Reconfigurable mesostructures with prestressing, reverse stiffness and shape memory effects

Journal Pre-proof Reconfigurable mesostructures with prestressing, reverse stiffness and shape memory effects Chao Song, Jaehyung Ju

PII: DOI: Reference:

S2352-4316(19)30293-7 https://doi.org/10.1016/j.eml.2019.100625 EML 100625

To appear in:

Extreme Mechanics Letters

Received date : 29 August 2019 Revised date : 26 December 2019 Accepted date : 30 December 2019 Please cite this article as: C. Song and J. Ju, Reconfigurable mesostructures with prestressing, reverse stiffness and shape memory effects, Extreme Mechanics Letters (2020), doi: https://doi.org/10.1016/j.eml.2019.100625. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2020 Elsevier Ltd. All rights reserved.

Journal Pre-proof Reconfigurable mesostructures with prestressing, reverse stiffness and shape memory effects

Chao Song, Jaehyung Ju1 UM-SJTU Joint Institute, Shanghai Jiao Tong University

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800 Dongchuan Road, Shanghai 200240, China

Abstract:

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Most thermally triggered reconfigurable mesostructures with shape memory polymers (SMPs) require direct mechanical training at high temperatures. In this work, we suggest a method to generate reconfiguration of mesostructures using preload and reverse stiffness combined with shape memory effects, producing programmable deformations at high temperatures. We analyze the transformation mechanism of the reconfigurable structures, providing a design guideline on the thermomechanical deformation for preloading and geometric conditions of multi-materials. Applying preload to a mechanical assembly, we demonstrate a temperature-triggered shape-change of mesostructures using a reverse stiffness effect at a temperature above its glass transition, followed by recovery with a shape memory effect. Using an analytical model verified by experiments and finite element (FE)-based simulations, we demonstrate the unconventional thermal transformation with recovery for three patterns: circle-triangle, circle-square, and circle-hexagon. This work shows that the strain energy conversion by reverse stiffness of two materials, which are designed with prestressing and triggered by temperature, can open a new field of the design of reconfigurable metamaterials.

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Keywords: reconfigurable structures; reverse stiffness; prestress; shape memory effect; mechanical metamaterials; pattern transformation; negative thermal expansion

I. Introduction

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Shape plays a vital role in defining functions and properties for both natural organisms and humanmade non-living structures. In nature, some creatures are capable of changing their shape to an external environment [1]: e.g., rapid folding of the Venus flytrap after being touched by insects, expansion of pinecones during drying, and blossom of flowers in response to temperature and light. Smart materials have been used for implementing shape-shifting of artificial structures, deforming in exposure to external stimuli: e.g., shape memory polymers (SMPs) [2], shape memory alloys (SMAs) [3], piezo-ceramics [4], electroactive polymers [5], and hydrogels [6]. Invented by Vernon et al. [2], SMPs and their composites are the most widely used active materials with versatile programmable deformations when subjected to external stimuli – heat [7-9], moisture [10], light [11-13], pH [14] and magnetism [15]. In addition to the versatile programmable capability, low fabrication cost, lightweight,

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Corresponding author; [email protected] 1

Journal Pre-proof ability to undergo large deformations, and excellent biocompatibility enabled SMPs to be a group of the most popular smart materials for the design of reconfigurable structures in many applications biomedical devices [16-18], aerospace structural components [19], electronic devices [20] and selfassembling structures[7, 21].

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SMPs have been popular for a smart design of cellular solids [22-24] with a better functional strategy. Introducing several out of numerous examples, He et al. [25] added the shape memory effect to the design of soft cellular structures. Combining an SMP with chiral structures, Rossiter et al. [26] designed a deployable auxetic structure. Zhang et al. [27] presented a simple approach to fabricate heat-shrinkable cellular structures using intrinsic nonhomogeneous thermal residual stress by Fused Deposition Modeling (FDM)-type 3D printing [28, 29]. Some groups demonstrated multi-switchable patterns with a multi-shape memory effect of Nafion [30, 31]. Li et al. [32] showed a switchable SMP membrane with color diffraction to a transparent film while harnessing the mechanical instability and shape memory effect. They all showed the novel design, demonstrating large deformations of cellular structures with SMP. However, their works are either directly combing existing mechanical characteristics of discovered cellular solids with SMP or building uniform prestrain in the SMP to fabricate cellular structures, which limits the reconfigurability and the variety of deformation modes of cellular solids. Moreover, most studies on implementing shape-programming with SMPs require direct mechanical training at a temperature above the glass transition 𝑇𝑔 .

