Convexity of the Strain-Energy Function in a Two-Scale Model of Ideal Fabrics

A two-scale model is used to generate the macro-scale constitutive response of a sheet of woven fabric from a micro-scale model of interacting yarns regarded as crossed elasticae in contact. The model furnishes a macro-scale strain-energy function for an orthotropic membrane idealized as being weak in shear compared to the extensional resistance of material curves representing the yarns. The operative Legendre–Hadamard inequality for the membrane is derived and shown to be satisfied by a suitably relaxed version of the computed strain-energy function.     

Micromechanical study of elastic moduli of loose granular materials

In micromechanics of the elastic behaviour of granular materials, the macro-scale continuum elastic moduli are expressed in terms of micro-scale parameters, such as coordination number (the average number of contacts per particle) and interparticle contact stiffnesses in normal and tangential directions. It is well-known that mean-field theory gives inaccurate micromechanical predictions of the elastic moduli, especially for loose systems with low coordination number. Improved predictions of the moduli are obtained here for loose two-dimensional, isotropic assemblies. This is achieved by determining approximate displacement and rotation fields from the force and moment equilibrium conditions for small sub-assemblies of various sizes. It is assumed that the outer particles of these sub-assemblies move according to the mean field. From the particle displacement and rotation fields thus obtained, approximate elastic moduli are determined. The resulting predictions are compared with the true moduli, as determined from the discrete element method simulations for low coordination numbers and for various values of the tangential stiffness (at fixed value of the normal stiffness). Using this approach, accurate predictions of the moduli are obtained, especially when larger sub-assemblies are considered. As a step towards an analytical formulation of the present approach, it is investigated whether it is possible to replace the local contact stiffness matrices by a suitable average stiffness matrix. It is found that this generally leads to a deterioration of the accuracy of the predictions. Many micromechanical studies predict that the macroscopic bulk modulus is hardly influenced by the value of the tangential stiffness. It is shown here from the discrete element method simulations of hydrostatic compression that for loose systems, the bulk modulus strongly depends on the stiffness ratio for small stiffness ratios.     

Grain- and macro-scale kinematics for granular micromechanics based small deformation micromorphic continuum model

Macro-scale deformation of granular solids comprising large number of grains (>10⁶) are most efficiently described within the framework of continuum mechanics. It is notable, however that the micro-scale deformations in these materials are concentrated at the grain-boundaries or grain-contacts. Thus, the deformation energies in these systems must be modeled by considering the deformations concentrated in the neighborhood of the grain-boundaries or grain-contacts. To address this issue, grain-interactions has been widely described in the Hertzian sense by considering the relative movement of points on either side of a grain boundary or contact treated as an imperfect interface. This communication introduces the relevant kinematic variables given in the terms of the grain displacements, spins and size that can be used to estimate the relative movement of a grain boundary or contact. The macro-scale kinematic variables useful for continuum modeling are then identified with the grain-scale kinematic variables. The deformation energy density of the granular solid can thus be expressed both in terms of the grain-scale as well as the macro-scale kinematic variables providing the necessary pathway for micro-macro identification which can lead to non-classical micromorphic continuum models that incorporate grain-scale representation.     

延性金属层裂自由面速度曲线特征多尺度模拟研究

以延性金属钽为研究对象,对钽在平板撞击下的层裂行为进行了多尺度下的数值模拟研究,从微观视角对自由面速度曲线上的典型特征进行了新的解读。在宏观尺度,对比分析了光滑粒子流体动力学法（smootfied particle hydrodynamics, SPH）与Lagrange网格法以及几种本构模型的模拟结果及其适用性。通过与实验数据的对比表明,Steinberg-Cochran-Guinan本构模型在层裂模拟中与实验数据吻合较好,通过改变加载条件获得了不同应变率下的自由面速度曲线,分析了不同应变率下的自由面速度曲线中的典型特征。在微观尺度,采用分子动力学方法获得层裂区域内损伤演化情况,揭示了宏观尺度自由面速度曲线典型特征所蕴含的物理内涵。分析表明,层裂表现为材料内部微孔洞形核、长大和聚集的损伤演化过程,自由面速度曲线上的典型特征与层裂区域的损伤演化过程存在密切关联。Pullback信号是层裂区域内微孔洞形核的宏观表征;自由面速度曲线的下降幅值在一定程度上反映了微孔洞的形核条件,由此计算得到的层裂强度实际上是微孔洞的形核强度。此外,Pullback信号后的速度回跳速率反映了微损伤演化的速率。     

Micro-mechanical analysis of deformation characteristics of three-dimensional granular materials

