain), the slope of the stress-strain curve increasesrapidly due to the transition into a stretching-dominated deforma-tion mode. This leads to a J-shaped, nonlinear stress-strain responsethat widely exists in biological materials (for example, human skinsand heart valves) (53, 54). The complete extension of the horseshoemicrostructures typically defines a critical strain (ecr) that marks thetransition point of the J-shaped stress-strain curves. As shownby Fig. 1E,the J-shaped stress-strain curves can be effectively tuned by controllingthe time of water absorption. As the saturated network material ex-periences the dehydration process, the stress-strain curve moves left-ward gradually until the J shape vanishes, indicating a good recovery.FEA can capture the tunability of the stress-strain response in a quan-titative manner, as evidenced by the reasonably good correspondencewith experiments (Fig. 1F).

Because of the design flexibility enabled by tailoring the micro-structure geometries, the above network composite design providesan ideal platform to offer desired swelling ratios in a wide range. Figure 2summarizes a collection of theoretical and experimental results thatelucidate the effects of three dominant design parameters, includ-ing the arc angle q, width ratio W2/W1, and length ratio s/rq. Forrelatively slender horseshoe microstructures, we develop a mechan-ics model that simplifies the sandwich microstructures as planarbeams consisting of only the supporting layer (W1) and the activelayer (W2), with a negligible stiffness contribution from the soft,thin encapsulation layer. Assuming planar cross-sections duringdeformation, the theory of composite beam (see SupplementaryMethods and fig. S5 for details) shows that the curved beam (withcurvature radius r) maintains an arc shape, as the active layer un-dergoes a swelling ratio (ehydrogel). Because of the strain mismatchbetween the active layer and the supporting layer, the arc radiuschanges to rdeformed and is solved as

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0 0.2 0.4 0.6 0.80

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Polymer(RGD8530)

Hydrogel(Sup705)

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Initial state Hydration 15 min Hydration 30 min Hydration 45 min Dehydration 15 min Dehydration 35 min

x

y

0 20 40 60 80 100 120Time (min)

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3.5Hydration DehydrationHydration (FEA)

Dehydration (FEA)Hydration (Exp)Dehydration (Exp)

Fig. 1. Design concepts of softmechanicalmetamaterialswith large negative swelling ratios and tunable stress-strain curves. (A) Schematic illustration of soft networkcomposite design, with inset denoting a representative unit cell. (B) Cross-sectional view and exploded view of sandwiched horseshoe microstructure consisting ofsupporting layer (RGD8530; in blue), active layer (SUP705; in red), and encapsulation layer (TangoBlackPlus; in green). The two images at the bottom illustrate a cartoonof the designed microstructure and corresponding image of a 3D-printed sample. (C) Experimental (top) and computational (bottom) results on the evolving configura-tions of a representative network material during the hydration and dehydration processes. The design parameters are the arc angle q = 0°, width ratio W2/W1 = 2.5,normalized widthW1/r = 0, and length ratio s/rq = 0.67. (D) Swelling-induced strain components as a function of processing time for the networkmaterial in (C). (E) Measuredstress-strain curves of the network materials in (C) at different stages of hydration and dehydration. Square and triangular symbols denote the results during hydration anddehydration, respectively. (F) Calculated stress-strain curves of the network materials at different stages of hydration, in comparison to experimental results. (G) Experimental(top) and computational (bottom) results on the deformation sequences of a hydrated (~45min) networkmaterial under a uniaxial stretching. Scale bars, 5mm (B) and 40mm(C and G).

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rdeformed ¼1þ E2

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where E1 and E2 are the elastic moduli of the supporting layer and theactive layer, respectively (see Supplementary Methods for details).Without any self-contact of microstructures, the effective strain of thenetwork material induced by the swelling of hydrogel layer can then beobtained as

ex‐swelling ¼ ey‐swelling

¼

ðstotal � sÞcos ls2rdeformed

� �þ 2rdeformed sin

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where stotal is the half-length of the straight microstructure in the limitof q = 0°, and l is the stretch ratio at the middle axis of the supportinglayer covered with hydrogel, as given by

l¼1þ E2

E1

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The isotropic strain response arises from the homogeneous micro-structure design. Figure 2A and fig. S5 show that the analytic solution(Eq. 2) corresponds reasonably closely to the results of FEA and exper-iment on the effective strain of the network material for a wide range ofarc angle q and length ratio (s/rq). In Fig. 2A, the dimensionless swellingratio �ehydrogel denotes the linear strain ehydrogel normalized by the value(0.21) at a nearly saturated state of the hydrogel. The negative arc anglerepresents the placement of the active layer to the inner side of the sup-porting layer, as opposed to the case of positive arc angle discussed above(fig. S1B). A distinct swelling behavior is evident for different arc

