非均质材料有限变形下的热弹性随机均化方法  

Stochastic homogenization method for heterogeneous materials under finite deformation on thermoelasticity

作　　者：王云飞[1] 马娟[1] 韩新玲[1] 贾长安[1] 

机构地区：[1]西安电子科技大学机电工程学院,陕西西安710071

出　　处：《西安电子科技大学学报》2017年第3期66-71,174,共7页Journal of Xidian University

基　　金：国家自然科学基金资助项目(11572233);国家自然科学基金青年基金资助项目(11102143);中央高校基本科研业务费专项资金资助项目(JBG150405)

摘　　要：在有限变形条件下,充分考虑微观结构具有不确定性时对二相非均质材料进行热弹性随机均化分析.将蒙特卡洛方法和多尺度有限元方法相结合,构建了有限变形下的热弹性随机均化框架.采用两步法分别对有限变形下非均质材料的宏观随机有效力学和有效热学性质进行了求解,并进一步对随机有效性质的数字特征值进行了推导,得到了应力张量、热流量张量、变形梯度张量等随机有效量.最后通过算例对所提方法进行了验证,得出了不同相关条件及边界条件下随机有效量的均值和变异系数.讨论了不同相关条件及边界条件下随机有效量在表征体积单元中的分布.结果表明,有限变形下微观结构中客观存在的随机性和相关性在热弹性的随机均化分析中不能忽略.Stochastic homogenization of heterogeneous materials is addressed in the context of thermoelasticity at finite deformation, where the uncertainty in the microstructure is fully considered. The stochastic homogenization in finite thermoelasticity is presented by the multi-scale finite element combined with the Monte-carlo method, and the macroscopically random effective mechanic and thermal properties are solved by using a two-step technique. The numerical characteristics of random effective properties such as stress tensor, heat flux tensor, deformation gradient are then derived. Finally, the feasibility of the method proposed in this work is validated with a numerical example, in which the mean values and the coefficient of variations of random effective quantities under different correlative and boundary conditions are obtained. The distributions of random effective quantities within a representative volume element under different correlative and boundary conditions are also discussed. Obviously, the randomness and correlation existing in the microstructure are not neglected during the process of homogenization of heterogeneous materials under finite deformation.

关 键 词：热弹性 随机均化 非均质材料 随机有效性质 数字特征值 

分 类 号：TB33[一般工业技术—材料科学与工程] O343.2[理学—固体力学]