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Recently, Yuan et al. [33] proposed thermomechanically switchable lattice structures by utilizing a reverse stiffness effect between an amorphous polymer and an elastomer at a transition temperature. Unlike the conventional switchable structures with SMP, their method uses a preload at room temperature. Motivated by this new approach and being equipped with an added new function of shape recovery by two thermo-cycles, we introduce new thermomechanically transformable mesostructures. Using two materials - thermoplastic polyurethane (TPU) and polylactic acid (PLA) 3D printed via FDM, we demonstrate that the mechanical assemblies with selective preloading at room temperature can dramatically transform (up to 𝜀~ − 19.2%) at the first thermo-cycle and successfully recover to the original shape for reuse at the second thermo-cycle.

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The paper is organized as follows: Section 2 describes the overall procedure of the thermo-mechanical transformation and recovery. Section 3 details the principle of deformation with an analytical model. Section 4 experimentally demonstrates the transformation and recovery of three mesostructures, followed by the comparison of the analytical models and finite element (FE)-based simulations. We also provide phase maps of the thermomechanical transformation for varying geometric combinations of two materials, which can be used as a potential design guideline. Section 5 concludes with the essential findings of this work.

II. The reconfigurable procedure with reverse stiffness Figure 1 is a schematic illustration of the overall concept of the temperature-triggered reconfigurable structures of this work both in terms of materials (Figure 1a) and structures (Figure 1b). First, we 3D print two sets of structures using an FDM-type 3D printer (S1 in Figure 1b) – core structures made of TPU and circular rings made of PLA. We preload the core, mechanically assembling with the rings at room temperature, 𝑇𝐿 (~20℃). We apply heat to the assembled structure up to a high temperature 𝑇𝐻 (~80℃), allowing thermomechanical deformation by an exchange of strain energy from the core 2

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and the ring associated with prestressing and a reverse stiffness effect between the two materials with temperature change (S2 and S3 in Figure 1b); the ring shape changes to a polygon at 𝑇𝐻 . The reconfigured structure can maintain its shape even after being cooled down to 𝑇𝐿 (S4 in Figure 1b). After being disassembled at 𝑇𝐿 , the PLA polygons are recovered to the original ring shape at 𝑇𝐻 due to the shape memory effect (S5 and S6 in Figure 1b). The recovered rings maintain their shape after being cooled down again to 𝑇𝐿 (S7 in Figure 1b). For a detailed description of the transformation procedure, we further explain the individual steps with a thermomechanical model in the next section.

Figure 1. Transformation procedure of the reconfigurable mesostructure with preloading, reverse stiffness, and shape memory effects; (a) Comparison between the conventional method with the shape memory effect and the current work (b) Detailed procedure of transformation of the designed mesostructure. Note that core structures made of TPU and rings

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made of PLA are illustrated in yellow and blue, respectively.

Note that only the PLA rings function as an SMP within the running temperature window (𝑇𝐿 ≤ 𝑇 ≤ 𝑇𝐻 ) in this work. Unlike the conventional SMPs indicated in green in Figure 1a – i) external loading at 𝑇𝐻 , ii) cooling down to 𝑇𝐿 while retaining the external loading, iii) releasing the loading, and iv) recovery with shape memory effect at 𝑇𝐻 , our method utilizes preloading at 𝑇𝐿 followed by thermal transformation at 𝑇𝐻 by the reverse stiffness of the two constituent materials.

