复合材料周期性线弹性微结构的拓扑优化设计

提出复合材料周期性线弹性微结构拓扑优化设计的模型，模型1设计具有极值弹性特性的复合材料，模型2设计工况最刚微结构单胞。通过该模型和均匀化技术可以获得优化的微结构单胞，进而改善或者得到最优宏观特性的复合材料。为了便于制造和应用，用胞体材料而不是多相材料来得到复合材料的极值弹性特性和最大刚度。优化结果表明，该模型与数值方法相结合可以有效地实现微结构的拓扑优化设计。     

Modeling the effects of material non-linearity using moving window micromechanics

In the analysis of materials with random heterogeneous microstructure the assumption is often made that material behavior can be represented by homogenized or effective properties. While this assumption yields accurate results for the bulk behavior of composite materials, it ignores the effects of the random microstructure. The spatial variations in these microstructures can focus, initiate and propagate localized non-linear behavior, subsequent damage and failure. In previous work a computational method, moving window micromechanics (MW), was used to capture microstructural detail and characterize the variability of the local and global elastic response. Digital images of material microstructure described the microstructure and a local micromechanical analysis was used to generate spatially varying material property fields. The strengths of this approach are that the material property fields can be consistently developed from digital images of real microstructures, they are easy to import into finite element models (FE) using regular grids, and their statistical characterizations can provide the basis for simulations further characterizing stochastic response. In this work, the moving window micromechanics technique was used to generate material property fields characterizing the non-linear behavior of random materials under plastic yielding; specifically yield stress and hardening slope, post yield. The complete set of material property fields were input into FE models of uniaxial loading. Global stress strain curves from the FE–MW model were compared to a more traditional micromechanics model, the generalized method of cells. Local plastic strain and local stress fields were produced which correlate well to the microstructure. The FE–MW method qualitatively captures the inelastic behavior, based on a non-linear flow rule, of the sample continuous fiber composites in transverse uniaxial loading.     

复合材料扭转轴截面微结构拓扑优化设计

提出复合材料扭转轴截面微结构拓扑优化设计新模型，模型的优化目标是获得具有最大宏观剪切特性加权和的单胞形式．通过模型和均匀化方法及优化技术可以获得优化的微结构单胞，进而改善或者得到最优宏观弹性特性的复合材料．为了便于制造和应用，胞体材料用来获得复合材料的极值剪切模量．最后的优化结果表明，该模型连同数值处理技巧可以非常有效地实现微结构的拓扑优化设计．     

多相材料微结构多目标拓扑优化设计

在采用多尺度均匀化方法求解微结构等效特性的基础上，提出了多相材料 微结构的多目标优化设计模型. 以组分材料用量为约束，采用周长控制消除棋盘格，结合有 限元方法和对偶凸规划求解技术，对两相和三相材料微结构多项等效模量的组合进行了优化 设计. 研究比较了微结构网格粗细、材料组分以及三相材料微结构优化中的两相实体材料弹 性模量相对比例不同对优化结果的影响. 数值算例验证了优化模型和优化算法的有效性，表 明了相关因素对优化结果的影响.     

HOMOGENIZATION—BASED TOPOLOGY DESIGN FOR PURE TORSION OF COMPOSITE SHAFTS

In conjunction with the homogenization theory and the finite element method, the mathematical models for designing the corss-section of composite shafts by maximizing the torsion rigidity are developed in this paper. To obtain the extremal torsion rigidity, both the cross-section of the macro scale shaft and the representative microstructure of the composite material are optimized using the new models. The micro scale computational model addresses the problem of finding the periodic microstructures with extreme shear moduli. The optimal microstructure obtained with the new model and the homogenization method can be used to improve and optimize natural or artificial materials. In order to be more practical for engineering applications, cellular materials rather than ranked materials are used in the optimal process in the existence of optimal bounds for the elastic properties. Moreover, the macro scale model is proposed to optimize the cross-section of the torsional shaft based on the tailared composites. The validating optimal results show that the models are very effective in obtaining composites with extreme elastic properties, and the cross-section of the composite shaft with the extremal torsion rigidity. The project supported by the National Natural Science Foundation of China (10172078 and 10102018)     

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.     