The deformation characteristics of idealized granular materials have been studied from the micro-mechanical viewpoint, using Bagi’s three-dimensional micro-mechanical formulation for the strain tensor [Bagi, K., 1996. Mechanics of Materials 22, 165–177]. This formulation is based on the Delaunay tessellation of space into tetrahedra. The set of edges of the tetrahedra can be divided into physical contacts and virtual contacts between particles. Bagi’s formulation expresses the continuum, macro-scale strain as an average over all edges, of their relative displacements (between two successive states) and the complementary-area vectors. This latter vector is a geometrical quantity determined from the set of edges, i.e. from the structure of the particle packing.Results from Discrete Element Method simulations of isotropic and triaxial loading of a three-dimensional polydisperse packing of spheres have been used to investigate statistics of the branch vectors and complementary-area vectors of edges (subdivided into physical and virtual contacts) and of the relative displacements of edges. The investigated statistics are probability density functions and averages over groups of edges with the same orientation. It is shown that these averages can be represented by second-order Fourier series in edge orientation.Edge orientations are distributed isotropically, contrary to contact orientations. The average lengths of the branch vectors and the normal component of the complementary-area vectors are distributed isotropically (with respect to the edge orientation) and their average values are related to each other and to the volume fraction of the assembly. The other two components of the complementary-area vector are zero on average.The total deformation of the assembly, as given by the average of the relative displacements of the edges of the Delaunay tessellation follows the uniform-strain prediction. However, neither the deformation of the physical contact network nor of the virtual contact network has this property. The average relative displacement of physical edges in the normal direction (determined by the branch vector) is smaller than that according to the uniform-strain assumption, while that of virtual contacts is larger. This is caused by the high interparticle stiffness that hinders compression. The reverse observation holds for the tangential component of the relative displacement vector. The contribution of the deformation of the empty space between physical contacts to the continuum, macro-scale strain tensor is therefore very important for the understanding and the prediction of the macro-scale deformation of granular materials.     

Modelling turbulence around and inside porous media based on the second moment closure

To predict turbulence in porous media, a new approach is discussed. By double (both volume and Reynolds) averaging Navier–Stokes equations, there appear three unknown covariant terms in the momentum equation. They are namely the dispersive covariance, the macro-scale and the micro-scale Reynolds stresses, in the present study. For the macro-scale Reynolds stress, the TCL (two-component-limit) second moment closure is applied whereas the eddy viscosity models are applied to the other covariant terms: the Smagorinsky model and the one-equation eddy viscosity model, respectively for the dispersive covariance and the micro-scale Reynolds stress. The presently proposed model is evaluated in square rib array flows and porous wall channel flows with reasonable accuracy though further development is required.     

Measuring the temperature of fluid in a micro-channel using thermochromic liquid crystals

Thermochromic liquid crystal (TLC) thermometry, which has been previously used at the macro-scale, is applied quantitatively in a microfluidic device for the first time. Much like the micro-scale version of the PIV technique, TLC thermometry implementation at the micro-scale must account for constraints on imaging and illumination configurations and the proximity of the measurements to interfaces and surfaces from which light scatters. Unlike ??PIV, TLC thermometry requires the use of white light, so unwanted reflections are managed using circular polarization filtering, which is implemented for the first time and may also have applications at the macro-scale. The validity and precision of the TLC thermometry technique are tested by imposing a linear temperature gradient along a micro-channel filled with stationary fluid. Additional work is required to develop the technique into a fully functional form and to realize the potential for use in various microfluidic applications including ??lab-on-a-chip?? devices, MEMS switches, inkjet printer nozzles, and for use with simultaneous velocity measurements.     

Flow characterization of high-pressure dense-phase pneumatic conveying of coal powder using multi-scale signal analysis

Flow characterization of high-pressure dense-phase pneumatic conveying of coal powder is not fully understood. To further reveal the dynamic behavior of coal particles in dense-phase pneumatic conveying pipelines, a method for the scale decomposition of particle motion based on empirical mode decomposition and Hurst analysis of experimental electrostatic signals is reported. This allows the multi-scale motion characteristics of single coal particles and particle clusters to be determined. Micro-, meso-, and macro-scale subsets were reconstructed, which reflected the different behaviors of the coal particles: specifically, dynamic features of the micro-scale subset represented features of single particle collisions and frictional interactions; dual fractal characteristics of the meso-scale subset described the motion of coal particle clusters; and features of the macro-scale subset reflected persistent dynamic behavior of the entire pneumatic conveying system. Motion behavior of single particles and particle clusters could be respectively investigated by considering the relative energies of the micro- and meso-scale contributions to the electrostatic signal. This was verified both by theoretical analysis and experiment.     

