非饱和颗粒材料的多孔连续体有效压力与有效广义Biot应力

多孔连续体理论框架下的非饱和多孔介质广义有效压力定义和Bishop参数的定量表达式长期以来存在争议,这也影响了对与其直接相关联的非饱和多孔介质广义Biot有效应力的正确预测.基于随时间演变的离散固体颗粒-双联液桥-液膜体系描述的Voronoi胞元模型,利用由模型获得的非饱和颗粒材料表征元中水力-力学介观结构和响应信息,文章定义了低饱和度多孔介质局部材料点的有效内状态变量:非饱和多孔连续体的广义Biot有效应力和有效压力,导出了其表达式.所导出的有效压力公式表明,非饱和多孔连续体的有效压力张量为各向异性,它不仅对非饱和多孔连续体广义Biot有效应力张量的静水应力分量的影响呈各向异性,同时也对其剪切应力分量有影响.文章表明,非饱和多孔连续体中提出的广义Biot理论和双变量理论的基本缺陷在于它们均假定反映非混和两相孔隙流体对固相骨架水力-力学效应的有效压力张量为各向同性.此外,为定义各向同性有效压力张量和作为加权系数而引入的Bishop参数并不包含对非饱和多孔连续体中局部材料点水力-力学响应具有十分重要效应的基质吸力.所导出的非饱和多孔介质广义Biot有效应力和有效压力公式(包括反映有效压力...     

含孔隙变厚度FG圆板的湿热力学响应

功能梯度材料(functionally graded materials, FGM)是组份含量按特定方向连续变化的非均匀复合材料,可有效解决传统复合材料组份之间结合能力弱和不同组份性能难以协调等问题,达到诸如缓和应力集中和优化应力分布等效果,使整体材料在保持细观结构完整性的同时充分发挥各组份材料的性能优势.由于制备技术等原因或出于特殊功能的需要,微孔或孔隙是各类型FGM中的常见缺陷.从细观结构上看,多孔FGM中的孔隙包含了单一组份内的材料孔隙和组份微粒间的结构间隙,这些孔隙将对FGM的力学性能,尤其是在湿热环境下的力学行为产生影响.本文考虑FGM中的两类细观孔隙(材料孔隙和结构孔隙),提出了令各类孔隙依赖于各自组份变化,再线性叠加得到的整体孔隙计算式.考虑组份材料和孔隙填充物(液相水和水蒸气)性质的温度相关性,建立了湿热相关FGM材料模型.针对厚度沿径向变化的旋转圆板结构,应用该FGM材料模型,推导了圆板的非线性稳态湿热控制方程及考虑湿热弹性本构的位移控制方程,采用微分求积法(differential quadrature method,DQM),获得了圆板的湿热场、位移场和应力分布.在数值算例中,利用退化模型的解析解对本文的数值计算方法进行了验证,继而通过改变各关键参数,讨论了两类孔隙率、梯度指数和圆板厚度变化对含孔隙FGM变厚度旋转圆板湿热力学响应的影响规律.      

Averaging Anisotropic Elastic Constant Data

A method of averaging the data on the anisotropic elastic constants of a material is presented. The anisotropic elastic constants are represented by the elasticity tensor which is expressed as a second rank tensor in a space of six dimensions. The method consists of averaging eigenbases of different measurements of the elasticity tensor, then averaging the eigenvalues referred to the average eigenbasis. The eigenvalues and eigenvectors are obtained by using a representation of the stress-strain relations due, in principle, to Kelvin [17, 18]. The formulas for the representation of the averaged elasticity tensor are simple and concise. The applications of these formulas are illustrated using previously reported data, and are contrasted with the traditional analysis of the same data by Hearmon [9]. An interesting result that emerges from this analysis is a method dealing with variable composition anisotropic elastic materials whose elastic constants depend upon the particular composition. In the case of porous isotropic materials, for example, it is customary to regress the Young's modulus against porosity. The results of this paper suggest a structure or paradigm for extending to anisotropic materials this empirical method of regressing elastic constant data against composition or porosity.     