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III. Analytical modeling of the reconfigurable procedure After printing the core and ring components individually, we assemble them with an interference fit at 𝑇𝐿 as illustrated in Figures 2a and 2b. During the mechanical assembly, both the core and the ring experience internal stress together while only the core deforms due to the low stiffness of TPU at 𝑇𝐿 . It is worthwhile to note that the stiffness of PLA is ~14 times greater than that of TPU at 𝑇𝐿 as shown in Figure 2c on their temperature-dependent storage moduli. As the temperature increase, PLA shows a sudden drop of stiffness after passing its glass transition temperature 𝑇𝑔 (~55℃), eventually showing “a reverse stiffness effect”; PLA begins to have a lower stiffness than TPU has at 𝑇 > 64.5℃ (Figure 2c). Within the running temperature of this work, the stiffness-change of TPU below its 3

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𝑇𝑔 (~ − 30℃) can be neglected on this transformation of the mesostructure. It is worthwhile to note that the stiffness of TPU also drops from 140 to 40 MPa when temperature changes from 20 to 80℃. However, the stiffness-drop of TPU is not as remarkable as that of PLA.

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Figure 2. (a) Geometry of a PLA ring and a TPU core (rib) for individual 3D printing, (b) a free-body diagram of the mechanically assembled structure, and (c) temperature-dependent storage moduli of PLA and TPU with a reverse stiffness effect near 64.5℃

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During S1 in Figure 1, the core is compressed for buckling, being assembled with the ring with a radius 𝜌 at 𝑇𝐿 as illustrated in Figures 2a and 2b. The assembled structure of Figure 2b stays in static equilibrium, providing a free-body diagram with a geometric constraint: 𝑙𝑝 = √3𝑙𝑡 = √3𝜌 and 𝐹𝑡 = √3𝐹𝑝

(1)

where the subscripts 𝑝 and 𝑡 denote PLA and TPU, respectively. 𝐹 and 𝑙 denote the force on each side and the effective length of curved beams, respectively. We put the assembled structure quickly into hot water at 𝑇𝐻 (S2 in Figure 1), causing to lose its

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static equilibrium; 𝐹𝑡 ≠ √3𝐹𝑝 .

During S3 in Figure 1, the ring releases the prestress at 𝑇𝐻 , deforming by a reverse stiffness effect. Note that the initial circular shape of the ring with prestressing transforms into a triangle affected by the prestress on the three vertices in Figure 2b. Assuming a negligible viscoelastic effect of PLA beyond its glass transition range (40℃~70℃ )[34], we can express a deformed geometry of the ring beam: 𝐹𝑝 𝛿𝑝 (𝑥) 𝐸𝑝 𝐼𝑝

= 𝛿𝑝′′ (𝑥) +

1 𝜌

(2)

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Journal Pre-proof where 𝛿𝑝 (𝑥) denotes the lateral displacement of the curved PLA beam and 𝐸𝑝 denotes Young’s modulus of PLA at 𝑇𝐻 . 𝐼𝑝 (= ℎ𝑏𝑝3 ⁄12) denotes the area moment of inertia of the PLA beam. The variable ℎ denotes the thickness of the beam.

Solving Equation (2) yields: 𝐹𝑝

𝛿𝑝 (𝑥) =

𝐹𝑝 𝜌

+𝑒

√𝐸 𝐼 𝑥 𝑝 𝑝

−√

𝑐1 + 𝑒

𝐹𝑝 𝑥 𝐸𝑝 𝐼 𝑝

𝑐2 ,

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𝐸𝑝 𝐼𝑝

(3)

where 𝑐1 and 𝑐2 are the parameters which can be obtained from the boundary conditions: 𝛿𝑝 (0) = 0 and 𝛿𝑝 (𝑠𝑝 ) = 0. 𝑠𝑝 (= 2𝜋𝜌⁄3) is the arc length of the curved beam of PLA, as shown in Figure 2b. Solving Equation (3) with the boundary conditions, we can obtain: −√

