考虑非局部效应的热弹性理论及其在微纳尺度的应用

With the development of micro- and nanoscale electromechanical systems and the wide applications of ultrashort pulse lasers, the nonlocal effect of the responses increases when the material is subjected to thermnal loading, and the existing thermoelastic models are inadequate to predict the thermomechnical responses. Although there exists several heat conduction laws with nonlocal effect considered, however, they are quitely different from each other, as a result, completely different descriptions may occur for same problem, which may certainly induce different results. In the project, we aim to establish a thermoelastic theory with nonlocal effect contained in both heat transfer sense and deformation sense by combing the progresses of nonlocal elasticity and insights on nonlocal heat transfer. The model may be obtained by using the variational principle based on thermodynamics. If the deformation is neglected, the proposed model may be degenerated into nonlocal heat conduction, and its validity may be evaluated by compared with existed nonlocal heat conduction models. For applications, several basic issues in micro- and nanoscale thermoelastic analysis are considered, and the nonlocal parameter’s effect on the results is studied, based on which the mechnism of micro- and nanoscale heat conduction as well as deformation may be elucidated. Meanwhile, efficient numerical methods for such problems are developed. All these investigations could benefit the strength and stiffness analysis as theoretical basis and technical support, and further extend the continuum mechnics and actuate the multiscale and multiphysics mechnics.

随着微纳机电系统的发展和超短脉冲激光的广泛应用，结构受热冲击时响应的非局部效应愈加显著，已有的热弹性理论已无法满足准确预测微纳结构热弹响应的要求。虽然已有考虑非局部效应的热传导理论，但模型众多、形式各异，预测结果存在明显差异。本项目通过将非局部弹性理论和微纳尺度非局部热传导有机结合，基于热力学，从变分原理出发，建立同时考虑传热和变形的非局部效应的热弹性理论。忽略弹性变形时，新建理论可退化为非局部热传导理论，与现有非局部传热模型及其运用的对比，可验证新建模型的有效性。作为应用，选取微纳尺度热弹耦合的几个基本问题，考虑非局部参数对响应的影响，探求微纳尺度传热和变形的物理机理。同时，发展适于非局部热弹理论的高效数值求解方法。通过本项目的研究，不仅可为热环境下微纳结构的强度、刚度分析提供理论依据和技术支撑，而且可进一步拓展连续介质力学理论体系，推动多尺度力学和多场耦合力学的发展。

随着微纳机电系统的发展和超短脉冲激光的广泛应用，结构受热冲击时响应的非局部效应愈加显著，已有的热弹性理论无法满足准确预测微纳结构热弹响应的要求。项目通过将非局部弹性理论和非局部热传导理论有机结合，建立了同时考虑传热和变形的非局部热弹耦合理论，并拓展至热弹扩散理论。发展了拉普拉斯积分变换+数值积分逆变换的高效精确求解方法。利用所建非局部热弹理论研究了非均匀温度场微纳尺度欧拉梁的屈曲、半无限大体的热冲击瞬态响应、计及层合结构层间阻抗的热冲击瞬态响应以及热和化学势冲击下的热弹扩散瞬态响应等，获得了非局部参数对热弹及热弹扩散瞬态响应的影响，为热环境下微纳结构的强度、刚度分析提供了理论依据和技术支撑，拓展了连续介质力学理论体系，推动多尺度力学和多场耦合力学的发展。项目还基于广义热弹（扩散）理论研究了层合结构、含裂纹结构、生物介质等在超短脉冲激光作用下的瞬态热弹（扩散）响应，加深了对超短脉冲激光作用下结构瞬态响应的深刻理解，为微纳尺度材料加工等提供理论指导。