一种孔隙介质力学模型及在水泥基材料的应用

基于细观力学和断裂力学的基本理论提出一个新的分析模型, 对孔隙介质的力学性能进行了分析. 依据孔隙介质内部孔隙的几何描述和状态参数,如孔隙率、形状、尺度及分布等,通过等效夹杂理论获得孔隙介质的等效本构方程,其最终变量为应力、应变和孔隙的形态参数. 根据断裂理论中材料承受载荷作用下破坏增长过程中的能量守恒,对孔隙介质变形过程中机械能、弹性应变能和载荷提供的势能进行分析, 根据能量守恒定律建立能量守恒方程,其最终变量也为应力、应变和孔隙的形态参数. 根据等效本构方程和能量守恒方程,获得孔隙介质承受载荷作用下的应力应变关系. 最后将该力学模型应用于水泥基材料,计算水泥基材料的力学性能并与文献中的结果进行对比分析,结果显示模型的计算结果准确有效.      

基于微面有效应力矢量的各向异性屈服准则

基于微面模型，定义损伤变量为微面上有效承载面积的减少. 将Kachanov的一维有效 应力概念推广到三维，提出微面有效应力矢量的概念. 根据微面的有效应力矢量，将无损材 料的宏观应力张量及不变量与微面应力矢量的积分关系拓展到有损材料，得到了有损材料的 宏观有效应力张量及其不变量与宏观名义应力张量、微面面积损伤组构张量之间的关系. 将 无损材料的以应力张量不变量表示的Drucker-Prager准则推广到有损材料，建立了含缺陷 材料的各向异性屈服准则. 对有损材料，宏观有效应力张量与Murakami的有效应力张量具 有相同的形式，各向异性强度准则与Liu等提出的扩展Hill准则有相同的形式，当不考虑 静水应力对屈服的影响时，它与Hill准则具有相同的形式.     

Dependency of Tortuosity and Permeability of Porous Media on Directional Distribution of Pore Voids

Single-phase fluid flow in porous media is usually direction dependent owing to the tortuosity associated with the internal structures of materials that exhibit inherent anisotropy. This article presents an approach to determine the tortuosity and permeability of porous materials using a structural measure quantifying the anisotropic distribution of pore voids. The approach uses a volume averaging method through which the macroscopic tortuosity tensor is related to both the average porosity and the directional distribution of pore spaces. The permeability tensor is derived from the macroscopic momentum balance equation of fluid in a porous medium and expressed as a function of the tortuosity tensor and the internal structure of the material. The analytical results generally agree with experimental data in the literature.     

A homogenization-based constitutive model for isotropic viscoplastic porous media

An approximate model based on the “second-order” nonlinear homogenization method is proposed to estimate the effective behavior of isotropic, viscoplastic, porous materials. The model is constructed in such a way that it reproduces exactly the behavior of a “composite-sphere assemblage” in the limit of hydrostatic loadings, and therefore coincides with the hydrostatic limit of Gurson’s criterion in the special case of ideal plasticity. As a consequence, the new model improves on earlier homogenization estimates, which have been found to be quite accurate for low triaxialities but overly stiff for sufficiently high triaxialities and nonlinearities. Additionally, the estimates delivered by the model exhibit a dependence on the third invariant of the macroscopic stress tensor, which has a nontrivial effect on the effective response of the material at moderate triaxialities. The proposed model is compared with exact results obtained for a special class of porous materials with sequentially laminated microstructures. The agreement is found to be quite good for the entire range of stress triaxialities, and all values of the porosity and nonlinearity considered.     

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。     

Effect of pore distribution on the statistics of peak stress and overall properties of porous material

This paper addresses the effect of pore distribution on the overall properties and local stress fields in a porous material. Thermal and elastic fields in materials with uniform microstructure are compared with those of materials containing distinguishable clusters of circular or elliptic shape. The numerical simulation combines multipole expansion of local fields with the multi-particle unit cell method. Our work demonstrates that statistics of the peak stresses follow Gumbel’s rule derived for statistics of extreme values and are directly related to statistics of nearest neighbors. Based on this correspondence, an analytical expression for statistics of maximal stresses in a porous material with arbitrary microstructure is constructed in terms of porosity and statistics of minimal distances between the nearest neighbors. At the same time, the numerical analysis indicates that overall elastic constants and thermal (or electrical) conductivity are almost insensitive to the actual distribution of pores – uniform or with distinguishable pore clusters – at least in the examined interval of porosity (up to 50%).     

