硅纳米材料的高阶本构模型及其在尺寸效应和表面效应研究中的应用

项目名称： 硅纳米材料的高阶本构模型及其在尺寸效应和表面效应研究中的应用

项目编号： No.11472316

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 孙玉周

作者单位： 中原工学院

项目金额： 75万元

中文摘要： 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。

中文关键词： 硅纳米材料；高阶理论；多尺度；Cauchy-Born；准则；无网格法

英文摘要： 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.

英文关键词： Si Nanomaterials;High-order theory;Multiscale method;Cauchy-Born rule;Mesh-free method