Currently reported cylindrical metastructures mainly act as the load-bearing components, or only present the single function of programming either Poisson’s ratio (PR) or coefficient of thermal expansion (CTE). Here, by curling the planar metamaterials, a series of multi-functional cylindrical metastructures is originally devised to simultaneously incorporate programmable CTE and PR. The deformation characteristics are systematically analyzed. It is identified that the number of circumferential cells N remarkably affects the deformation characteristics. When N is small, the warp effect induced by the curved members is remarkable. The quantitative analysis figures out that when N is larger than specific critical values, the PR and CTE of the cylindrical metastructures approach to those of the planar metamaterials. Thus, a design strategy is identified, namely, with adequate circumferential cells, both the PR and CTE of the cylindrical metastructures are independent on the variable N, and are equal to those of the corresponding planar metamaterials. Most importantly, by modulating the geometric parameters, the PR and CTE of the devised cylindrical metastructures can be simultaneously programmed to be wide ranges. The excellent programmability in both PR and CTE enables the cylindrical metastructures to be potentially used in engineering applications where precise control of deformation induced both by mechanical and thermal loads is in urgent need.

当前报道的圆柱形元结构主要充当承重组件，或者仅呈现对泊松比（PR）或热膨胀系数（CTE）进行编程的单一功能。在这里，通过卷曲平面超材料，最初设计了一系列多功能圆柱形超结构，以同时包含可编程CTE和PR。系统分析了变形特征。可以看出，圆周孔的数量N显着影响变形特性。当N小时，由弯曲构件引起的翘曲效果显着。定量分析表明，当N如果大于特定的临界值，则圆柱状元结构的PR和CTE接近平面元材料的PR和CTE。因此，确定了一种设计策略，即具有足够的周向单元，圆柱形结构的PR和CTE都独立于变量N，并且等于相应的平面形超材料的PR和CTE 。最重要的是，通过调节几何参数，可以同时将所设计的圆柱形亚结构的PR和CTE编程为较宽的范围。PR和CTE均具有出色的可编程性，因此圆柱形的微结构可以潜在地用于急需精确控制由机械和热负荷引起的变形的工程应用中。