基于介观结构的饱和与非饱和多孔介质有效应力

基于描述含液颗粒材料介观结构的Voronoi 胞元模型和离散颗粒集合体与多孔连续体间的介-宏观均匀化过程, 定义饱和与非饱和多孔介质有效应力. 导出了计及孔隙液压引起之颗粒体积变形的饱和多孔介质广义有效应力. 用以定义广义有效应力的Biot 系数不仅依赖于颗粒材料的多孔连续体固体骨架及单个固体颗粒的体积模量(材料参数),同时与固体骨架当前平均广义有效应力及单个固体颗粒的体积应变(状态量) 有关. 提出了描述非饱和多孔介质中非混和固体颗粒、孔隙液体和气体等三相相互作用的具介观结构的Voronoi 胞元模型.具体考虑在低饱和度下双联(binary bond) 模式的摆动(pendular) 液桥系统介观结构. 导出了基于介观水力-力学模型的非饱和多孔介质的各向异性有效应力张量与有效压力张量. 考虑非饱和多孔介质Voronoi 胞元模型介观结构的各向同性情况,得到了与非饱和多孔连续体理论中唯象地假定的标量有效压力相同的有效压力形式.但本文定义的与确定非饱和多孔介质有效应力和有效压力相关联的Bishop 参数由基于三相介观水力-力学模型, 作为饱和度、孔隙度和介观结构参数的函数导出,而非唯象假定.      

Calculating the Anisotropic Permeability of Porous Media Using the Lattice Boltzmann Method and X-ray Computed Tomography

A lattice Boltzmann (LB) method is developed in this article in a combination with X-ray computed tomography to simulate fluid flow at pore scale in order to calculate the anisotropic permeability of porous media. The binary 3D structures of porous materials were acquired by X-ray computed tomography at a resolution of a few microns, and the reconstructed 3D porous structures were then combined with the LB model to calculate their permeability tensor based on the simulated velocity field at pore scale. The flow is driven by pressure gradients imposed in different directions. Two porous media, one gas diffusion porous layer used in fuel cells industry and glass beads, were simulated. For both media, we investigated the relationship between their anisotropic permeability and porosity. The results indicate that the LB model is efficient to simulate pore-scale flow in porous media, and capable of giving a good estimate of the anisotropic permeability for both media. The calculated permeability is in good agreement with the measured date; the relationship between the permeability and porosity for the two media is well described by the Kozeny–Carman equation. For the gas diffusion layer, the simulated results showed that its permeability in one direction could be one order of magnitude higher than those in other two directions. The simulation was based on the single-relaxation time LB model, and we showed that by properly choosing the relaxation time, it could give similar results to those obtained using the multiple-relaxation time (MRT) LB method, but with only one third of the computational costs of MRTLB model.     

空心材料导热性能预测研究

本文建立了一种预测空心材料导热性的方法。研究了空心材料的导热性。用柱形空心材料分析了体分比和孔洞的排列方式对整体材料导热性的影响，用圆柱形、方柱形空心材料和含裂纹材料，分析了空心形状对材料导热性的影响。同他人的实验结果和某些现有的理论模型比较表明，本文方法是有效的。本文的结果能够很好地解释实验结果。     

Permeability anisotropy due to consolidation of compressible porous media

The characterisation of flow through porous media is important for all solid–liquid separation and fluid transport realms. The permeability of porous media can be anisotropic and furthermore, the extent of anisotropy can be increased as a result of an applied compressive force. However, the understanding of how anisotropy develops is incomplete. An overview of research on permeability anisotropy is given and an expression for predicting anisotropy as a function of void ratio is offered. The two underlying assumptions of the proposed model are: flow in different directions occurs within the same network of pores and deformation is primarily due to the compression of the particles in the direction of the applied force rather than due to particle rearrangement. The assumption of network connectivity allows permeability anisotropy to be described as a function of flow path tortuosity only. Results are presented for hydraulic anisotropy measured in lignite that has been upgraded by a compression dewatering method known as mechanical thermal expression. The lignite permeability is shown to be up to eight times greater in the direction perpendicular to compression, suggesting that the rate of dewatering could be significantly increased by choosing the drainage to also be perpendicular to the direction of the applied compressive force. It is illustrated that the proposed anisotropy model can be used to accurately predict the experimentally determined permeability anisotropy ratios for lignite, as well as for other materials including sand, clay and kaolin.     

