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.     

Sensitivity of the macroscopic elasticity tensor to topological microstructural changes

A remarkably simple analytical expression for the sensitivity of the two-dimensional macroscopic elasticity tensor to topological microstructural changes of the underlying material is proposed. The derivation of the proposed formula relies on the concept of topological derivative, applied within a variational multi-scale constitutive framework where the macroscopic strain and stress at each point of the macroscopic continuum are volume averages of their microscopic counterparts over a representative volume element (RVE) of material associated with that point. The derived sensitivity—a symmetric fourth order tensor field over the RVE domain—measures how the estimated two-dimensional macroscopic elasticity tensor changes when a small circular hole is introduced at the microscale level. This information has potential use in the design and optimisation of microstructures.     

Multi-scale plasticity modeling: Coupled discrete dislocation and continuum crystal plasticity

A hierarchical multi-scale model that couples a region of material described by discrete dislocation plasticity to a surrounding region described by conventional crystal plasticity is presented. The coupled model is aimed at capturing non-classical plasticity effects such as the long-range stresses associated with a density of geometrically necessary dislocations and source limited plasticity, while also accounting for plastic flow and the associated energy dissipation at much larger scales where such non-classical effects are absent. The key to the model is the treatment of the interface between the discrete and continuum regions, where continuity of tractions and displacements is maintained in an average sense and the flow of net Burgers vector is managed via “passing” of discrete dislocations. The formulation is used to analyze two plane strain problems: (i) tension of a block and (ii) crack growth under mode I loading with various sizes of the discrete dislocation plasticity region surrounding the crack tip. The computed crack growth resistance curves are nearly independent of the size of the discrete dislocation plasticity region for region sizes ranging from to . The multi-scale model can reduce the computational time for the mode I crack analysis by a factor of 14 with little or no loss of fidelity in the crack growth predictions.     

Characterization of macroscopic tensile strength of polycrystalline metals with two-scale finite element analysis

The objective of this contribution is to develop an elastic-plastic-damage constitutive model for crystal grain and to incorporate it with two-scale finite element analyses based on mathematical homogenization method, in order to characterize the macroscopic tensile strength of polycrystalline metals. More specifically, the constitutive model for single crystal is obtained by combining hyperelasticity, a rate-independent single crystal plasticity and a continuum damage model. The evolution equations, stress update algorithm and consistent tangent are derived within the framework of standard elastoplasticity at finite strain. By employing two-scale finite element analysis, the ductile behaviour of polycrystalline metals and corresponding tensile strength are evaluated. The importance of finite element formulation is examined by comparing performance of several finite elements and their convergence behaviour is assessed with mesh refinement. Finally, the grain size effect on yield and tensile strength is analysed in order to illustrate the versatility of the proposed two-scale model.     

A micromorphic model for the multiple scale failure of heterogeneous materials

The multi-scale micromorphic theory developed in our previous paper [Vernerey, F.J., Liu, W.K., Moran, B., 2007. Multi-scale micromorphic theory for hierarchical materials. J. Mech. Phys. Solids, doi:10.1016/j.jmps.2007.04.008] is used to predict the failure of heterogeneous materials illustrated by a high strength steel alloy possessing two populations of hard particles distributed at two distinct length scales in an alloy matrix. To account for the effect and size of microstructural features during fracture, additional kinematic variables are added, giving rise to the couple stresses associated with each population of particles. The various stress and strain measures must satisfy a set of coupled multi-scale governing equations derived from the principle of virtual power. A three-scale constitutive model is then developed to represent the failure of the alloy from nucleation, growth and coalescence of voids from each population of particles. For this, three distinct yield functions, each corresponding to a different scale, are introduced. Cell model simulations using finite elements are performed to determine the constitutive relations based on the key microstructural features. Two-dimensional failure analyses are then presented in tension and in shear, and show good agreement with direct numerical simulation of the microstructure.     

Multi-scale framework for the thermo-viscoelastic analyses of polymer composites

This paper presents a multi-scale framework for analyzing coupled heat conduction and viscoelastic deformation of polymers reinforced with solid spherical particles. The viscoelastic and thermal properties of the polymer constituents are temperature dependent. A simplified micromechanical model for the particle reinforced composite is formulated to obtain the effective thermal properties and viscoelastic responses. The micromechanical model is implemented at material points within elements in the finite element (FE) analyses.     

Effect of Multi-Scale Porosity in Local Permeability Modelling of Non-Crimp Fabrics

The influence of multi-scale porosity of fibre reinforcements on local permeability is investigated, in order to determine the possibility of simplifying permeability models for more efficient permeability calculations. Unit cell models of a biaxial Non-Crimp Fabric are developed and used to investigate, whether or not the porous bundles can be excluded, when modelling the local permeability. Numerical accuracy of calculations is controlled to guarantee the quality of the results and the conclusions drawn from them. It is found that fibre bundles with high fibre density can be excluded from permeability models, while bundles with low fibre volume fractions need to be included. A new method to model the local permeability of multi-scale reinforcements is developed and verified for low fibre density in the bundles. In this method, the effects of the flow inside the fibre bundles are included through modifications of the boundary conditions of a single-scale model representing the interbundle regions. The local permeability of multi-scale reinforcements can, therefore, be calculated by models with simplified fluid domains for all fibre bundle porosities, instead of being calculated by models consisting of the entire multi-scale geometry.     

Trans-scale mechanics： looking for the missing links between continuum and micro/nanoscopic reality

Problems involving coupled multiple space and time scales offer a real challenge for conventional frame-works of either particle or continuum mechanics. In this paper, four cases studies （shear band formation in bulk metallic glasses, spallation resulting from stress wave, interaction between a probe tip and sample, the simulation of nanoindentation with molecular statistical thermodynamics） are provided to illustrate the three levels of trans-scale problems （problems due to various physical mechanisms at macro-level, problems due to micro-structural evolution at macro/micro-level, problems due to the coupling of atoms/ molecules and a finite size body at micro/nano-level） and their formulations. Accordingly, non-equilibrium statistical mechanics, coupled trans-scale equations and simultaneous solutions, and trans-scale algorithms based on atomic/molecular interaction are suggested as the three possible modes of trans-scale mechanics.     

泡沫铝弹性接触静力学行为的多尺度模拟

对泡沫铝的宏、细观组织结构,基于MC方法建立与材料制备工艺相应的数值模型,作为多尺度模拟的前提.通过计算模拟和统计分析大量数值试样的力学性能,得到了不同制备工艺制得的泡沫铝的弹性模量的分散性特点.借鉴代表性体积单元方法(RVE)和完全多格方法(FMG)的思想,采用基于"巨原子"模型的多尺度关联方法,并以简化的物理势场描述巨原子问的关系,设计了原子-巨原子-有限元多尺度算法.通过算例探讨了与理想刚性平面接触时,泡沫铝接触表面的应力集中情况.     

Modelling of long term kinetic evolution: a fruitful relationship between experiment and theoretical development

Recent developments in multi-scale modelling, based on atomic scale calculations, are leading to a growing conviction that modelling will soon be used to design material components for nuclear reactors. In this article we discuss this assumption on the basis of the relationship between experimental studies and theoretical calculations of the microstructural evolution of materials under irradiation. In the first part of the paper, the available numerical models for long term microstructural evolutions are briefly reviewed. The experimental methods are presented in a second part. In the third part, several examples of fruitful relationships between modelling and experiments are discussed. To cite this article: A. Barbu, C. R. Physique 9 (2008).