= −220° 98.0%D

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FEAModelExperiment

= 0° = −220°

Fig. 2. Large isotropic swelling and dependence on the microstructure geometries. (A) Results of experiments (square symbols), FEA (solid lines), and theoretical model(hollow circles) on swelling-induced strains versus the dimensionless swelling ratio �ehydrogel of the hydrogel, for networkmaterials with fixed s/(rq) = s0.67 andW2/W1 = 2.5, and sixdifferent arc angles (q). The sudden plateau in the cases of q = 90° and 180° results from self-contact of microstructures during the shrinkage. (B and C) FEA results on thedistribution of swelling-induced strains at �ehydrogel ¼ 1 over a wide range of length ratios [s/(rq)] and width ratios (W2/W1) for two representative arc angles (q = −220°and 0°). (D) Optical images and FEA results of the configurations at the initial, intermediate, and final states of hydration for the network material with q = −220° as in (A).(E and F) Similar results for two different network materials (with q = −90° and 0°) in (A). Thickness (that is, the dimension along the out-of-plane direction) is fixed at 3.18 mm inthese analyses. Scale bars, 20 mm.

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angles, as shown in Fig. 2 (D to F). Specifically, for q = −220°, a largepositive swelling ratio (linear strain of up to ~98%) can be achieved byexpanding the horseshoemicrostructures with water absorption, as evi-denced by the deformed configurations (Fig. 2D) from both the exper-iment and the FEA. For q = −90°, the network material undergoes anexpansion at the initial stage of hydration, and the associated swellingratio (ex-swelling) increases to approach a peak value (10.8%) at the di-mensionless swelling ratio of �ehydrogel ¼ 0:42. Beyond this critical point,the swelling ratio (ex-swelling) decreases with further water absorptionand becomes negative at �ehydrogel ¼ 0:74. At the state of �ehydrogel ¼ 1,the shrinkage reaches its maximum, corresponding to a negative swell-ing ratio of ex-swelling = −4.3% based on FEA (and −5.1% based on theexperiment). This represents an unusual type of swelling behavior—expanding first and then shrinking during hydration. For q = 0°, as dis-cussed in Fig. 1, the straight microstructures enable a large negativeswelling (ex-swelling = −47.8 and −47.1% based on FEA and the experi-ment, respectively). Further increase of the arc angle (for example, toq = 90° or 180°) leads to a reduced negative swellability, as shown inFig. 2A, due to the self-contact of microstructures that occurs at an ear-lier stage of hydration (fig. S6). In the examples studied here, the net-work designs with q = −220° and 0° offer the largest expansion andshrinkage, respectively, and both show a monotonous dependence onthe swelling ratio (�ehydrogel) of hydrogel.

Figure 2 (B and C) highlights the effect of length ratio (s/rq) andwidth ratio (W2/W1) on the swellability of two representative networkdesigns (q = 0° and −220°), as characterized by the effective strain at�ehydrogel ¼ 1. Both figures show an increased magnitude of effectivestrain (that is, |ex‐swelling|) at a larger length ratio (s/rq). For a givenlength ratio (for example, s/rq = 0.67), the magnitude of effective strainusually increases first with increasing width ratio (W2/W1) because theactuation force increases, as shown in Fig. 2B for the designwithq =0°. Ata critical width ratio (W2/W1 ≈ 3.2 in Fig. 2B), the magnitude of ef-fective strain ex-swelling reaches a peak, after which |ex‐swelling| decreases.This can be attributed to the reduced offset of the neutral mechanicalplane relative to the middle of the hydrogel layer, with the furtherincrease of the width ratio beyond W2/W1 = 3.2. Because of thismechanism, we observed an optimal value of width ratio (W2/W1)independent of the length ratio (s/r q) (Fig. 2B), which can maximizethe shrinkage of the network material. A similar dependence can bealso found for the design with q = −220° (Fig. 2C). According to thesedependences, we can expect a reduced swellability with an increasingfilling ratio of the cellular network material or equivalentlydecreasing the porosity. For the design with straight microstructures(that is, q = 0°) and fixed length ratio (s/stotal = 0.75), the magnitudeof swelling-induced strain decreases gradually from ~47.2% to 11.0%(and to 3.5%), as the filling ratio (defined on the basis of the un-deformed configuration) increases from 5% to 12.5% (and to 22.5%)(fig. S7).

