扩展的多尺度有限元法基本原理

阐述一种适用于非均质材料力学性能分析的扩展的多尺度有限元法（Extended Multiscale Finite Element Method,EMsFEM）的基本原理．该方法的基本思想是利用数值方法构造能反映胞体单元内部材料非均质影响的多尺度基函数,在此基础上求得粗网格层次的等效单元刚度阵,从而在粗网格尺度上对原问题进行求解,很大程度地减少计算量．以该方法进行的具有周期和随机微观结构的材料计算示例,通过与传统有限元法的结果比较,说明这一方法的有效性．EMsFEM的优势在于,能容易地进行降尺度计算,可较准确地求得单元内部的微观应力应变信息,在非均质材料强度和非线性分析中有很大的应用潜力．     

基于声子晶体的层叠式方柱型减振结构设计

基于声子晶体特性提出一种层叠式方柱型声子晶体单胞结构,通过冲击响应谱分析和随机振动分析考察其周期性结构减振特性,并与相应非周期结构对比.计算结果表明该声子晶体周期性结构对于冲击载荷和随机振动载荷均有较好的减振特性.在三组分材料参数中影响单胞带隙特性的主要因素是外层材料密度和中间层材料弹性模量.声子晶体结构的减振效果随周期数的增加而愈加明显.组分材料力学性能参数和周期型结构周期数是声子晶体结构减振设计的主要因素.     

基于Cosserat理论的平面等参元

为解释材料在微尺度下的尺度效应,基于Cosserat理论,从势能泛函驻值条件出发提出构造8节点Serendipity平面等参元,并建立平面有限元法．每个节点拥有3个独立节点自由度,分别为2个方向的线位移和1个逆时针方向的角位移．用该方法分析含中心小孔的无限平板在单轴拉伸情况下的应力集中问题．数值计算结果与Cosserat理论的解析解非常符合,表明应力集中因数k受泊松比μ,常数c及a／l值的影响很大;由于偶应力的存在,小孔周围的应力分布明显小于经典弹性力学理论的预测．通过对材料常数c的调节可以将该方法推广应用于基于Mindlin偶应力理论的数值分析中．     

基于内聚力模型的界面破坏分析

界面破坏是材料与结构失效的常见形式,准确分析模拟界面损伤演化和最终破坏对评估材料乃至结构性能至关重要.在简要介绍内聚力模型的基础上,用Abaqus中的内聚力单元分别对均质材料和非均质材料界面破坏过程进行模拟,数值结果与理论结果吻合良好,表明内聚力单元适用于材料界面破坏分析.     

多稳态力学超材料带隙特性及调控研究

多稳态力学超材料具有多重稳定状态和几何重构特性,在变形吸能和能带调控等方面有重要的研究价值.本研究提出了一种多稳态力学超材料.该超材料是由具有双稳态特性的曲杆和相关实体支撑结构组成.结合有限单元法和布洛赫定理,计算了结构的能带结构,分析了不同稳态条件下结构的带隙特性,得到了几何参数对结构带隙的影响规律,并研究了由5×5个单胞组成的阵列结构中部分单胞变形时,整体结构的传输率.研究发现,双稳态连杆的变形状态可显著改变结构的带隙,尤其是在低频范围内产生了更宽的带隙.整体结构中局部一行或一列单胞变形即可在该方向对应带隙频率范围内实现弹性波传播的衰减.     

周期性复合材料单胞结构优化设计

提出了一种基于网格的周期性多孔复合材料单胞模拟方法,以孔洞的形状、大小、位置为优化变量,建立了以材料在某个方向上的导热性能最好为目标的两相材料单胞优化模型,并用遗传算法进行求解,数值结果验证了优化模型和优化算法的有效性,获得了多种最优单胞结构。     

C/SIC复合材料结构动态特性研究

针对C/SiC轻质复合材料结构,将三维编织C/SiC复合材料看作是组分材料的空间结构物,由有序的细观结构单胞叠合而成.采用细观结构单胞作为离散单元对三维编织复合材料结构进行宏观网格剖分,利用有限元方法研究复合材料悬臂板动态特性.计算结果与理论值符合较好.     

