基于声电驱动的微梁线性/非线性弹性变形尺度效应的实验及理论研究

When the feature size of structures is reduced to the order of microns, the elastic deformation shows significant size effect. In order to describe the size effect of the deformation behavior of microstructures, researchers introduced the length scale parameters reflecting higher-order deformation mechanisms in the traditional constitutive relations and established non-classical continuum mechanics models such as strain gradient elasticity theory. However, the experimental verification of the applicability of non-classical mechanical models and the quantitative characterization of material intrinsic length scale parameters are lacking. Therefore, establishing and perfecting the related experimental methods and devices is the primary work to study the size effect of materials. This project intends to develop a capacitive static micro-force actuator which can apply a load as small as 1 μN/m to the micro-beam on the basis of the existing acoustic excitation dynamic experimental platform; prepare metal micro-beams with the thickness in the range of 2-15 μm, and investigate the size effect of static and dynamic linear/nonlinear elastic deformation of micro-beams experimentally. Static analysis and dynamic analysis are respectively used to characterize the material length scale parameters and analyze the consistency, to verify the application of non-classical theory in predicting the static and dynamic mechanical behavior of microstructures and reveal the physical mechanism of elastic size effect. The project is expected to obtain rich experimental results on the size effect of elastic deformation of microstructures, which is of great significance to the the expansion and improvement of the continuum mechanics in the micro-nano scale.

当结构的特征尺寸降低至微米量级时，其弹性变形呈现出明显的尺度效应。为描述微结构变形行为的尺度效应，研究者们在传统本构关系中引入反映材料高阶变形机制的尺度参数，建立了应变梯度弹性理论等非经典连续介质力学模型。而非经典力学模型适用性的实验验证及材料内禀特征尺度参数的定量表征工作却很缺乏，因此建立和完善相关的实验方法和装置是研究材料尺度效应的首要工作。本项目拟在已有声激励动态实验平台的基础上，研制可对微梁施加小至1μN/m载荷的电容式静态微力执行器；制备厚度在2-15μm范围的金属微梁试件，实验研究微梁静动态线性/非线性弹性变形的尺度效应，从静态分析和动态分析两方面分别表征材料的特征尺度参数并分析其一致性，验证非经典理论在预测微结构静动态力学行为时的适用性，揭示微结构弹性尺度效应的物理机制。本项目有望获得丰富的微结构弹性变形尺度效应实验研究结果，对连续介质力学在微纳尺度的拓展和完善具有重要意义。

特征尺寸在微米量级的结构和器件，其力学行为具有显著的尺寸效应。本项目针对微结构力学行为尺度效应的实验表征和非经典连续介质力学理论的适用性问题开展了深入研究。主要成果包括：1.研制了分辨力达1μN的微力测量系统，结合动态测试平台，组建了完善的微结构静动态力学行为实验测量系统；2.实验研究了微尺度镍悬臂梁静态弯曲和线弹性高阶振动响应行为，证实了微梁无量纲弯曲刚度和无量纲高阶（二阶和三阶）频率的尺度效应；3.实验研究了微尺度镍悬臂梁的非线性振动和超谐波共振响应，结果表明微梁的非线性行为具有明显的尺度依赖性；4.基于修正的偶应力理论建立了微尺度梁单元线性和非线性静动态力学行为的理论模型，对比实验研究结果，验证了非经典连续理论的适用性。在项目执行期间，在国内外权威期刊上发表论文9篇；参加学术会议5人次；协助培养博士研究生3名，硕士研究生4名。