Excluding the isotropic expansion/shrinkage during water absorp-tion, anisotropic swelling/deswelling is also achievable by exploitingheterogeneous horseshoe microstructures in the representative unit cellof network materials. By simply tailoring the selections of length ratio(s/rq) and arc angle (q) for the differently oriented horseshoe micro-structures, a variety of usual swelling responses can be accessed. Figure 3and figs. S8 to S10 demonstrate a representative collection of examplesdesigned for this purpose. In particular, Fig. 3A presents the swellingpath in the space of strain components (ex-swelling and ey-swelling) forour designednetworkmaterials, in comparison to the traditional hydro-gels (31), polymers (55), and elastomers (56), as well as a buckling-


guided metamaterial design (45). The traditional soft materials (for ex-ample, elastomers, polymers, and hydrogels) usually offer an isotropicpositive swelling, with the linear expansion strain that can exceed 150%for specially designed hydrogels (31). In terms of the isotropic negativeswelling, the materials presented here can reach a linear strain of −48%,exceeding that (−16%) reported previously (45). In terms of the aniso-tropic swelling, the traditional composite materials are typically con-strained by the swellability of the constituent materials, which givelimited levels of responses. By contrast, the current network design, be-cause of the versatile flexibility, is able to offer a diversity of anisotropicswelling responses, including some unusual behavior (for example,expanding along one direction while shrinking along the perpendic-ular direction). Figure 3B shows an example that shrinks only alongthe horizontal direction (x) during hydrationwhile staying undeformedalong the perpendicular direction (y). This is achieved by using hydrogellayers only at the two diagonally oriented horseshoemicrostructures andthickening the vertically oriented microstructures to suppress the de-formations along this direction. More details of this design are in fig.S9A. Anisotropic negative swelling is also possible (Fig. 3C and fig.S9B) by exploiting different length ratios (s/r q = 0.67 versus 0.25)for the differently oriented microstructures. In this example, the ratio(Ky/x = ey-swelling/ex-swelling) is maintained at approximately 0.27 duringthe entire process. Figure 3D illustrates a network material designedto respond to water absorption in the form of expansion along the y di-rection and shrinkage along the x direction. Here, the hydrogel layersare adopted only at the horizontally orientedmicrostructures, such thata lateral expansion can be achieved through a rotation of the passivecomponents oriented diagonally (see fig. S9C for details). Figure 3Epresents another type of design to offer a similar response through dis-tinct placements of the hydrogel layer relative to the supporting layer atthe different microstructures (see fig. S9D for details). In this example,the ratio (Ky/x) of swelling-induced strains varies considerably duringthe deformation process. Additional examples that offer anisotropicpositive swelling ratios are provided in figs. S8 and S10. In all of theabove cases, FEA results correspond well with the experimental mea-surements (figs. S9 and S10). Excluding the above experimental demon-strations as summarized in Fig. 3A, the proposed network design is alsoable to cover most of the blank spaces between the plotted red curves,thereby substantially expanding the accessible regime of existing softmaterials in the space of swelling ratios ex-swelling and ey-swelling.

Because of the versatile control of the microstructure geometriesthrough water absorption, a systematic tunability of the stress-straincurve is achievable, taking into account the responses along two prin-cipal directions simultaneously. Figure 4A shows a network materialthat becomes softer as the hydration proceeds. The J-shaped stress-strain curves shift rightward nearly at the same pace for the uniaxialstretching along the x and y directions (Fig. 4, B and C, and fig. S11).The elastic modulus at the infinitesimal deformations decreases bynearly three orders ofmagnitude from the dry state to the hydrated state(fig. S12A). The critical strains (ecr-x and ecr-y) that mark the transitionpoint of the J-shaped stress-strain curves can be tunedwell by controllingthe time of hydration (fig. S12B). In contrast to the case of x-directionalstretching, the diagonally oriented horseshoe microstructures serveas the main load-bearing components for the y-directional stretching,as shown by the deformation sequences in Fig. 4 (B and C). Figure 4Dpresents a network material that expands along the x direction andshrinks along the y direction during hydration, similar to the designin Fig. 3E. As a result, the stress-strain curve along the x directionmovesrightward, while the one along the y direction moves leftward, as

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hydration proceeds, as shown by the FEA calculations and experi-ments (Fig. 4D, middle and right). This indicates a decrease of elasticmodulus Ex and critical strain ecr-y, as well as an increase of Ey andecr-x (fig. S12, C and D). Figure 4E demonstrates another type of me-chanical tunability by exploiting the network designs (as in Fig. 3C)withan anisotropic negative swelling. The resulting stress-strain curvesmove rightward for both the x and y directions, but at different rates(fig. S12, E and F).


