含约束薄膜的单轴拉伸的理论与数值研究  

ANALYTICAL AND NUMERICAL INVESTIGATIONS FOR THIN-FILM WITH CONSTRAINT UNDER UNIAXIAL TENSION

作　　者：张朝晖[1] 高原[1] 聂君锋[2] 胡强[1,3] 庄茁[1] 

机构地区：[1]清华大学航天航空学院教育部应用力学重点实验室,北京100084 [2]清华大学核能与新能源技术研究院,北京100084 [3]海军装备研究院航空装备论证研究所,上海200436

出　　处：《工程力学》2011年第11期31-37,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(10772096)

摘　　要：基于微态理论与应变梯度弹性理论框架,对含约束薄膜的单轴拉伸问题进行了研究。推导出在不同微观约束边界条件下薄膜单轴拉伸的解析解,较好的预测了薄膜内的边界层效应。通过分析两种理论之间的内在联系,发现可选取微态理论中的耦合因子作为罚参数,使得微态理论可以退化至应变梯度弹性理论。计算结果表明施加罚参数后的有限元解在边界层区域外与应变梯度弹性解析解吻合较好,即由于耦合因子的罚参数特性,使得基于微态理论开发的有限元程序可以应用于应变梯度弹性理论的模拟解答。The thin-film with constraint under uniaxial tension is investigated based on the micromorphic theoryand the strain gradient elasticity theory, respectively. The analytical solutions are presented for the uniaxial tension of the thin-film under different microscopic constraint boundary conditions. The presence of the boundary layer effect is predicted. By comparing the relations between these two theories, it is found that the micromorphic theory can reduce to the strain gradient elasticity theory by choosing the coupling factor as the penalty parameter. The numerical simulation results with penalty parameter agree well with those analytical solutions of the strain gradient elasticity except for the boundary layer region. It is also shown that the subroutine originally developed for the micromorphic theory can simulate the strain gradient elasticity problem due to the penalty parameter approach.

关 键 词：微态理论 应变梯度弹性 有限元 罚参数 边界层 单轴拉伸 

分 类 号：O34[理学—固体力学]