𝑐1 =

𝐸𝑝 𝐼𝑝

1−𝑒

𝐹𝑝 𝜌

−√

𝑒

𝐹𝑝 𝑠 𝐸𝑝 𝐼 𝑝 𝑝

𝐹𝑝 𝑠 𝐸𝑝 𝐼 𝑝 𝑝

√

−𝑒

√

𝐹𝑝 𝑠 𝐸𝑝 𝐼𝑝 𝑝

and 𝑐2 =

𝐸𝑝 𝐼𝑝

𝑒

𝐹𝑝 𝜌

−√

𝑒

𝐹𝑝 𝑠 𝐸𝑝 𝐼 𝑝 𝑝

𝐹𝑝 𝑠 𝐸𝑝 𝐼 𝑝 𝑝

−1

√

−𝑒

𝐹𝑝 𝑠 𝐸 𝑝 𝐼𝑝 𝑝

(4)

𝑙𝑝 𝑠𝑝

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Considering the dominant deformation mode of the ring - bending and the negligible longitudinal stretch, we can obtain 𝑙𝑝 at stage 3 in Figure 1 as; =

𝑠𝑝

(5)

𝑠 ′ ∫0 𝑝 √𝑥 2 +𝛿𝑝 (𝑥)2 𝑑𝑥

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From Equations (3) and (5), we can obtain the relationship between 𝑙𝑝 and 𝐹𝑝 . The prestrained curvature of a rib on the core at stage 3 can be characterized with a buckling function of an Euler beam [35] as 2√2𝑠𝑡 𝜋

𝐹

1

𝐹

𝜋𝑥

𝑡 𝑡 √𝐹 − 1 [1 − 2 (𝐹 − 1)] cos ( 𝑠 ) 𝑐𝑟

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𝛿𝑡 (𝑥) =

𝑐𝑟

𝑡

(6)

where 𝑠𝑡 is the length of the TPU rib on the core. 𝐹𝑐𝑟 (= 𝜋 2 𝐸𝑡 𝐼𝑡 ⁄𝑠𝑡 2 ) denotes the critical force for a column buckling of the TPU rib. 𝐸𝑡 is Young’s modulus of TPU at 𝑇𝐻 . Finally, we can obtain 𝑙𝑡 at stage 3 in Figure 1 as: 𝑙𝑡

𝑠𝑡

=

𝑠𝑡 𝑠 ′ ∫0 𝑡 √𝑥 2 +𝛿𝑡 (𝑥)2 𝑑𝑥

(7)

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The assembled structure is cooled down to 𝑇𝐿 without transformation during S4 in Figure 1 due to the shape-fixity effect of PLA. For conventional SMPs, the shape-fixity is generally applied by an external loading at 𝑇𝐻 followed by cooling. However, in this work, the shape-fixity of the PLA ring is automatically carried out by the exchange of strain energy between PLA and TPU through the reverse stiffness effect. After finishing the first thermo-cycle, we disassemble the structure (S5 in Figure 1). At stage 5, the TPU core returns to its original shape by unloading within the elastic range. The PLA triangle recovers to its original ring-shape when exposed to 𝑇𝐻 again due to the shape memory effect (S6 in Figure 1). The 5

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It is worthwhile to note that we do not use the shape memory effect of both PLA and TPU in this work. Indeed, TPU has a shape memory effect near its 𝑇𝑔 (~ − 30℃). However, it does not provide a shape memory effect inside the temperature window (20 ≤ 𝑇 ≤ 80℃ ) that we are interested in this work. The prestrained core structure only provides a prestress to the outer ring of PLA. Any materials that are weaker than PLA at a low temperature yet stiffer than PLA at a high temperature can be used for the core structure, e.g., PEGDA [33], Polyethylene [36], Polypropylene-Polyamide [37], and even a flexible metal-strip. We select TPU in this work due to its easy accessibility and manufacturability with 3D printing.

IV. Results

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To verify the analytical model, we conduct experiments with three sets of mesostructure for varying unit cells and packing conditions. Every unit cell consists of circular rings made of PLA and prestrained core structures made of TPU having a different number of legs depending on the targeted transformable shapes. The PLA ring and the TPU core are shown in purple and blue in Figure 3, respectively, with a thickness of 2𝑚𝑚 for both materials. 𝜌 of the ring is 19𝑚𝑚 and 𝑙𝑡 of the TPU rib on the core is 25𝑚𝑚 for all the cases.