DISCUSSIONIn summary, the design concepts, fabrication techniques, and quantita-tive design methods reported here provide access to soft mechanicalmetamaterials that can achieve large effective negative swelling ratiosand tunable stress-strain curves, with desired isotropic/anisotropic fea-tures. The demonstrated unusual swelling behaviors encompass atransition from expansion to shrinkage during hydration and a con-current expansion along a direction and shrinkage along perpendicular

0 0.2 0.4 0.6 0.8 1−0.6

0

0.2

−0.4

C

x direction

y direction

Ky/x

−0.2

0.4

0 0.2 0.4 0.6

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in (

x-s

wel

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x direction

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x direction

y direction

Ky/x

-0.5

0

0.5

1.0

-0.5 0 0.5 1.0 1.5

1.5Previous metamaterial design (Ref. [45])

Representative elastomers (Ref. [55])

Representative hydrogels (Ref. [31])Our work

A

Stra

in (

y-s

wel

ling)

Strain (x-swelling)

Dimensionless swelling ratio of hydrogel ( )hydrogel

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x direction

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x

y

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Representative polymers (Ref. [56])

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ling ,

y-s

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Dimensionless swelling ratio of hydrogel ( )hydrogel Dimensionless swelling ratio of hydrogel ( )hydrogel Dimensionless swelling ratio of hydrogel ( )hydrogel

Fig. 3. Strategic heterogeneous designs for large anisotropic swellings. (A) Swelling path illustrated in the space of strain components (ex-swelling and ey-swelling) fornetworkmaterials designed in the current work, as compared to traditional soft materials [elastomers (55), polymers (56), and hydrogels (31)] and ametamaterial design reportedpreviously (45). (B) Measured and computed swelling-induced strain components (ex-swelling and ey-swelling) for a design that shrinks only along the x direction and stays almostundeformed along the y direction during hydration. Images on the bottom represent configurations at the initial and final states of hydration. (C) Similar results for a design thatshrinks along both the x and y directions during hydration, but at different rates. (D and E) Similar results for two designs that shrink along the x direction and expand along the ydirection during hydration. Solid lines and square symbols denote FEA and experiment results, respectively. Scale bars, 20 mm.

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direction. The validated design methods allow the determination of tai-lored microstructure geometries to yield desired length/area changes.The proposed network design is basically scale-free, but fabricationcapabilities set the size limit of the network materials. The commercialmultimaterial PolyJet 3D printer, which we used in the current work,offers a minimum layer thickness of 30 mm during 3D printing, which


sets the limit of width (W3 = 90 mm) for the encapsulation layer, since afew layers are required to form a relatively reliable structure. A good neg-ative swelling can be observed when the design in Fig. 2F is scaled downby a factor of 0.6 (fig. S16). To fabricate even smaller network materialswith similar swelling performances, other advancedmanufacturing tech-niques [for example, multimaterial projection microstereolithography

A

D

E

B C

0 0.2 0.4 0.6Strain (

x-appl)

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y-appl)

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ss (

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0

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x-appl = 0.42x-appl = 0.7

x-appl = 0y-appl = 0.37

y-appl = 0.68y-appl = 0

x

y

y

x

Fig. 4. Tunable stress-strain curves. (A) Schematic illustration of a network design with isotropic swelling (left) and uniaxial stress-strain curves along the x and y direc-tions (middle and right) for the material at different stages of hydration (�ehydrogel = 0.0, 0.5, 0.7, and 1.0). (B and C) Optical images that show deformation sequences of ahydrated (�ehydrogel = 1.0) network material under uniaxial stretching along the x and y directions. (D and E) Schematic illustration of two network designs with anisotropicswelling and uniaxial stress-strain curves along the x and y directions for thematerial at different stages of hydration [�ehydrogel = 0.0, 0.2, 0.4, and 0.6 in (D) and �ehydrogel = 0.0,0.4, 0.6, and 0.8 in (E)]. In (A), (D), and (E), solid lines and square symbols denote FEA and experiment results, respectively. Scale bars, 40 mm (B and C) and 20mm (all of theother images).