Asymptotic analysis of the equilibrium equation of a fluid-saturated porous medium by the homogenization method

The homogenization of static elasticity equations describing the stress strain state of fluid-saturated porous medium is considered. In this paper, the homogenization method is used to determine the pore pressure transfer tensor, which (a coefficient in the isotropic case) is an important parameter influencing the stress-strain state of fluid-saturated rocks. It shows what a part of the pressure in the fluid is “active” in the formation of macroscopic strains.The pore pressure transfer tensor is calculated for model and real geological specimens. The dependence of this tensor on the porosity, pore shape, and Poisson ratio is investigated. The use of the computational technique for determining the effective properties of rocks shows that it is practically important in the engineering geology.     

The order of a damage tensor

In this paper, the stress deformation constitutive relations for continua are discussed and a stress deformation constitutive relation expressed by functional tensorial expression is found. When we study the anisotropic damage of anisotropic materials either from a macroscopic continuum mechanics model or from a microdefect model, there exists a limit to the order of a damage tensor, and the condition under which the damage variable may be described by a tensor lower than those of the highest order is found.     

Application of the asymptotic homogenization method to find the expansion coefficient of a water-saturated porous medium during freezing processes

An approach is proposed to determine the effective relative expansion coefficient of a porous medium filled with water during its freezing. This approach is based on an asymptotic homogenization method. An explicit formula is derived to find the expansion coefficient in the case of open pores. In the case of closed pores, the expansion coefficient is a second-rank tensor. Its determination requires to solve the so-called local problems in a representative volume element. The proposed approach can be used to determine the effective expansion coefficient during the freezing of water in the soil. Its efficiency is confirmed for model and realistic geological structures.     

多孔材料孔隙尺寸对渗透系数影响的数值模拟

采用有限元方法数值模拟了多孔材料的孔隙尺寸与等效渗透系数之间的非线性关系.有限元模型中的固体骨架和孔隙根据孔隙率的大小随机生成,模型中的材料参数和单元属性用ANSYS中的APDL参数化语言赋值.根据有限元随机模拟断面的流量分布和稳态渗流问题的达西定律,计算在不同孔隙尺寸的等效渗透系数,研究等效渗透系数与孔隙尺寸之间的关系.计算结果表明,在孔隙率不变的情况下,等效渗透系数与孔隙尺寸的平方成正比,该结论与经验公式相一致.而孔隙尺寸不变的条件下,随着孔隙率的增加等效渗透系数近似呈线性增加.     

A new stochastic method of reconstructing porous media

We present a new stochastic method of reconstructing porous medium from limited morphological information obtained from two-dimensional micro- images of real porous medium. The method is similar to simulated annealing method in the capability of reconstructing both isotropic and anisotropic structures of multi-phase but differs from the latter in that voxels for exchange are not selected completely randomly as their neighborhood will also be checked and this new method is much simpler to implement and program. We applied it to reconstruct real sandstone utilizing morphological information contained in porosity, two-point probability function and linear-path function. Good agreement of those references verifies our developed method’s powerful capability. The existing isolated regions of both pore phase and matrix phase do quite minor harm to their good connectivity. The lattice Boltzmann method (LBM) is used to compute the permeability of the reconstructed system and the results show its good isotropy and conductivity. However, due to the disadvantage of this method that the connectivity of the reconstructed system’s pore space will decrease when porosity becomes small, we suggest the porosity of the system to be reconstructed be no less than 0.2 to ensure its connectivity and conductivity.     

Phenomenological theory of failure criterion for composite materials

In this paper, some current anisotropic failure criteria in the forms of tensor polynomials are investigated. In order to determine the interaction coefficients of the failure criterion, a non-linear optimization method is proposed. The results obtained by different theories as well as the optimization method are compared with the test data of some composite materials. The comparison shows that the optimization method is effective.     

弹脆性材料的损伤本构关系及应用

本文根据连续损伤力学方法,对弹脆性材料损伤的力学响应进行一般分析。理论分析中,材料与损伤都是各向异性的。还导出了计算损伤张量、有效弹性张量、真实应力张量以及损伤能耗率张量的实用表达式。