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

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 ), 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.