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As we described with the fundamental building block on the reconfigurable structure of this work in Figure 2, the designed unit cell can transform a circular PLA shape into a triangle, called “a circletriangle transformation.” The circle-triangle transformation can provide a maximum macroscopic thermomechanical deformation with hexagonal packing, as shown in Figure 3a. It gives an enormous negative thermal expansion up to (𝐶𝑇𝐸 ∗ ~ − 0.0032/℃). Due to the localized prestress on the ring and the reverse stiffness effect, we could build metamaterials with vast negative thermal expansion whose value is an order of magnitude higher than other metamaterials available in the literature [24, 36]. The extremely high value of the negative thermal expansion coefficient is hardly archivable with the fabrication of 3D printing of multi-material because the direct printing of multi-material generally does not produce localized prestress on the structures.

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Similarly, we can extend the transformation from a circular shape of PLA to square and hexagon as shown in Figures 3b and 3c, which can be called the circle-square and circle-hexagon transformations, respectively. For a maximum macroscopic packing condition, the circle-square and circle-hexagon transformations require square and triangular packing conditions, respectively (Figures 3b and 3c). It is worthwhile to note that the number of legs of the core determines the transformed shape of the ring. Observing the configurations at 0𝑠 and 20𝑠 in Figure 3, the deformations of the core are not remarkable compared to those of rings during the thermal transformation by the reverse stiffness effect. Note that the preloaded rib on the core at 𝑇𝐿 do not necessarily become straight after the thermomechanical shape-change at 𝑇𝐻 . The magnitude of the prestrain of the core contributes to the level of prestressing of the ring, which is the primary source of deformation of the mesostructures at 𝑇𝐻 . Both the prestrain and geometry of the core control the prestress on the ring. We will discuss this in Figures 5 and 6 more in terms of design parameters and strain energy states. We also observe a slight out-of-plane deformation [26] of the PLA structures at 𝑇𝐻 for all the transformation cases. The reason is thought to be the non-uniform residual stress from the bottom 6

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layer during the FDM-based 3D printing [28, 29]. We discuss this in the supplementary information in more detail.

Figure 3. Reconfigurable thermomechanical transformation with a localized prestress and reverse stiffness effect; (a) the circle-triangle transformation with hexagonal packing, (b) the circle-square transformation with square packing, and (c) the

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circle-hexagon transformation with triangular packing. The length of the scale bar in white is 25mm. Video files are available to download in the supplementary information.

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Figure 4 experimentally demonstrates the recovery process of the three PLA polygons to the original circular shape (S6 in Figure 1). Putting the disassembled polygons from the core structures into hot water at 𝑇𝐻 , we can start observing the shape memory effect of PLA – a change of polygons to circles.

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Figure 4. Recovery process with the shape memory effect of PLA; (a) the triangle-circle transformation with hexagonal

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packing, (b) the square-circle transformation with square packing, and (c) the hexagon-circle transformation with triangular packing. The length of the scale bar in white is 25mm. Video files are available to download in the supplementary information.

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Based on the analytical model of the thermomechanical deformation, we construct a phase map of the reconfigurability of the mesostructures as a design guideline for the construction of functional structures, as shown in Figure 5. To investigate the geometric effect of the two materials on thermomechanical deformation at 𝑇𝐻 , we select two design parameters – i) 𝛼(= 𝑏𝑡 ⁄𝑏𝑝 ), the ratio of the thickness of a TPU core to a PLA ring and ii) 𝛽(= 𝑠𝑡 ⁄𝜌 ) the ratio of the arc length of a TPU core to the radius of the curvature of a PLA ring, as illustrated in Figure 2. The variable 𝛼 indicates a relative stiffness of the ring to the core. The variable 𝛽 determines the magnitude of the interference fit – a level of prestress on the ring by preloading of the core. From an initial circular shape with a radius 𝜌 , the ring changes to an 𝑁 -polygon with an edge length of 2πρ⁄𝑁 after thermomechanical deformation. We define a shape factor 𝜃 =

