含孔或夹杂热电材料二维力学问题研究

Thermoelectric materials are becoming more promising in the environmental and energy fields due to their inherent thermoelectric conversion characteristics. It is found that the conversion performance of thermoelectric materials can be effectively improved by introducing defects or low-dimensional nanostructures such as pores, metal particles, carbon nanotubes and carbon fibers. However, the introduction of these inhomogeneities can bring thermoelectric materials with new mechanical challenges like thermal stress concentration, strength and reliability problems. To deal with these challenges, an in-depth and systematic research is carried out in this project on the two-dimensional mechanical problems of thermoelectric materials containing single, multiple, and periodic distribution of holes or inclusions with arbitrary shape at macro and micro scales. In order to study the problems of micro-holes or -inclusions, the project introduces the complete Gurtin-Murdoch low-order surface energy model and high-order surface roughness theoretical model for the first time, and constructs a theoretical framework model for two-dimensional periodic thermoelectric materials. The main purposes of this project are to explore the influence of the size, geometry, volume fraction of the holes or inclusions as well as the surface effects and surface roughness at the micro scale on the stress concentration of the thermoelectric matrix and the overall effective stiffness of material and to promote the development of thermoelectric material theory. The results have the potentials to provide theoretical guidance and scientific basis for the mechanical performance analysis and the safety and reliability design of thermoelectric devices.

热电材料因其固有的热电转换特性，故而在环境和能源领域有着广泛的应用前景。研究发现，热电材料的转换性能可通过引入缺陷或低维纳米结构如孔洞、金属颗粒、碳纳米管以及碳纤维等而得到有效提升。可是，这些非均匀相的引入也会使热电材料面临新的力学方面的挑战，如材料的热应力集中、强度以及可靠性等问题。基于此，本项目将分别对宏观和微观尺度下含单个、多个以及周期分布的任意形状孔或夹杂热电材料的二维力学问题展开深入系统的研究。同时，为研究微孔或夹杂问题，将首次引入完整的Gurtin-Murdoch低阶表面能模型和表面粗糙度高阶理论模型，并构建二维周期热电材料的理论框架模型。通过本项目的研究，旨在探索孔或夹杂的大小、几何形状、体积分数以及微观尺度下的表面效应和表面粗糙度等因素对热电基体内部应力集中情况以及材料整体有效刚度的影响规律，发展热电材料理论，为热电器件的力学性能分析和安全可靠性设计提供理论指导和科学依据。

热电材料因其固有的热电转换特性，故而在环境和能源领域有着广泛的应用前景。研究发现，热电材料的转换性能（即能量转换效率）可通过引入缺陷或低维纳米结构（如孔洞、金属颗粒、碳纳米管以及碳纤维等）而得到有效提升。但同时，这些非均匀相的引入也会使热电材料面临新的力学方面的挑战，如材料内部的热应力集中、强度以及可靠性等问题。基于此，本项目应用理论与数值相结合的方法，对含任意非均匀相（孔洞或夹杂）热电材料的二维力学问题展开深入系统的研究。研究内容涉及宏观和微观尺度下的单个、多个以及周期有序分布的任意形状孔或夹杂问题。通过引入完整的低阶Gurtin-Murdoch模型表征微纳米尺度下材料的表面效应，实现研究工作从宏观到微观的转变。同时，通过引入保角映射函数的高阶项，建立表征表面粗糙度的高阶理论模型，实现对微纳米尺度下非均匀相粗糙表面的模拟。本项目系统地研究了受热、电、力载荷单独或耦合作用的单个、多个以及周期分布的非均匀相周围热应力的分布与应力集中情况，揭示了非均匀相对热电基体内部热应力集中以及材料力学行为和性能的影响，取得了一系列具有创新性的成果，为发展热电理论以及热电器件的力学性能分析和安全可靠性设计提供理论指导和科学依据。