平衡态分子动力学 Green-Kubo 方法计算氮化硼 单层结构热导率的模型尺寸效应研究

分子动力学模拟可以直接表征体系原子的行为,因此成为研究氮化硼相关材料微观导热机理的重要工具,但目前尚没有关于氮化硼材料模型尺寸对其热传导相关性质影响规律的研究。该文采用平衡态分子动力学并结合 Green-Kubo 方法,研究了纯净氮化硼单层结构热导率、声子色散关系以及态密度随模拟尺寸的变化规律,并解释了其内部机理。实验发现,氮化硼单层材料热导率随着模拟尺寸的增大而减小,并在单层面积约 4.1 nm×4.1 nm 时收敛于(349±22)W/(m?K),此收敛值远小于平衡态分子动力学计算中石墨烯热导率的收敛尺寸(10 nm×10 nm),这说明氮化硼单层中声子之间的散射大于石墨烯。此外,不同于热导率,氮化硼单层结构的声子色散曲线、态密度几乎不受模拟尺寸的影响。该研究结果可为采用平衡态分子动力学研究氮化硼相关材料的微观导热机理提供重要参考。     

脑白质电导率各向异性及非均质对头皮脑电分布的影响

脑白质电导率的各向异性和非均质分布是广泛存在的,因此衡量其对脑电正问题计算的影响显得十分重要。而现有研究方法忽略了白质各向异性电导率的非均质性。把白质电导率的非均质划分为四类,分别讨论了各种非均质电导率对脑电正问题的影响。从仿真结果看,认为电导率数值上的偏差是最主要的非均质因素,同时忽略大脑白质电导率非均质会对脑电正问题造成10%左右的计算误差,因而认为非均质的影响是不可忽略的,需要建立能够反映WM非均质且各向异性的电导率模型。     

基于模体演化的时序链路预测方法

时序链路预测是动态网络分析的重要组成部分,具有极大的理论和应用价值. 传统的时序链路预测方法往往直接对边的演化规律进行分析,忽略了网络中其他微观结构的演化对链路形成的影响. 基于此分析,本文引入非负张量分解和时间序列分析对网络模体的演化规律进行研究,进而提出一种基于模体演化的链路预测方法. 在三个真实数据集上的实验结果表明,该方法能有效提高链路预测精度.     

A generalized Hill’s lemma and micromechanically based macroscopic constitutive model for heterogeneous granular materials

Based on the Hill’s lemma for classical Cauchy continuum, a generalized Hill’s lemma for micro–macro homogenization modeling of gradient-enhanced Cosserat continuum is presented in the frame of the average-field theory. In this context not only the strain and stress tensors defined in classical Cosserat continuum but also their gradients are attributed to assigned micro-structural representative volume element (RVE), that leads to a higher-order macroscopic Cosserat continuum modeling and enables to incorporate the micro-structural size effects. The enhanced Hill–Mandel condition for gradient-enhanced Cosserat continuum is extracted as a corollary of the presented generalized Hill’s lemma. The derived admissible boundary conditions for the modeling are deduced to direct the proper presentation of boundary conditions to be prescribed on the RVE in order to ensure the satisfaction of the Hill–Mandel energy condition.With the link between the discrete particle assembly and its effective Cosserat continuum in an individual RVE, the boundary conditions prescribed on the RVE modeled as Cosserat continuum are transformed into those prescribed to the peripheral particles of the RVE modeled as the discrete particle assembly. The micromechanically based macroscopic constitutive model and corresponding rate forms of the macroscopic stress–strain relations taking into account the local microstructure and its evolution are formulated with neither need of specifying the macroscopic constitutive relation nor need of providing macroscopic material parameters.     

非均质点阵结构材料性能快速预测方法研究

随着智能设计方法和先进制造技术的快速发展,高端装备呈现出智能化、轻量化、多功能化、仿生化和制造一体化等发展趋势。虽然点阵结构具有轻质高强、减振降噪、抗冲击吸能等优异性能,然而其一直存在微观建模复杂且性能表征分析耗时的难题。为此,本文提出了一种基于切割水平集的非均质点阵微结构建模与数据驱动的材料性能快速预测方法。首先,每个微结构原型由一个水平集函数隐式表示,多个微结构原型组成一个复合点阵微结构,通过改变微结构原型的类型和数量可组合成多种非均质微结构构型。然后,采用均匀化理论计算点阵微结构的等效弹性矩阵并生成数据集,并通过神经网络建立其切割高度变量到等效弹性矩阵与体积分数之间的映射,所得代理模型可快速预测出点阵微结构的材料性能参数,从而替代昂贵的均匀化计算。实验结果表明,本文提出的预测方法可精确表征非均质点阵微结构,构建的代理模型可大幅减少点阵微结构性能计算成本,且具有较高的精度和鲁棒性。     

Microstructure based two-scale modelling of soft tissues

A technique suitable for the modelling of large deforming biological tissues with a nearly periodic microstructure is presented in this work. The proposed approach takes into account the heterogeneous material constitution and geometrical arrangement of the tissues at the microstructural level. The global material properties are described in terms of the homogenized (effective) parameters. Numerical simulations are focused on the mechanical behaviour of an arterial wall.     