Scale effects in plasticity of random media: status and challenges

When the separation of scales in random media does not hold, the representative volume element (RVE) of classical continuum mechanics does not exist in the conventional sense, and various new approaches are needed. This subject is discussed here in the context of plasticity of random, microheterogeneous media. The first principal topic considered is that of hierarchies of mesoscale bounds, set up over a statistical volume element (SVE), for elastic–plastic-hardening microstructures; these bounds, with growing mesoscale, tend to converge to RVE responses. Following a formulation of the said hierarchies from variational principles and their illustration on two specific examples of power-law hardening materials, we turn to rigid-perfectly-plastic materials. The latter are illustrated by simulations in the setting of a planar random chessboard. The second principal topic is the analysis of spatially non-uniform response patterns of randomly heterogeneous plastic materials. We focus here on the geodesic properties of shear-band patterns, and then on the correlation of strain fields to the underlying microstructures. In the case of perfectly-plastic materials, shear-bands become slip-lines, but their spatial disorder is still present, and is described in ensemble sense by wedges of randomly scattered characteristics.     

Material sensitivity analysis in homogenization of linear elastic composites

Summary  The main goal of the paper is to present theoretical aspects and the finite element method (FEM) implementation of the sensitivity analysis in homogenization of composite materials with linear elastic components, using effective modules approach. The deterministic sensitivity analysis of effective material properties is presented in a general form for an n-components periodic composite, and is illustrated by the examples of 1D as well as of 2D heterogeneous structures. The results of the sensitivity analysis presented in the paper confirm the usefulness of the homogenization method in computational analysis of composite materials the method may be applied to computational optimization of engineering composites, to the shape-sensitivity studies and, after some probabilistic extensions, to stochastic sensitivity analysis of random composites. Received 10 November 2000; accepted for publication 24 April 2001     

Discrete fracture modeling of asphalt concrete

A heterogeneous fracture approach is presented for modeling asphalt concrete that is composed of solid inclusions and a viscous matrix, and is subjected to mode-I loading in the fracture test configuration. A heterogeneous fracture model, based on the discrete element method (DEM), is developed to investigate various fracture toughening mechanisms of asphalt materials using a high-resolution image processing technique. An energy-based bilinear cohesive zone model is used to model the crack initiation and propagation of materials, and is implemented as a user-defined model within the discrete element method. Experimental fracture tests are performed to investigate various fracture behavior of asphalt concrete and obtain material input parameters for numerical models. Also, bulk material properties are necessary for each material phase for heterogeneous numerical models; these properties are determined by uniaxial complex modulus tests and indirect tensile strength tests. The main objective of this study is to integrate the experimental tests and numerical models in order to better understand the fracture mechanisms of asphaltic heterogeneous materials. Experimental results and numerical simulations are compared at different test conditions with excellent agreement. The heterogeneous DEM fracture modeling approach has the potential capability to understand various crack mechanisms of quasi-brittle materials.     

A concurrent micromechanical model for predicting nonlinear viscoelastic responses of composites reinforced with solid spherical particles

A concurrent micromechanical model for predicting nonlinear viscoelastic responses of particle reinforced polymers is developed. Particles are in the form of solid spheres having micro-scale diameters. The composite microstructures are idealized by periodically distributed cubic particles in a matrix medium. Each particle is assumed to be fully surrounded by polymeric matrix such that contact between particles can be avoided. A representative volume element (RVE) is then defined by a single particle embedded in the cubic matrix. A spatial periodicity boundary condition is imposed to the RVE. One eighth unit-cell model with four particle and polymer subcells is generated due to the three-plane symmetry of the RVE. The solid spherical particle is modeled as a linear elastic material. The polymeric matrix follows nonlinear viscoelastic behaviors of thermorheologically simple materials. The homogenized micromechanical relation is developed in terms of the average strains and stresses in the subcells and traction continuity and displacement compatibility at the subcells’ interfaces are imposed. A stress–strain correction scheme is also formulated to satisfy the linearized micromechanical and the nonlinear constitutive relations. The micromechanical model provides three-dimensional (3D) effective properties of homogeneous composite responses, while recognizing microstructural geometries and in situ material properties of the heterogeneous medium. The micromechanical formulation is designed to be compatible with general displacement based finite element (FE) analyses. Experimental data and analytical micromechanical models available in the literature are used to verify the capability of the above micromechanical model for predicting the overall composite behaviors. The proposed micromodel is also examined in terms of computational efficiency and accuracy.     

