基于均匀化理论的混凝土宏细观力学特性研究

在细观层次上将混凝土视为由砂浆基质、骨料及其界面组成的三相复合材料,在此基础上,采用有限元方法,对混凝土弹性本构关系进行数值模拟,利用位移渐近展开技术和均匀化理论建立了多尺度力学框架下的有限元平衡方程,重点考察了单胞尺寸对宏观力学性能的影响,得到了相对最大骨料粒径的最小单胞尺寸,即5～10倍最大骨料粒径.作为例证,对混凝土三点弯梁进行了宏细观尺度数值仿真研究,结果表明:基于本文方法可以较好地反映混凝土的宏观力学行为.此外,由于骨料、砂浆的相互作用,应力分布呈现出宏观渐变平滑与细观局部突变的特征.     

Hardness-packing density scaling relations for cohesive-frictional porous materials

Recent progress in instrumented nanoindentation makes it possible today to test in situ phase properties and structures of porous materials that cannot be recapitulated ex situ in bulk form. But it requires a rigorous indentation analysis to translate indentation data into meaningful mechanical properties. This paper reports the development and implementation of a multi-scale indentation analysis based on limit analysis, for the assessment of strength properties of cohesive-frictional porous materials from hardness measurements. Based on the separation-of-scale condition, we implement an elliptical strength criterion which results from the nonlinear homogenization of the strength properties of the constituents (cohesion and friction), the porosity and the microstructure, into a computational yield design approach to indentation analysis. We identify the resulting upper bound problem as a second-order conical optimization problem, for which advanced optimization algorithms became recently available. The upper bound yield design solutions are benchmarked against solutions from comprehensive elastoplastic contact mechanics finite element solutions and lower bound solutions. Furthermore, from a detailed parameter study based on intensive computational simulations, we identify characteristic hardness-packing density scaling relations for cohesive-frictional porous materials. These scaling relations which are developed for two pore-morphologies, a matrix-pore morphology and a polycrystal (perfect disordered) morphology, are most suitable for the reverse analysis of the strength parameters of cohesive-frictional solids from indentation hardness measurements.     

Multiscale cohesive failure modeling of heterogeneous adhesives

A novel multiscale cohesive approach that enables prediction of the macroscopic properties of heterogeneous thin layers is presented. The proposed multiscale model relies on the Hill's energy equivalence lemma, implemented in the computational homogenization scheme, to couple the micro- and macro-scales and allows to relate the homogenized cohesive law used to model the failure of the adhesive layer at the macro-scale to the complex damage evolution taking place at the micro-scale. A simple isotropic damage model is used to describe the failure processes at the micro-scale. We establish the upper and lower bounds on the multiscale model and solve several examples to demonstrate the ability of the method to extract physically based macroscopic properties.     

An integrated approach of homogenization-ultrasound-assisted extraction followed by high-speed countercurrent chromatography for rapidly preparative separation naphthoquinones and diarylheptanes from Juglands mandshurica Maxim. exocarp

This research investigated the effectiveness of an integrated method for the extraction and separation of naphthoquinones and diarylheptanes from exocarp of Juglands mandshurica Maxim. (namely, green walnut husks). The target compounds were obtained by ultra-turrax homogenization (UTH) coupled with ultrasound-assisted extraction (UAE) technology followed by high-speed countercurrent chromatography (HSCCC). The UTH-UAE extraction method achieved higher efficiency with 2.49- and 2.36-fold to those by UAE, and 1.39- and 1.34-fold to those by UTH in a short time. HSCCC was adopted for further separation and purification; six target compounds, namely, regiolone (RE), juglone (JU), myricatomento-genin (MG), galleon (GA), 2-oxatrycyclo[13.2.2.13,7]eicosa-3,5,7(20),15,17,18-hexaen-10-16-diol (OE), and juglanin A (JA), were separated with more than 95.37% purities and more than 84.71% final recovery rates, respectively. In this study, the integrated strategy of extraction and separation could get high purity compounds quickly, which would provide time and solvent saved method for the natural products separation from plants.     