Two<Emphasis Type="Bold">-</Emphasis>scale concurrent topology optimization with multiple micro materials based on principal stress orientation

This paper studies two-scale concurrent topology optimization with multiple micro heterogeneous materials subjected to volume constraints. In previous work on concurrent two-scale optimization, either only one material with optimal microstructure is assumed or multiple micro materials are included but are distributed in prescribed geometrical domains. Here the selection of micro heterogeneous materials is based on the criterion for principal stress orientation in the macro structure. To meet this requirement, an additional constraint, called misplaced material volume constraint, is introduced to constrain the volume fraction of material that is misplaced in macro structure to be less than a small parameter ε. This constraint comprises several piecewise smooth penalty functions, each of which is a proper modification of Heaviside function. One advantage of the misplaced material volume constraint is that, without much modification to the original formulation, the optimized macro material is distributed in line with the use criterion and the material microstructures automatically converge to different optimized topologies. Three numerical examples are presented to show the effectiveness of the proposed method.     

Optimal shape design in biomimetics based on homogenization and adaptivity

Optimal shape design of microstructured materials has recently attracted a great deal of attention in materials science. The shape and the topology of the microstructure have a significant impact on the macroscopic properties. The paper is devoted to the shape optimization of new biomorphic microcellular silicon carbide ceramics produced from natural wood by biotemplating. This is a novel technology in the field of biomimetics which features a material synthesis from biologically grown materials into ceramic composites by fast high-temperature processing. We are interested in finding the best material-and-shape combination in order to achieve the optimal prespecified performance of the composite material. The computation of the effective material properties is carried out using the homogenization method. Adaptive mesh-refinement technique based on the computation of recovered stresses is applied in the microstructure to find the homogenized elasticity coefficients. Numerical results show the reliability of the implemented a posteriori error estimators.     

Homogenization of Periodically Varying Coefficients in Electromagnetic Materials

In this paper, we employ the periodic unfolding method for simulating the electromagnetic field in a composite material exhibiting heterogeneous microstructures which are described by spatially periodic parameters. We consider cell problems to calculate the effective parameters for a Debye dielectric medium in the case of a circular microstructure in two dimensions. We assume that the composite materials are quasi-static in nature, i.e., the wavelength of the electromagnetic field is much larger than the relevant dimensions of the microstructure.     

Homogenization method for heterogeneous material based on boundary element method

In this paper, formulations for homogenization method based on the boundary element method, for heterogeneous elastic materials having periodic microstructure, are presented. The formulations are developed using a novel use of the method of weighted residuals. Both the trial and test functions are expressed by asymptotic expansions with respect to the size ε of the unit cell. Two types of boundary element formulations for the analysis of unit cell, are proposed; single-region boundary element method with volume integrals and multi-region boundary element method. Convenient formulae to compute effective (homogenized) elastic constants, are presented.     

Design of piezocomposite materials and piezoelectric transducers using topology optimization—Part I

Summary Currently developments of piezocomposite materials and piczoelectric actuators have been based on the use of simple analytical models, test of prototypes, and analysis using the finite element method (FEM), usually limiting the problem to a parametric optimization. By changing the topology of these devices or their components, we may obtain an improvement in their performance characteristics. Based on this idea, this paper discusses the application of topology optimization combined with the homogenization method and FEM for designing piezocomposite materials. The homogenization method allows us to calculate the effective properties of a composite material knowing its unit cell topology. New effective properties that improves the electromechanical efficiency of the piezocomposite material are obtained by designing the piezocomposite unit cell. This method consists of finding the distribution of the material and void phases in a periodic unit cell that optimizes the performance characteristics of the piezocomposite. The optimized solution is obtained using Sequential Linear Programming (SLP). A general homogenization method applied to piczoelectricity was implemented using the finite element method (FEM). This homogenization method has no limitations regarding volume fraction or shape of the composite constituents. The main assumptions are that the unit cell is periodic and that the scale of the composite part is much larger than the microstructure dimensions. Prototypes of the optimized piezocomposites were manufactured and experimental results confirmed the large improvement. Department of Mechanical Engineering and Applied Mechanics Department of Mechanical Engineering and Applied Mechanics     

Correlations between production process, states and mechanical properties of microspecimens made of zirconia

For a safe design of micromechanical components, a reliable database of their properties is required. The existing material properties of macroscopic specimens normally cannot be used due to the neglect of some important aspects of the “micro world”, e.g. the ratio of surface to volume is much higher which results in a larger influence of surface defects on the material strength. Detailed analysis of the microstructure and surface topography of microcomponents in combination with their mechanical properties is very expedient for straight-forward optimization of the manufacturing process. Using the resulting data of the properties investigated, correlations between production process, states and mechanical properties of the micro bending specimens made of ZrO₂ using low-pressure injection molding were identified. These correlations will be used to established a concept for dimensioning of mechanically loaded microparts.