材料弹塑性性能数值模拟的多尺度方法

将均匀化方法和渐近分析(Asymptotic Analysis)与参变量变分原理相结合提出了一种模拟复合材料非线性性能的多尺度数值方法.该方法用渐近分析建立宏-细观变量之间的联系,利用参变量变分原理计算非线性响应,求解过程采用迭代算法.为提高计算精度,针对Von-Mises准则和Tsai-Hill准则,提出了一个基于参变量变分原理的改进算法,算例表明该方法可以显著消除传统方法采用线性展开式构造线性互补条件所带来的误差.     

松质骨弹性模量计算的均匀化方法

对松质骨建立了六种单胞微观结构模型，采用均匀化方法和有限元方法计算松质骨的宏观等效弹性模量。给出了六种单胞模型的松质骨弹性模量与材料密度(体分比）的关系，与实验数据进行了对比，分析了不同微观结构模型在不同骨骼中的应用。结果表明，本文方法及六种单胞模型可以对松质骨微观结构和材料性能进行有效的模拟计算。同时本文又着重对松质骨的宏观等效弹性模量与体分比的指数关系进行了探讨。     

用均匀化理论分析蜂窝结构的等效弹性参数

在线弹性范围内,根据均匀化理论,并结合有限元方法推导出适用于二维周期性结构的均匀化的有限元格式（Homo FEM）,计算出不同相对密度下的规则蜂窝结构的等效弹性模量Ee和泊松比νe.同时,利用蜂窝结构的代表胞元模型,用常规的有限元方法（FEM）模拟计算出相应的等效弹性参数.最后将两种数值计算结果与己有的理论公式进行了比较和分析讨论.结果表明:在考察的相对密度全场范围内（0～0.4）,HOmO FEM得到的蜂窝结构的 Ee和νe 与 FEM使用平面实体单元模拟计算得到的结果一致吻合,反映出 Homo FEM数值方法的客观准确性和可行性.而 Gibson公式和 W-K得到的等效弹性模量值 Ee只是在较小相对密度的情况下（小于0.15）与数值计算结果吻合.当结构的相对密度较大时,必须考虑胞棱附近区域由应力集中导致的复杂的应力和应变分布的影响.     

Convergence of FFT‐based homogenization for strongly heterogeneous media

The FFT‐based homogenization method of Moulinec–Suquet has recently attracted attention because of its wide range of applicability and short computational time. In this article, we deduce an optimal a priori error estimate for the homogenization method of Moulinec–Suquet, which can be interpreted as a spectral collocation method. Such methods are well‐known to converge for sufficiently smooth coefficients. We extend this result to rough coefficients. More precisely, we prove convergence of the fields involved for Riemann‐integrable coercive coefficients without the need for an a priori regularization. We show that our L² estimates are optimal and extend to mildly nonlinear situations and L^p estimates for p in the vicinity of 2. The results carry over to the case of scalar elliptic and curl ? curl‐type equations, encountered, for instance, in stationary electromagnetism. Copyright © 2014 John Wiley & Sons, Ltd.     

On critical parameters in homogenization of perforated domains by thin tubes with nonlinear flux and related spectral problems

Let u_? be the solution of the Poisson equation in a domain perforated by thin tubes with a nonlinear Robin‐type boundary condition on the boundary of the tubes (the flux here being β(?)σ(x,u_?)), and with a Dirichlet condition on the rest of the boundary of Ω. ? is a small parameter that we shall make to go to zero; it denotes the period of a grid on a plane where the tubes/cylinders have their bases; the size of the transversal section of the tubes is O(a_?) with a_???. A certain nonperiodicity is allowed for the distribution of the thin tubes, although the perimeter is a fixed number a. Here, is a strictly monotonic function of the second argument, and the adsorption parameter β(?) > 0 can converge toward infinity. Depending on the relations between the three parameters ?, a_?, and β(?), the effective equations in volume are obtained. Among the multiple possible relations, we provide critical relations, which imply different averages of the process ranging from linear to nonlinear. All this allows us to derive spectral convergence as ?→0 for the associated spectral problems in the case of σ a linear function of u_?. Copyright © 2014 John Wiley & Sons, Ltd.     

高速通道压裂裂缝的高导流能力分析及其影响因素研究

高速通道压裂是近年在非常规致密油气资源开采中出现的新工艺, 已在世界范围内推广实施, 并取得了良好的增产效果. 该技术可使支撑剂在人工压裂缝中形成簇团式分布, 从而形成油气高速流动通道, 提高裂缝的导流能力. 但目前对于高速通道压裂裂缝高导流能力的形成机理及其影响因素尚不清楚. 对此, 本文从流体力学理论出发, 首先将高速通道压裂裂缝内形成的支撑剂簇团视为渗流区域, 簇团间的大通道视为自由流动区域; 然后基于Darcy-Brinkman方程建立了裂缝内的流动数学模型, 采用均匀化理论对该流动数学模型进行了尺度升级, 推导得到了高速通道压裂裂缝的渗透率, 揭示了其高导流能力的形成机理; 并以此为基础, 分析了不同支撑剂簇团形状、大小以及分布方式等因素对其导流能力的影响, 可为高速通道压裂工艺参数设计与优化提供基础.     

Constitutive equation of a gas-filled two-phase medium

A set of equations governing the consolidation of a two-phase medium consisting of a porous elastic skeleton saturated with a highly compressible liquid (gas), is described. The homogenization method was utilized to deduce the equations. For the equivalent macroscopic medium, mass and momentum conservation equations and the flow equation of pore liquid are presented. Sample material constants were calculated using laboratory test results which were carried out at the Institute of Geotechnics, Technical University of Wroclaw.     

基于拓扑描述函数的特定性能复合材料设计

提出了一种基于拓扑描述函数进行特定性能复合材料设计的新方法. 采用拓扑描 述函数作为设计变量，把复合材料微结构的设计问题转化为一个在周期性单胞上的拓扑优 化问题. 拓扑描述函数以及相应正则化机制的引入不仅可以有效消除棋盘格式等数值不稳定 现象，而且能够有效地抑制传统算法处理此类优化问题时所引发的边界扩散效应. 数值结果 表明所提出的方法可以稳定高效地实现具有特定性能的复合材料微结构设计.     

含有序孔洞的多孔氧化铝薄膜的力学性能测量和数值模拟

高纯铝箔在特定的溶液下经过电化学阳极氧化腐蚀,可在其表面生成一层多孔的非晶氧化铝层,其孔径分布非常均匀,孔大致呈六方密排布。由于此类薄膜具有规则的纳米级孔径,大的比表面积,良好的自组织排列性,所以其日益受到人们的关注。然而,到目前为止,对于此类薄膜力学性能的研究还很少,所以在一定程度上限制其功能的开发和应用。为了获得此类多孔膜的弹性常数,本文首先由实验出发,通过光力学检测(双光束散斑干涉)的方法得到薄膜拉伸时的整体表观弹性模量。然后对薄膜建立二维有限元模型,运用均匀化理论反推出其基体(无孔结构)的弹性模量,同时考察了不同的基体泊松比对模型整体表观模量的影响,并且用一般有限元方法验证了沿特定方向拉伸时均匀化模型计算的有效性。