Research progress in the design, manufacturing, characterization, and evaluation of tailorable thermal expansion mechanical metamaterials
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摘要: 我国太空探测事业的蓬勃发展对航天装备的可靠性提出了诸多挑战。在温度急剧变化的环境下，精确控制大型空间结构、精密探测设备和微电子封装等材料与结构的热变形成为亟待突破的瓶颈问题。因此，发展具有可调控热膨胀系数的力学超材料具有重要意义。本文针对可调控热膨胀力学超材料设计制备与表征评测等方面的研究现状与进展进行了概述，系统整理了可调控热膨胀力学超材料的设计方法，总结了热膨胀与刚度、泊松比等力学参数的协同调控策略，探讨了可调控热膨胀力学超材料拓扑优化方法，介绍了热膨胀可调力学超材料制备工艺与性能评测方法。本文还对可调控热膨胀力学超材料的发展趋势进行了展望，为其在航天装备中的深入应用提供指导与借鉴。Abstract: The vigorous development of China's space exploration industry has posed numerous challenges to the reliability of aerospace equipment. In environments with drastic temperature changes, precise control of thermal deformation in materials and structures such as large-scale space structures, precision detection equipment, and microelectronic packaging has become a bottleneck issue that urgently needs to be broken through. Therefore, it is of great significance to develop mechanical metamaterials with tailorable thermal expansion coefficients. This article provides an overview of the current status and progress of research on the design, preparation, and characterization of tailorable thermal expansion mechanical metamaterials. It systematically sorts out the design methods of tailorable thermal expansion mechanical metamaterials, summarizes the collaborative control strategies of thermal expansion, stiffness, Poisson's ratio, and other mechanical parameters, explores the topological optimization methods of tailorable thermal expansion mechanical metamaterials, and introduces the preparation techniques and performance evaluation methods of thermally tailorable mechanical metamaterials. This article also looks into the development trends of tailorable thermal expansion mechanical metamaterials, providing guidance and reference for their in-depth application in aerospace equipment.
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图 1 (a)月球表面温差；(b)材料热膨胀示意图；(c)常见工程材料热膨胀系数
Figure 1. (a) Temperature difference on the lunar surface; (b) Schematic diagram of material thermal expansion; (c) Thermal expansion coefficients of common engineering materials
图 2 拉伸机制主导的可调控热膨胀力学超材料：(a)三角结构[10]；(b)凹角结构[11]
Figure 2. Sretching mechanism-dominated tailorable thermal expansion mechanical metamaterials: (a) Triangular structure[10]; (b) Re-entrant structure[11]
a, b—Length of cell edge; δa, δb and δy—Deformation of cell along a, b edges and y direction after temperature changes; θ1, θ2—Structural angle
图 3 拉伸机制主导的2D、3D可调控热膨胀力学超材料
Figure 3. 2D and 3D tailorable thermal expansion mechanical metamaterials dominated by stretching mechanism-dominated
l—Length of cell edge; t—Thickness of cell edge
图 5 弯曲机制主导的可调控热膨胀力学超材料
Figure 5. Lattice structure with tailorable thermal expansion mechanical metamaterials dominated by bending mechanism
图 6 两类可调控热膨胀力学超材料的热膨胀系数可实现的最大负热膨胀系数
Figure 6. Tailorable range of the thermal expansion coefficient for two types of tailorable thermal expansion mechanical metamaterials
图 8 刚度-热膨胀双调控力学超材料
Figure 8. Dual-tailorable mechanical metamaterial with stiffness and thermal expansion coefficient
CTE—Coefficient of thermal expansion; Δy—Deformation of cell along y direction after temperature changes; β—Structural angle; L—Length of cell edge; dL—Deformation of cell edge after temperature changes; h—Height of cell; dh—Change of height after temperature changes; θ—Structural angle; dθ—Change of structural angle after temperature changes; ΔT—Change of temperature
图 9 泊松比-热膨胀双调控力学超材料
PR—Possion's rate; Δx, Δy, Δz—Deformation of cell along x, y and z direction after temperature changes
Figure 9. Dual-tailorable mechanical metamaterial with Poisson's ratio and thermal expansion coefficient
图 10 可调控热膨胀力学超材料的刚度和泊松比可调控范围
Figure 10. Tailorable range of stiffness and Poisson's ratio of tailorable thermal expansion mechanical metamaterials
图 11 拓扑优化得到的可调控热膨胀力学超材料
Figure 11. Topologically optimized tailorable thermal expansion mechanical metamaterials
ANTE—Anisotropic negative thermal expansion; IPTE—Isotropic positive thermal expansion; APTE—Anisotropic positive thermal expansion
图 12 可调控热膨胀力学超材料的制备方法
Figure 12. Fabrication methods for tailorable thermal expansion mechanical metamaterials
图 13 可调控热膨胀力学超材料的性能测试方法
Figure 13. Testing methods for the performance of tailorable thermal expansion mechanical metamaterials
LActuation—Length of actuation material; LFrame—Length of frame material; NTE—Negative thermal expansion; ZTE—Zero thermal expansion; PTE—Positive thermal expansion; Disp.—Displacement
表 1 几种典型可调控热膨胀力学超材料及其最大负热膨胀系数
Table 1. Several typical tailorable thermal expansion mechanical metamaterials and their maximum negative thermal expansion coefficients
Metamaterial structure Maximum negative thermal
expansion coefficient α/°CDesign mechanism Research method Ref. 2D triangular cell −6.0×10−6 Tensile-dominated Theoretical calculation [10] 2D re-entrant lattice −1.4×10−5 Tensile-dominated Simulation [25] 2D curved beam cell −2.0×10−5 Bending-dominated Theoretical calculation + Simulation [21] 2D re-entrant cell −2.0×10−5 Tensile-dominated Theoretical calculation + Simulation [11] 2D chiral lattice −3.4×10−5 Bending-dominated Simulation [22] 3D star-shaped lattice −4.2×10−5 Tensile-dominated Simulation [19] 3D cubic lattice −5.6×10−5 Tensile-dominated Simulation [19] 3D triangular lattice −6.0×10−5 Tensile-dominated Theoretical calculation [16] 2D triangular lattice −7.7×10−5 Tensile-dominated Theoretical calculation + Simulation [18] 
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