ML-LBM: Predicting and Accelerating Steady State Flow Simulation in Porous Media with Convolutional Neural Networks

Transport in Porous Media - Fluid mechanics simulation of steady state flow in complex geometries has many applications, from the micro-scale (cell membranes, filters, rocks) to macro-scale...     

用双视场电子散斑干涉实现检测表面的变尺度同时测量

结构或材料中所含的微小缺陷对其宏观力学性能具有重要的影响，探讨这些微小缺陷引起的微变形及其在结构整体变形中所占的份额，对于有效地评估结构和材料的整体性能及局部演化过程都具有重要的理论和工程价值，本文应用双视场电子散斑干涉技术，实现了对被测对象表面的全场变形和局部微观场变形的同时实时检测，给出了宏观及局部位移场分布，并结合有限元数值分析与实验结果进行了比较。     

Granular micromechanics based micromorphic model predicts frequency band gaps

Granular materials are typically characterized by complex structure and composition. Continuum modeling, therefore, remains the mainstay for describing properties of these material systems. In this paper, we extend the granular micromechanics approach by considering enhanced kinematic analysis. In this analysis, a decomposition of the relative movements of interacting grain pairs into parts arising from macro-scale strain as well as micro-scale strain measures is introduced. The decomposition is then used to formulate grain-scale deformation energy functions and derive inter-granular constitutive laws. The macro-scale deformation energy density is defined as a summation of micro-scale deformation energy defined for each interacting grain pair. As a result, a micromorphic continuum model for elasticity of granular media is derived and applied to investigate the wave propagation behavior. Dispersion graphs for different cases and different ratios between the microscopic stiffness parameters have been presented. It is seen that the model has the capability to present band gaps over a large range of wave numbers.     

随机复合材料结构非线性热-力耦合模拟的统计高阶多尺度方法

对于具有复杂随机细观构造的复合材料结构的非线性热-力耦合问题的随机多尺度建模和计算仍是一个具有挑战性的问题。本文发展了一个新的统计高阶多尺度方法,克服了随机多尺度问题直接模拟时巨大的计算量,实现了具有随机复合材料结构非线性热-力耦合问题的数值模拟。借助统计多尺度渐近分析和泰勒级数方法,本文严格推导了可以精确分析随机复合材料结构宏-细观尺度非线性热-力耦合响应的统计高阶多尺度计算模型。然后,通过局部误差分析证明了统计高阶多尺度计算模型中高阶校正项在保持计算模型局部能量和动量守恒的重要意义。进一步,建立了可以高效模拟随机复合材料结构非线性热-力耦合行为的具有离线和在线两阶段的时空多尺度算法。最后,通过数值实验验证了统计高阶多尺度方法的计算高效率和高精度。     

考虑均一微结构的结构/材料两级协同优化

以结构最小柔顺性为目标,提出了考虑均一微结构的结构/材料两级协同优化方法。出于制造考虑,假设了材料微结构在宏观上具有相同的构形。为实现拓扑优化,本方法在两个尺度上独立定义了单元密度作为设计变量,分别引入了SIMP(Solid Isotropic Material with Penalization)和PAMP(Porous Anisotropic Material with Penalization)方法对密度进行惩罚,并且采用了周长约束控制微结构拓扑的复杂度。借助均匀化方法建立了结构和材料之间的联系,从而将两个尺度上的设计纳入到一个优化模型中,实现了协同求解。数值算例验证了本方法的有效性和正确性,讨论了各参数的影响,优化结果体现了类桁架材料的优越性。     

Film thickness measurement techniques applied to micro-scale two-phase flow systems

Recently semi-empirical models to estimate flow boiling heat transfer coefficient, saturated CHF and pressure drop in micro-scale channels have been proposed. Most of the models were developed based on elongated bubbles and annular flows in the view of the fact that these flow patterns are predominant in smaller channels. In these models, the liquid film thickness plays an important role and such a fact emphasizes that the accurate measurement of the liquid film thickness is a key point to validate them. On the other hand, several techniques have been successfully applied to measure liquid film thicknesses during condensation and evaporation under macro-scale conditions. However, although this subject has been targeted by several leading laboratories around the world, it seems that there is no conclusive result describing a successful technique capable of measuring dynamic liquid film thickness during evaporation inside micro-scale round channels. This work presents a comprehensive literature review of the methods used to measure liquid film thickness in macro- and micro-scale systems. The methods are described and the main difficulties related to their use in micro-scale systems are identified. Based on this discussion, the most promising methods to measure dynamic liquid film thickness in micro-scale channels are identified.     