𝑙𝑝3 −𝑙𝑝1 𝑠𝑝 −𝑙𝑝1

during S3 of Figure 1 to quantify the deformation

from an initial circular shape to a polygon. Note that 𝑙𝑝1 and 𝑙𝑝3 are the projected length of a curved 𝑙𝑝 −√3𝜌

PLA segment along the x-direction (Figure 2b) at stages 1 and 3, respectively. Therefore, 𝜃 = 2 , and

𝑙𝑝 −𝜌 1 𝜋𝜌−𝜌 3

,

for the circle-triangle, circle-square, and circle-hexagon patterns. It is worthwhile

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𝑙𝑝 −√2𝜌 𝜋𝜌−√2𝜌

𝜋𝜌−√3𝜌

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to note that 𝜃 = 0 indicates no thermal deformation on the PLA ring. On the other hand, 𝜃 = 1 implies a full transformation of the ring to an 𝑁-polygon. For a parameterization of 𝛼 in Figure 5, we vary 𝑏𝑝 for a fixed 𝑏𝑡 (= 4𝑚𝑚 ). We parameterize 𝛽 by varying 𝑠𝑡 for a fixed 𝜌 (= 42.5𝑚𝑚). The phase maps reveal that 𝛽 is a crucial design parameter to transform the mesostructures from one shape into another; 𝛽 is highly sensitive to the transformation for the circle-hexagon reconfiguration (Figure 5c). Due to the large numbers of the rib on the core of the circle-hexagon, a small prestrain on the core can produce a large prestress on the 8

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Note that the deformed configurations below the phase-maps correspond to the numbered red marks in Figure 5. We generate the deformed shapes of the core and the ring using a MATLAB drawing function based on the calculation of 𝛿𝑝 (𝑥) and 𝛿𝑡 (𝑥) in Equations (3) and (6). As both 𝛼 and 𝛽 increase, the rings tend to deform toward perfect polygons. It is worthwhile to note that the configurations of the rib of the core in Figure 5 need not necessarily be straight after the thermomechanical deformation by the reverse stiffness, as confirmed from the experiments in Figure 3. This means that the strain energy of the core is not necessarily zero after the thermomechanical deformation; the partially released strain energy transforms the initial ring-shape of PLA to polygons.

Figure 5. Phase-maps of the transformation of the reconfigurable chiral structures for varying 𝛼(= 𝑏𝑡 ⁄𝑏𝑝 ) and 𝛽(= 𝑠𝑡 ⁄𝜌): (a) the circle-triangle transformation; (b) the circle-square transformation; (c) the circle-hexagon transformation.

The color

bars indicate the shape factor 𝜃. The corresponding deformed shapes at 𝑇𝐻 on the bottom are generated by the analytical model.

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We conduct simulations of the thermomechanical deformation with a commercial FE package (ABAQUS/Standard, SIMULIA) using a two-step method for loadings - buckling of the rib of the core followed by thermal loading to the assembled structures. To simulate S3, we use a viscoelastic analytical model of PLA together with a temperature-stiffness coupling. The detailed procedures on the simulation are available in the supplementary information. Figure 6a shows the deformed mesostructures at stage 3 for the three transformation patterns with comparison – the analytical model and experiment. Using an image processing, we obtain the deformed configuration at the central region of the mesostructures at 20𝑠 in Figure 3. The analytical model slightly overpredicts the deformation of the ring. However, overall, the analytical model shows a good agreement with the experiment. The deformed shapes by the FE simulations with nonlinear material-input show a good match with the tests on the thermal transformation, as shown in Figure 6b. 9

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We can obtain the strain energy distribution of TPU and PLA in the assembly before and after the reverse stiffness effect from the simulation (Figure 6c). During the transformation, we can verify that the core and the ring exchange the strain energy; The initial high strain energy of the core decreases while the low strain energy of the ring increases after the thermal deformation by the reverse stiffness effect. Note that the energy state of the core is not necessarily zero after the deformation, as shown in Figure 6c, where Figures 3 and 5 confirm the curved configurations of the core after deformation.