多相材料传热微结构的多目标优化设计

提出基于散热弱度的材料微结构热传导性能的预测方法,分别从理论和数值上验证该方法与均匀化方法的等效性;推导出微结构等效热传导系数的灵敏度计算格式,建立传热微结构拓扑优化的数学模型.以二维、三维多相材料等效热传导系数的加权组合为目标,采用凸规划对偶优化算法和二次型周长约束进行材料微结构的设计和材料分布的棋盘格控制.数值算例表明基于散热弱度的传热材料微结构设计是可行、有效的,可以为实际的材料设计提供依据.     

含大量随机分布细小纤维的单向纤维增强复合材料横向弹性性能参数计算的内嵌区域模型法

利用有限元方法求取单向纤维增强复合材料的横向弹性性能参数的计算模型包括三维模型、两维平面应变模型、单胞模型等等.由于单胞模型仅仅适用于纤维规则排列情况.在纤维随机分布且纤维大小亦为随机时,单向纤维增强复合材料横向弹性性能参数必须通过对于复合材料块体的计算才能获得.同时在随机分布纤维的数量增大时,三维模型和二维平面应变模型的计算量急剧增加,模型的处理能力不强.该文提出一种利用内嵌区域模型来计算含大量随机大小、随机分布细小纤维的单向纤维增强复合材料块体的横向弹性性能参数的方法,有效降低了计算量.在较低的计算费用下,能够快速获得单向纤维增强复合材料的横向弹性性能参数.     

功能梯度材料结构热力耦合概率分析方法

基于自洽平均微观力学W-T(Wakashima-Tsukamoto)模型和拉丁超立方抽样,建立一种功能梯度平板热力耦合概率分析方法.以材料物理属性和空间分布的不确定性随机参数作为概率分析的输入,以热应力作为输出,基于本征正交分解POD(Proper Orthogonal Decomposition)对热应力的随机时间历...     

Statistical characterization of meso-scale uniaxial compressive strength in brittle materials with randomly occurring flaws

Increasingly fine spatial resolution in numerical models of brittle materials promises to improve prediction and characterization of dynamic failure in these materials. However, as the resolution of these numerical models begins to approach the material micro-scale, the associated discretization requires a definitive connection to the microstructure. In many cases a numerical model (e.g., a finite element mesh) that explicitly resolves each flaw within the material is not feasible for macro-scale analyses. As an alternative, each element can be treated as a meso-scale continuum with constitutive properties that reflect the characteristics of the underlying microstructure. Small scale elements will exhibit random variations in the constitutive properties as a result of the random variations in the number and types of flaws and the flaw sizes contained within each element. The present paper proposes a technique for assigning probability distributions to these element properties, which can be thought of as the meso-scale constitutive properties. In particular, the strain-rate dependent compressive uniaxial strength of a ceramic is modeled using a two-dimensional analytical model developed by Paliwal and Ramesh (2008). The effect on the probability distribution of meso-scale (or element-level) strength from flaw density, flaw size distribution, flaw clustering, and strain rate are studied. Higher strain rates, more flaw clustering, and decreasing element size all contribute to greater scatter in uniaxial compressive strength. Variations in flaw size increase the scatter in the strength more for low strain rate loadings and less clustered microstructures. The results provide interesting comparisons to the classical assumption of a two-parameter Weibull-distributed strength, showing that a three-parameter Weibull distribution and even a lognormal distribution fit better with the simulated strength data.     

Elasticity and strength of partially sintered ceramics

A discrete element model for the elastic and fracture behavior of partially sintered ceramics is presented. It accounts for the granular character of the material when a large amount of porosity (typically >0.2-0.4) is left after sintering. The model uses elastic force-displacement laws to represent the bond formed between particles during sintering. Bond fracture in tension and shearing is accounted for in the model. Realistic numerical microstructures are generated using a sintering model on random particle packings. In particular, packings with fugitive pore formers are used to create partially sintered microstructures with large pores. The effective elastic response and the strength of these microstructures are calculated in tension and compression. The link between important microstructural features such as bond size or coordination number and macroscopic behavior is investigated. In particular, it is shown that porosity alone is not sufficient to account for the mechanical properties of a partially sintered material.     

