本项目应用高阶梯度连续理论研究硅纳米材料的力学特性，通过建立高阶本构模型开展理论分析，通过建立无网格计算框架开展数值模拟，基于高阶本构模型建立研究尺寸效应和表面效应的新方法。首先从高阶梯度连续的基本理论出发，针对微结构特征选择合适的代表单元，借助高阶Cauchy-Born 准则推导本构关系，应用变分原理推导平衡方程，建立规范的研究方法。项目不仅基于高阶梯度连续理论开展理论分析，还将利用无网格法形函数满足高阶连续的优点，建立数值计算框架对硅纳米材料进行整体数值模拟，研究屈曲失效等现象的力学规律。项目将深入研究高阶材料常数的物理意义，利用积分方程技术，借助于特定的力学模型建立积分方程方法，深入研究硅纳米材料的尺寸效应。此外，通过考虑表面变形能的影响，推导高阶表面Cauchy-Born准则，并考虑高阶面力的影响，深入研究硅纳米材料的表面效应。项目也将针对高阶材料常数的物理意义开展部分实验研究。

This proposal aims to employ the higher-order gradient continuum theory to study the mechanical properties of Si nanomaterials. The higher-order constitutive model will be established to carry out the theoretical study for their basic mechanical characteristic, and mesh-free numerical scheme will be developed to implement the numerical simulation in the theoretical frame of higher-order gradient continuum. Based on the higher-order constitutive model, new methods will be developed to study size effect and surface effect of Si nanomaterials. From the basic theory of higher-order gradient continuum, a universal theoretical system will firstly be developed by choosing the appropriate atomic unit as representative cell, employing the higher-order Cauchy-Born rule to derive the higher-order constitutive relatioship, and applying the variation method to derive the equilibrium equation. Besides theoretical analysis for their basic mechanical characteristic, this proposal will build a mesh-free computational scheme to implement the global simulation for Si nanomaterials because the mesh-free shape function can satisfy the higher-order continuum automatically. Numerical simulation will focus on the mechanism of some phenomena such as buckling. By studying the physical meaning of the derived higher-order material constants, the integral equation technique will be used to develop a new method to study the size effect of Si nanomaterials in virtue of some special mechanical models. Moreover, this proposal attempts to provide a new idea to study the surface effect by deriving a higher-order surface Cauchy-Born rule, associated with the consideration of the higher-order surface stress. Some experimental investigations will also be conducted to understand the physical meaning of the higher-order material constants.