Designing Mechanical Metamaterials with Kirigami‐Inspired, Hierarchical Constructions for Giant Positive and Negative Thermal Expansion

Abstract

Advanced mechanical metamaterials with unusual thermal expansion properties represent an area of growing interest, due to their promising potential for use in a broad range of areas. In spite of previous work on metamaterials with large or ultralow coefficient of thermal expansion (CTE), achieving a broad range of CTE values with access to large thermally induced dimensional changes in structures with high filling ratios remains a key challenge. Here, design concepts and fabrication strategies for a kirigami‐inspired class of 2D hierarchical metamaterials that can effectively convert the thermal mismatch between two closely packed constituent materials into giant levels of biaxial/uniaxial thermal expansion/shrinkage are presented. At large filling ratios (>50%), these systems offer not only unprecedented negative and positive biaxial CTE (i.e., −5950 and 10 710 ppm K−1), but also large biaxial thermal expansion properties (e.g., > 21% for 20 K temperature increase). Theoretical modeling of thermal deformations provides a clear understanding of the microstructure–property relationships and serves as a basis for design choices for desired CTE values. An Ashby plot of the CTE versus density serves as a quantitative comparison of the hierarchical metamaterials presented here to previously reported systems, indicating the capability for substantially enlarging the accessible range of CTE.

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“…Figure 4l presents an Ashby plot of CTE versus density that covers the LCE lattices reported here, along with other mechanical metamaterials and engineering materials with negative CTE. [32,[71][72][73][74][75][76] Note that these results are all based on experimental measurements, and the CTE of LCE metamaterials is calculated based on the thermal strain in the temperature range of [30 °C, T NI ]. The LCE metamaterial with horseshoe microstructures fabricated with lowtemperature synthesis method offers a high biaxial actuation strain (≈53%) in a narrow range of temperature change from 30 to 46 °C (Figure S27 and Movie S5, Supporting Information).…”

“…According to the comparison in Figure 4l, LCE metamaterials developed in this work offer the largest value of negative biaxial CTE (−33 125 ppm K −1 ; from 30 to 46 °C), noting that the maximum value reported previously is −5950 ppm K −1 (from 19 to 29 °C). [32] In principle, any negative biaxial CTE with magnitude lower than the maximum value are accessible, through use of a lower prestrain to form the LCE metamaterial.…”

“…k) Ashby plot of the Young's modulus (i.e., initial elastic modulus) versus activation time for the same active materials shown in j). l) Ashby plot of effective coefficient of thermal expansion (CTE) versus density for NTE materials, representative mechanical metamaterials reported previously (i.e., planar lattice structures,[71,72] topology optimized structures,[73,74] chiral metamaterials,[75,76] and kirigami-inspired hiearchical metamaterials[32] ), and LCE lattice metamaterials proposed in the current work. m) Optical images of live/dead staining of control group and LCE group at day 3.…”

“…The measured effective biaxial coefficient of thermal expansion (CTE) reaches −33 125 ppm K −1 (from 30 to 46 °C), which is more than 5.5 times higher than the maximum value (−5950 ppm K −1 , from 19 to 29 °C) of experimental testing reported previously. [32] Based on the developed fabrication schemes, we report a biocompatible, breathable, hemostatic patch that consists of a layer of LCE metamaterial to offer tunable, biaxial contraction when mounted on the skin, and a dressing layer to provide, simultaneously, the chemical treatment. Our in vivo animal experiments on round and cross-shaped wounds (corresponding to tear and incised wounds, respectively) treated with different strategies (including dressing, suturing, patch without actuation, and patch with actuation), showed accelerated skin regeneration through use of the shrinkable, hemostatic patch, while avoiding scar and keloid generation.…”

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“…This technique has also been achieved using thermal expansion rather than pneumatic pressure. [ 210 ] By embedding an array of cuts into stretchable sheets, the hierarchical patterns can be designed to form hinged squares. [ 211 ] This allows for a variety of buckling‐induced 3D deformation patterns to be triggered with specific stress–strain relationships.…”