Topology Optimization Design of Heat Convection Problems With Variable-Density Cells北大核心CSCD

为获得优异的散热结构设计,发展了一种基于腐蚀-扩散算子的变密度胞元层级结构设计方法.通过腐蚀-扩散算子得到了一系列拓扑相似但体积分数不同的变密度微结构,计算并拟合得到变密度微结构等效热传导系数曲线.在此基础上,采用移动渐近线法更新宏观设计变量,将变密度微结构植入相应体积分数的宏观单元中完成装配.通过数值算例对不同优化方法下温度场的热柔顺度、平均温度、方差等参数进行了比较分析,结果表明,变密度胞元层级结构比传统单尺度胞元结构和周期胞元结构具有更好的散热性能.     

高密度封装倒装焊的新简化模型及疲劳寿命分析

高密度封装结构中存在大量焊球，在进行有限元建模时，考虑到焊球数量多且尺寸小的特点，需简化焊球层模型．本文针对高密度封装结构中倒装焊及底填胶，提出了一种新的简化模型，采用非重点部位简化和材料均匀化相结合的方法，将内部焊球层和底填胶简化为均匀层，只保留外圈几层焊球．通过建立代表性体积单元，计算得到均匀化层的材料参数．讨论了外层焊球圈数对焊球层危险点应力的影响，发现保留外圈两层焊球就能得到非常精确的结果．利用新简化模型计算了高密度封装结构的疲劳寿命，所获得的结果与未均匀化模型结果误差在0.3%以内．     

Asymptotic stability of the spectrum of a parametric family of homogenization problems associated with a perforated waveguide

In this paper, we provide uniform bounds for convergence rates of the low frequencies of a parametric family of problems for the Laplace operator posed on a rectangular perforated domain of the plane of height H. The perforations are periodically placed along the ordinate axis at a distance $O(\epsilon )$ between them, where ε is a parameter that converges toward zero. Another parameter η, the Floquet-parameter, ranges in the interval $[-\pi ,\pi ]$. The boundary conditions are quasi-periodicity conditions on the lateral sides of the rectangle and Neumann over the rest. We obtain precise bounds for convergence rates which are uniform on both parameters ε and η and strongly depend on H. As a model problem associated with a waveguide, one of the main difficulties in our analysis comes near the nodes of the limit dispersion curves.     

考虑微结构连接性的双尺度结构自然频率拓扑优化

多孔材料因具有轻量化、高孔隙率和减振/散热等优良多物理特性,在航空航天等领域具有广阔应用前景。采用拓扑优化方法对含多种多孔材料的结构进行结构与材料微结构构型一体化设计,有助于获得具有优良力学性能的结构设计。然而,传统逆均匀化微结构设计方法无法确保不同多孔材料微结构之间的连接性,设计结果不具备可制造性。本文面向含多种多孔材料的双尺度结构基频最大化设计问题,考虑不同微结构之间的连接性,协同设计多孔材料的微结构构型及其在宏观尺度下的布局。采用均匀化方法计算多孔材料的宏观等效力学性能,通过对不同多孔材料微结构单胞的边界区域采用相同的拓扑描述确保双尺度优化过程中任意空间排布下不同微结构的连接性,并通过优化算法确定微结构间的连接形式及微结构拓扑。在宏观尺度,提出结合离散材料插值模型和RAMP插值模型RAMP (Rational Approximation of Material Properties)的多孔材料各向异性宏观等效刚度及质量插值模型,获得清晰的多孔材料宏观尺度布局并减轻优化过程中伪振动模态的影响。建立以双尺度结构基频最大化为目标,以材料用量为约束的优化列式,推导灵敏度表达式,并基于梯度优化算法求解双尺度结构拓扑优化问题。数值算例表明,采用本文优化方法能够有效确保基频最大化双尺度结构设计中不同多孔材料微结构之间的连接性,增强优化设计结果的可制造性。