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(44)] should be exploited. Considering the bottom-up feature of the pro-posed metamaterial design that builds on the horseshoe-shapedcomposite microstructures, it can also be extended to other 2D (for ex-ample, square, Kagome, honeycomb, etc.) or 3D (for example, tetra-hedral, octahedral, etc.) networks. The tunable stress-strain curvescan be used to achieve structures with varying stiffness, which canpotentially be exploited in deployable antennas and soft roboticsto actively control their configurations and/or motions. Collectively,the findings reported here open opportunities for the design of struc-tures that can achieve targeted length/area/volume changes, as requiredfor applications in aerospace (57), optical (58), and microelectronicareas (59).


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MATERIALS AND METHODSFabrication of the network materialsAll of the network materials in this work were fabricated using the multi-material PolyJet 3D printing technique (Objet350, Stratasys). The threedifferent materials (RGD8530, TangoBlackPlus, and SUP705) used inthe fabrication were all available from the multimaterial 3D printer(Object 350, Stratasys). Of these materials, TangoBlackPlus is a softelastomer (~0.5 MPa; see the stress-strain curve in fig. S13A) that mainlyconsists of exo-1,7,7-trimethylbicyclo[2.2.1]hept-2-yl acrylate and photo-initiators. RGD8530 is a kind of digital polymeric material (~65 MPa;see the stress-strain curve in fig. S13B) mixed by TangoBlackPlus andVeroWhite, a rigid polymer mainly consisting of exo-1,7,7-trimethylbicyclo[2.2.1]hept-2-yl acrylate, tricyclodecane dimethanol diacrylate, tita-nium dioxide, and photoinitiators. Both TangoBlackPlus and RGD8530can be cured by ultraviolet light at room temperature. SUP705 is a hy-drogel material (~0.2 MPa; saturated linear swelling strain of ~21%)that can swell when immersed in water (19). It is composed of poly(oxy-1,2-ethanediyl), a-(1-oxo-2-propenyl)-w-hydroxy-1,2-propyleneglycol, polyethylene glycol, glycerin, phosphine oxide, phenylbis(2,4,6-trimenthylbenzoyl)-, and acrylic acid ester.

Measurements of stress-strain curves and swelling ratiosThe hydration process was carried out at room temperature, with thehydration level controlled by the time of water absorption. The dehy-dration process was carried out in a drying oven (with air environment)maintained at 75°C. The photographs of the specimens at differentstages of hydration and dehydration were recorded using a digital cam-era (760D, Canon), from which the effective swelling ratios of thenetwork materials can be determined. The stress-strain curves weremeasured in the air environment using a commercial mechanical test-ingmachine, after the sampleswere taken from thewater. A low loadingrate (2 mm/min) was adopted to ensure that the deformations werenearly quasi-static and that the viscoelastic effect could be neglected.Since most of the mechanical testing was finished within an hour, thedeswelling deformations induced by water evaporation were negligiblein such a short time (fig. S14). Most of the experiments were performedon approximately three different samples for each design, and we ob-tained consistent results.

Finite element analysesThe commercial software ABAQUS (SIMULIA) was used to carry outthe FEA, in which the implicit solver was used to calculate the deforma-tions and stress-strain curves. The geometrical nonlinearitieswere takeninto account in the FEA. Eight-node linear hybrid brick elements withreduced integration were adopted, with refined meshes to ensure com-