Figure 6. Deformed configurations at stage 3 generated by (a) experiment and analytical model, and (b) FE simulation; (c) strain energy distribution before and after thermal transformation by the reverse stiffness effect

The structures in this work can replace the reconfigurable architectures designed with SMPs, which can be used for shape-changing and tunable components in various applications such as biomedical devices [16, 37], deployable and morphing structures [38, 39], tunable arrangements for elastic and 10

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acoustic wave control [27]. One can use our design for a thermally controlled disposable trap producing a large thermal deformation. One group introduced reconfigurable structures for a smart window design with a reversible stiffness effect [33], which is similar concept as our work. The control with prestrain at room temperature in this work can facilitate the mechanical training at high temperatures, which is typically required in the design of active structures with SMP. An accurate mechanical training at high temperatures is challenging to implement, especially when it comes to training complex geometry. Most examples of reconfigurable structures with SMP are with a simple strip – stretching, bending, and torsion [7, 39]. If it is required to use conventional mechanical training of SMP for building the structures in this work, one may need to make additional polygon fixtures to shape SMP rings at high temperatures. In this work, we demonstrate structures having thermomechanical stretching. However, the principle of reverse stiffness with prestressing can be extended to other deformation modes - bending and torsion, which is a potential subject of future work.

V. Conclusion

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An exchange of strain energy between two materials by the reverse stiffness effect with temperature is a potential transformation method for the functional design of mesostructures. An added shape memory effect can assist the recovery of the original shapes by relaxation of stress for each component at high temperatures. Unlike the conventional reconfigurable method with SMP, the reverse stiffness method, together with preloading at room temperature, shows potential for the design of reconfigurable structures with two thermal cycles – transformation and recovery. By integrating localized prestress on a structure with the reverse stiffness effect, one can design structural materials with substantial negative thermal expansion whose value is an order of magnitude higher than that of the metamaterials available in the literature. The phase maps provide a design-guideline for the thermomechanical transformation of mesostructures together with the optimum geometric requirement of two materials.

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•

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In this work, we propose a new method to build thermally-triggered reconfigurable structures. We demonstrate thermomechanical transformation and recovery of 3D printed and mechanically assembled structures using prestress, reverse stiffness, and shape memory effects. Analytical model, experiments, and simulations of thermally triggered reconfigurable mesostructures support the findings of this work:

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Through this work, we expand the design space of reconfigurable mesostructures by combining an 3D printing method with the smart design of mechanical assemblies.

VI. Experimental Section Dynamic mechanical analysis (DMA): On the polylactic acid (PLA), we 3D print rectangular samples (17.5 mm × 4.25 mm × 2.06 mm), applying a shear force with a constant shear strain of 1.76% at an oscillated frequency of 1 Hz while increasing temperature from 23 to 126°C at a rate of 3°C/min (DMA Q800, TA Instruments, DE, USA). Similarly, we 3D print rectangular samples (17.64 mm × 4.27 mm × 1.91 mm) of thermoplastic polyurethanes (TPU). We apply a tensile force with a constant tensile strain 11

Journal Pre-proof of 4.6% at an oscillated frequency of 1 Hz while changing the temperature from -70 to 67°C at a rate of 3°C/min (DMA Q800, TA Instruments, DE, USA).

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Thermal transformation: We use a fused deformation modeling (FDM) type 3D printer (Ultimaker 2+, Ultimaker B.V., Geldermalsen, The Netherlands) to fabricate the PLA and TPU parts. After assembling the parts – stage 2 of Figure 1, we put the assembly in hot water at 𝑇𝐻 . We record the transformation (Figure 3) with a cell phone camera (iPhone 6s plus, Apple Inc, CA, USA). Subsequently, we disassemble the PLA and TPU parts from the mesostructures at 𝑇𝐿 , putting the PLA rings into the hot water at 𝑇𝐻 again for recovery, which is recorded for Figure 4.

VII. Acknowledgment

The authors thank Dr. Zachiri McKenzie for proofreading the manuscript.

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The authors (Chao Song and Jaehyung Ju) declare no conflict of interest.