基于窗技术的多孔介质材料力学性质的数值均匀化方法  

Window-method based numerical homogenization scheme for mechanical behavior of porous medium

作　　者：胡江 苏怀智[2] 马福恒 

机构地区：[1]南京水利科学研亢院水文水资源与水利工程科学国家重点实验室,南京210029 [2]河海大学水利水电学院,南京210098

出　　处：《中国科学：技术科学》2015年第11期1180-1186,共7页Scientia Sinica(Technologica)

基　　金：国家自然科学基金(批准号:51409167);高等学校博士学科点专项科研基金(批准号:20130094110010);南京水利科学研究院中央级公益性科研院所基本科研业务费专项(批准号:Y714015);长江科学院开放研究基金(批准号:CKWV2014216KY)资助项目

摘　　要：相比解析均匀化方法,数值均匀化可以精细模拟表征元模型的受载过程和复杂力学行为,从本质上识别材料的有效力学性质,然而,当模型边界单元存在孔隙时,易使边界不满足线性位移边界条件,导致求解过程收敛较困难.为此,受自洽解析均匀化方法的启发,本文提出了"窗技术"优化方法,即通过增加外围基质"窗体"优化随机表征元网格模型,借助采用的表征元模型重构方法和数值网格离散方式,建立了更易非线性求解的表征元网格模型,基质窗体的性质由自洽方法迭代获得,从而发展了多孔介质材料有效力学性质的数值均匀化方法.在此基础上,探讨了窗体基质宽度和实际有效力学性质的关系;并以砂浆力学性质试验数据为依据,验证了方法的可行性和有效性.结果表明,文中方法可以可靠地模拟多孔介质材料表征元模型的受载响应,获得其有效力学性质.Compared with analytical homogenization methods, numerical homogenization methods can represent the complex mechanical responses of the detailed representative volume element（RVE）, and can be used to identify the effective mechanical behavior of multi-scale materials of porous medium. However, linear displacement boundary conditions do not satisfy local equilibrium if void pores distribute at the boundary, thus the effective properties are questionable since unnatural stress concentrations occurs. Inspired by the self-consistent scheme from analytical micromechanics, the window（i.e., homogenized matrix） method is proposed in this paper. The RVE, obtained from the reconstruction method and the finite element implementation method, is evenly embedded in a matrix of average stiffness and linear displacement boundary conditions are applied to its boundary. Thus the homogenized properties of the porous medium become easily solvable and more reliable. In addition, the influence of the width of the window on the effective properties was discussed. Based on the available experimental data, the proposed scheme was carried out to deduce the macroscopic material property of concrete. The results show that the proposed scheme can enhance the credibility of the current numerical homogenization for mechanical behavior of porous medium.

关 键 词：多孔材料 自洽方法 数值均匀化 表征元模型 力学性质 基质 

分 类 号：TB383.4[一般工业技术—材料科学与工程]