putational accuracy. Because of the relatively small thickness of thesupporting layer as compared to the entire sandwich structures, thestrains were typically quite small (for example, <3%) in the supportinglayer (RGD8530) such that a linear elastic constitutive relation can beused in the FEA for simplicity. TheYoung’smodulus (ERGD8530 = 65MPa)and Poisson’s ratio (nRGD8530 = 0.4) were determined by mechanicaltesting. For the encapsulation layer (TangoBlackPlus), aMooney-Rivlinhyperelastic constitutive relationwith a Poisson’s ratio of ~0.5 was used,and the uniaxial stress-strain curve measured in the experiment (fig.S13B) was imported in the simulations. The hydrogel layer (SUP705)was simplified as a linear elastic solid with an isotropic swelling, and thematerial constants included the Young’s modulus ESUP705 = 0.2 MPaand Poisson’s ratio nSUP705 = 0.5. To simulate the hydration process ofthe network material, an equal triaxial swelling strain was applied to thehydrogel layer to calculate the deformed configurations. The time-evolving swelling ratio of the hydrogel material after water absorp-tion was determined according to the experimental and FEA resultsof deformation history in a straight sandwich microstructure (fig.S2). On the basis of the deformed configurations at different stagesof hydration, a uniaxial stretching was then applied to the rectangular-shaped specimens of network material with the same geometry as thatin the experiment to calculate the stress-strain curve. Note that a hyper-elastic constitutive model can capture the mechanical responses of thehydrogel layermore accurately. A set of FEA that adopted theMooney-Rivlin law (with parameters C10 = 0.031, C01 = 0.0077, and D1 = 0 inABAQUS) to model the hydrogel layer served as a reference for com-parison. The results (fig. S15) showed that the magnitudes of swelling-induced strains based on the hyperelastic model were slightly lowerthan the results based on the linear-elastic model for two representa-tive designs. These slight differences can be attributed to the relativelylow levels of strain in most regions of hydrogels during deformation.

SUPPLEMENTARY MATERIALSSupplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/6/eaar8535/DC1Methods: Mechanics model of the swelling-induced deformationsfig. S1. Illustration of the sandwich configuration and two different placements of the hydrogellayer relative to the supporting layer.fig. S2. Deformations of a straight sandwich structure during the hydration and dehydrationprocesses.fig. S3. Distribution of the maximum principal strain for a representative unit cell of thenetwork material at the different stages of hydration and dehydration processes,corresponding to the different states shown in Fig. 1C.fig. S4. Distribution of the maximum principal strain for the network structure at the differentstages of uniaxial stretching, corresponding to the different states shown in Fig. 1G.fig. S5. Illustration of the mechanics model of the swelling-induced deformations and resultson the swelling-induced strains.fig. S6. Deformations of the network materials during hydration.fig. S7. Effect of the filling ratio on the swelling-induced strains of the network materials withstraight microstructures (that is, arc angle q = 0°).fig. S8. Soft network materials with anisotropic positive swelling ratios.fig. S9. FEA and experiment results on the swelling-induced deformations for the four designsin Fig. 3 (B to E).fig. S10. FEA and experiment results on the swelling-induced deformations for the two designsin fig. S8.fig. S11. Experimental (left) and computational (right) results on the deformation sequences ofa hydrated (~45 min) network material under a uniaxial stretching along the y direction, as inFig. 4C.fig. S12. Tunable elastic modulus and critical strain of the soft network materials.fig. S13. Measured mechanical properties of the constituent materials.fig. S14. Measured configurations of a representative network sample (that is, the initial stateof Fig. 1G) after it was taken from the water and put in the air environment under a naturalconvection condition for 0, 30, and 60 min.

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fig. S15. Computed swelling-induced strain (ex-swelling or ey-swelling) versus the dimensionlessswelling ratio of the hydrogel.fig. S16. Experimental demonstration of the network materials with two different scaling factors,with the sample in Fig. 2F to serve as a reference.


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AcknowledgmentsFunding: Y.Z. acknowledges the support from the National Natural Science Foundation ofChina (grant nos. 11502129 and 11722217), the Thousand Young Talents Program of China,


and the Tsinghua National Laboratory for Information Science and Technology. Authorcontributions: Y.Z. and D.F. designed and supervised the research. H.Z. led the mechanicsmodeling and experimental work with assistance from X.G. and J.W. Y.Z., H.Z., and D.F.wrote the manuscript and designed the figures. All authors commented on the manuscript.Competing interests: The authors declare that they have no competing interests. Dataand materials availability: All data needed to evaluate the conclusions in the paper arepresent in the paper and/or the Supplementary Materials. Additional data related to this papermay be requested from the authors.

Submitted 23 December 2017Accepted 26 April 2018Published 8 June 201810.1126/sciadv.aar8535

Citation: H. Zhang, X. Guo, J. Wu, D. Fang, Y. Zhang, Soft mechanical metamaterials withunusual swelling behavior and tunable stress-strain curves. Sci. Adv. 4, eaar8535 (2018).

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curvesSoft mechanical metamaterials with unusual swelling behavior and tunable stress-strain

Hang Zhang, Xiaogang Guo, Jun Wu, Daining Fang and Yihui Zhang

DOI: 10.1126/sciadv.aar8535 (6), eaar8535.4Sci Adv

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