Exploring the relationship between critical state and particle shape for granular materials

The relationship between critical state and particle shape corresponds to the most fundamental aspect of the mechanics of granular materials. This paper presents an investigation into this relationship through macro-scale and micro-scale laboratory experiments in conjunction with interpretation and analysis in the framework of critical state soil mechanics. Spherical glass beads and crushed angular glass beads of different percentages were mixed with a uniform quartz sand (Fujian sand) to create a sequence of mixtures with varying particle shape. On the micro-scale, particle shape was accurately measured using a laser scanning technique, and was characterized by aspect ratio, sphericity and convexity; a new shape index, taken as the average of the three shape measures and referred to as overall regularity, was proposed to provide a collective characterization of particle shape. On the macro-scale, both undrained and drained triaxial tests were carried out to provide evidence that varying particle shape can alter the overall response as well as the critical states in both stress space and volumetric compression space. The mixtures of Fujian sand and spherical glass beads were found to be markedly more susceptible to liquefaction than the mixtures of Fujian sand and crushed angular glass beads. The change in liquefaction susceptibility was shown to be consistent with the change in the position of the critical state locus (CSL) in the compression space, manifested by a decrease in the intercept and gradient of the CSL due to the presence of spherical glass beads. Quantitative relationships have been established between each of the critical state parameters and each of the shape parameters, thereby providing a way to construct macro-scale constitutive models with intrinsic micro-scale properties built in.     

On the elastic moduli of three-dimensional assemblies of spheres: Characterization and modeling of fluctuations in the particle displacement and rotation

The elastic moduli of four numerical random isotropic packings of Hertzian spheres are studied. The four samples are assembled with different preparation procedures, two of which aim to reproduce experimental compaction by vibration and lubrication. The mechanical properties of the samples are found to change with the preparation history, and to depend much more on coordination number than on density.Secondly, the fluctuations in the particle displacements from the average strain are analyzed, and the way they affect the macroscopic behavior analyzed. It is found that only the average over equally oriented contacts of the relative displacement these fluctuations induce is relevant at the macroscopic scale. This average depends on coordination number, average geometry of the contact network and average contact stiffness. As far as the separate contributions from particle displacements and rotations are concerned, the former is found to counteract the average strain along the contact normal, while the latter do in the tangential plane. Conversely, the tangential components of the center displacements mainly arise to enforce local equilibrium, and have a small and generally stiffening effect at the macro-scale.Finally, the fluctuations and the shear modulus that result from two approaches available in the literature are estimated numerically. These approaches are both based on the equilibrium of a small-sized representative assembly. The improvement of these estimate with respect to the average strain assumption indicates that the fluctuations relevant to the macroscopic behavior occur with short correlation length.     

基于渐进均匀化的平纹编织复合材料低速冲击多尺度方法

针对平纹编织复合材料低速冲击响应和损伤问题,提出了一种多尺度分析方法. 首先, 建立微观尺度单胞模型,引入周期性边界条件,采用最大主应力失效准则和直接刚度退化模型表征纤维丝和基体的损伤起始与演化,预测了纤维束的弹性性能和强度性能. 其次,将这些性能参数代入介观尺度单胞模型,基于Hashin和Hou的混合失效准则以及连续介质损伤模型对介观尺度单胞进行6种边界条件下的渐进损伤模拟.然后采用渐进均匀化方法,以介观尺度单胞为媒介预测了0$^\circ$和90$^\circ$子胞的性能参数,并建立平纹编织复合材料的子胞模型,进而扩展成为材料的宏观尺度低速冲击模型. 在此基础上,研究了平纹编织复合材料低速冲击下的力学响应与损伤特征.结果表明:宏观冲击仿真和试验吻合较好, 验证了多尺度方法的正确性;最大接触力、材料吸能和分层面积均随冲击能量的增大而增大,分层损伤轮廓逐渐从椭圆形向圆形转化;基体拉伸和压缩损伤的长轴方向分别与子胞材料主方向正交和一致,损伤面积前者远大于后者.      

A FRACTURE-ENERGY-BASED ELASTO-SOFTENING-PLASTIC CONSTITUTIVE MODEL FOR JOINTS OF GEOMATERIALS

On the basis of plasticity and fracture mechanics for quasi-brittle materials , this article presented a constitutive model for gradual softening behavior of joints of geomateri-als . Corresponding numerical tests are carried out at the local level. Characteristics of the model proposed are 1) plastic softening and dilatancy behavior are directly related to the fracture process of joint, and much less material and model parameters are required compared with those proposed by references ; 2) the process of decohesion coupled with friction-al sliding at both micro-scale and macro-scale is described.