材料三维微结构表征及其晶体塑性有限元模拟

材料的力学性能，尤其是在有限变形下所呈现的宏观各向异性，是材料结构设计和服役寿命考虑的关键因素。由于宏观模型不能较好地反映材料微观结构（晶粒的形貌和取向等）对宏观塑性各向异性的影响，因此，本文建立了能实际反映晶粒形貌的三维Voronoi模型，并基于晶体塑性理论对铝合金在有限变形下的响应进行计算。首先，建立反映材料微结构的代表性体积单元RVE模型进行计算，并与实验结果进行对比验证。然后，以单向拉伸为例，分析了有限变形过程中试件的晶粒形貌和取向分布等微观因素对宏观各向异性演化的影响，并从材料和结构两个层面讨论了微观结构对宏观力学性能的影响。结果表明，本文模型能够反映微观结构对宏观力学性能的影响，为实际生产制造领域构件的力学性能提供可靠的预测。     

复合材料有效弹性性质分析方法eeeeee

建立复合材料的有效性质与微结构参数的关联,是复合材料优化设计的基础。本文具体针对有效弹性性质,重点介绍了建立有效性的基本思路 和主要分析方法。首先讨论了代表单元的概念,然后分别从复合材料有效性质的普适关系、界限理论和近似方法三个不同的视角较全面的介绍了建立非均质材料有效性质的方法、主要结果和最新进展。重点从构型的概念和微结构分布形式上分析了各种模型间及分析方法之间的联系与差别。最后还就建立非均质材料有效性质中存在的问题和研究热点做了简单的介绍。     

考虑材料各向异性的熔丝制造PLA点阵结构弹性各向同性设计

增材制造技术的兴起激发了国内外学者对结构创新设计的热情. 然而, 增材制造材料的各向异性为结构力学性能的预测与设计带来了一定的困难. 为了准确预测熔丝制造聚乳酸(PLA)材料和点阵结构的弹性性能, 并实现点阵结构的弹性各向同性设计, 首先, 本文采用正交各向异性弹性模型来描述PLA材料的弹性行为, 通过实验和计算得到了正交各向异性模型需要的9个独立的弹性常数. 然后, 设计了一种力学性能可调的二维组合桁架点阵结构, 基于代表体元法, 在不考虑材料各向异性的情况下推导出了其平面内等效弹性性能的解析表达式及弹性各向同性条件. 最后, 根据PLA材料的各向异性调整点阵结构内部杆件的弹性模量和厚度, 并基于代表体元法重新推导出了点阵结构平面内等效弹性性能的解析表达式及其弹性各向同性条件. 研究结果表明, 正交各向异性弹性模型适用于描述熔丝制造PLA材料的弹性行为, 基于该模型能够准确预测PLA材料在任意方向上的弹性模量. 在预测与设计熔丝制造点阵结构的力学性能时需要充分考虑材料的各向异性. 在考虑材料的各向异性之后, 基于代表体元法调整点阵结构的几何尺寸, 能够实现部分点阵结构的弹性各向同性设计.      

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。     

两种五零能模式材料单胞构型及其性能分析

五零能模式材料是一种新型的人工超材料,虽属于弹性材料,但组成其单胞的特殊构型使其宏观静态表现为仅能承载一种受力状态,动态表现为仅能传播一种弹性波。本文首先构造了两种五零能模式材料的单胞构型,其具有不同的弹性特性,其中一种材料可传播弹性膨胀波,另一种可传播弹性剪切波。然后分别采用代表体元法和均匀化法分析这两种单胞的等效弹性模量。五零能模式材料的分析分为两步更直观,开始从单胞桁架模型入手,检验单胞构型是否满足五零能模式的定义,然后分析单胞实体模型,考察单胞构型的结构参数与其等效弹性模量的关系。研究表明对于这种低密度弹性材料的分析,代表体元法更适合。