低维微纳米结构多尺度准连续体接触模型及数值计算框架研究

According to the deficiency on the study of large deformation and contact behaviors of low dimensional micro/nano structures, such as the detailed microstructure information is not accurately described and the computational efficiency is lower, the project intend to construct multis-cale quasi-continuum contact model for the investigation of large deformation and contact mechanism of low dimensional micro/nano structures under finite temperature, based on the delicate micro/nano structures, by linking the deformation of microscopic and macroscopic level. On this basis, the efficient and feasible meshless numerical computational scheme is developed for the numerical simulations of the considered boundary value problems. Main points: (1) Based on the characteristic of the interaction between atoms, build the representative cell for the low dimensional micro/nano structures in contact to ensure that the contact mechanism can be described accurately. (2) Develop the temperature-related multi-scale quasi-continuum contact model and derive the corresponding nonlinear constitutive model, equilibrium differential equation, etc. for the study of the large deformation and contact mechanism of the low dimensional micro/nano structures. (3) Derive the incremental stiffness equation and stiffness matrix, and construct the meshless numerical computational scheme for the numerical simulations of the large deformation and contact behaviors of the low dimensional micro/nano structures. This project will play a significant role in expanding the study methods for investigating the large deformation and contact behaviors of low dimensional micro/nano structures and improving the computational efficiency.

针对低维微纳米结构大变形及接触行为研究中，微结构信息描述不够准确、计算效率低等问题，本项目拟在准连续体理论框架下，结合低维微纳米结构微观结构特点，关联其微观尺度和宏观尺度变形，建立用于描述低维微纳米结构在有限温度条件下大变形及接触机理的多尺度准连续体模型。在此基础上，结合无网格方法，构建求解相关边值问题高效、可行的数值计算框架。主要研究内容：(1) 根据相互接触的微纳米结构中原子相互作用特点，建立相应的接触代表单元模型，保证其接触机理能够得到准确的表达；(2) 建立考虑温度效应的低维微纳米结构多尺度准连续体接触模型，并系统推导相应的非线性本构关系及平衡微分方程等；(3) 推导出数值计算所需要的增量形式刚度方程及刚度矩阵，进而建立用于模拟低维微纳米结构大变形及接触行为的无网格数值计算框架。本研究对拓展低维微纳米结构大变形及接触问题的研究方法，提高该类问题的计算效率有着重要的理论和现实意义。

针对低维微纳米结构大变形及接触行为研究中，微结构信息描述不够准确、计算效率低等问题，本项目在准连续体理论框架下，结合低维微纳米结构微观结构特点，关联其微观尺度和宏观尺度变形，建立了用于描述低维微纳米结构在有限温度条件下大变形及接触机理的多尺度准连续体模型。在此基础上，结合无网格方法，构建了求解相关边值问题高效、可行的数值计算框架。主要研究结果：(1) 根据相互接触的微纳米结构原子离散性特点，建立了基于离散节点的接触代表单元模型，保证其接触机理能够得到准确的表达；(2) 建立了考虑温度效应的低维微纳米结构多尺度准连续体接触模型，并系统推导相应的非线性本构关系及平衡微分方程等；(3) 推导了数值计算所需要的增量形式刚度方程及刚度矩阵，进而建立用于模拟低维微纳米结构大变形及接触行为的无网格数值计算框架。本研究对拓展低维微纳米结构大变形及接触问题的研究方法，提高该类问题的计算效率有着重要的理论和现实意义。