Efficient evaluation of the material response of tissues reinforced by statistically oriented fibres

For several classes of soft biological tissues, modelling complexity is in part due to the arrangement of the collagen fibres. In general, the arrangement of the fibres can be described by defining, at each point in the tissue, the structure tensor (i.e. the tensor product of the unit vector of the local fibre arrangement by itself) and a probability distribution of orientation. In this approach, assuming that the fibres do not interact with each other, the overall contribution of the collagen fibres to a given mechanical property of the tissue can be estimated by means of an averaging integral of the constitutive function describing the mechanical property at study over the set of all possible directions in space. Except for the particular case of fibre constitutive functions that are polynomial in the transversely isotropic invariants of the deformation, the averaging integral cannot be evaluated directly, in a single calculation because, in general, the integrand depends both on deformation and on fibre orientation in a non-separable way. The problem is thus, in a sense, analogous to that of solving the integral of a function of two variables, which cannot be split up into the product of two functions, each depending only on one of the variables. Although numerical schemes can be used to evaluate the integral at each deformation increment, this is computationally expensive. With the purpose of containing computational costs, this work proposes approximation methods that are based on the direct integrability of polynomial functions and that do not require the step-by-step evaluation of the averaging integrals. Three different methods are proposed: (a) a Taylor expansion of the fibre constitutive function in the transversely isotropic invariants of the deformation; (b) a Taylor expansion of the fibre constitutive function in the structure tensor; (c) for the case of a fibre constitutive function having a polynomial argument, an approximation in which the directional average of the constitutive function is replaced by the constitutive function evaluated at the directional average of the argument. Each of the proposed methods approximates the averaged constitutive function in such a way that it is multiplicatively decomposed into the product of a function of the deformation only and a function of the structure tensors only. In order to assess the accuracy of these methods, we evaluate the constitutive functions of the elastic potential and the Cauchy stress, for a biaxial test, under different conditions, i.e. different fibre distributions and different ratios of the nominal strains in the two directions. The results are then compared against those obtained for an averaging method available in the literature, as well as against the integration made at each increment of deformation.     

Micromechanical modelling and two-scale simulation of epoxy/glass composites with interphases and interfaces

Composite systems consisting of glass fibres and epoxy matrix with interphases and interfaces will be considered in the modelling approach. The interphase forms the transition zone between the epoxy matrix and the glass fibre. The interface is the layer between the glass fibre and the surrounding interphase. The macroscopic strength of the composite material is intrinsically related to the bond strength of the polymeric/solid interface and the micromechanical characteristics of the three phases (epoxy, glass and interphase). Homogenization is an appropriate methodology to link these two scales to predict the overall physical behaviour of the composite. The nonlinear behaviour of amorphous polymers, cohesive interface elements and the elastic behaviour of glass fibres as part of the considered composite material are presented, as well as a representative example to show the necessity of taking interface influences into account. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The practical use of noise to improve speech coding by analogue cochlear implants

The addition of noise to speech signals coded by an analogue multichannel cochlear implant has previously been shown in modelling studies to enhance the representation of speech cues by the fine time structure of evoked nerve discharges. The enhancement, however, occurred only for a range of noise levels, and this range was stimulus dependent. Theoretically, fine optimization of the noise levels would be unnecessary if each implant channel stimulated a group of cochlear nerve fibres such that each fibre in the group received an independent noise waveform in addition to the same information-bearing signal. We present results from computer simulations that suggest that current spread in the cochlea may be exploited to obtain a high degree of independence between the noise waveforms that stimulate adjacent fibres. The model simulated monopolar stimulation of a cochlear nerve by 11, 21 or 41 electrodes in the scala tympani. The correlation between the effective stimuli for pairs of nerve fibres and the correlation between the corresponding evoked discharges were calculated for two noise strategies. In one strategy, an independent noise current was applied to each electrode. Less correlation between effective stimuli was obtained with the alternate strategy that used inhibition between the noise sources.     

On a stochastic model for particle sedimentation in fluids

The engineering sciences have long been interested in models describing the settling (or sedimentation) of particle ensembles in viscous fluids. From a theoretical point of view, sedimentation constitutes a two phase many-body phenomenon with complex interaction and as such has proved to be quite inaccessible to modelling attempts with relevance in applications. A stochastic model was introduced by Pickard and Tory in 1977 and was subsequently revised. In this paper we expand and refine the stochastic model and present a satisfactory model-fitting procedure and parameter estimators based on transit times of sedimenting particles.     

泥沙的群体沉降速度

本文讨论了在浓度很高时候,泥沙的群体沉降速度.作者认为所谓泥沙的群体沉降速度问题从物理本质来说并不是真正的沉降速度问题,而是水在泥沙和水所组成的胶团形成的多孔介质中的渗流问题,也就是水流经这种多孔介质所形成的问题.作者根据这样的认识,写出了泥沙群体沉降速度的数学表达式,并且和黄委会水科所测量得到的实验数据进行了比较.比较的结果是令人满意的.     

Comparison of non-cohesive resolved and coarse grain DEM models for gas flow through particle beds

The Discrete Element Method (DEM) is a widely used approach for modelling granular systems. Currently, the number of particles which can be tractably modelled using DEM is several orders of magnitude lower than the number of particles present in common large-scale industrial systems. Practical approaches to modelling such industrial system therefore usually involve modelling over a limited domain, or with larger particle diameters and a corresponding assumption of scale invariance. These assumption are, however, problematic in systems where granular material interacts with gas flow, as the dynamics of the system depends heavily on the number of particles. This has led to a number of suggested modifications for coupled gas–grain DEM to effectively increase the number of particles being simulated. One such approach is for each simulated particle to represent a cluster of smaller particles and to re-formulate DEM based on these clusters. This, known as a representative or ‘coarse grain’ method, potentially allows the number of virtual DEM particles to be approximately the same as the real number of particles at relatively low computational cost. We summarise the current approaches to coarse grain models in the literature, with emphasis on discussion of limitations and assumptions inherent in such approaches. The effectiveness of the method is investigated for gas flow through particle beds using resolved and coarse grain models with the same effective particle numbers. The pressure drop, as well as the pre and post fluidisation characteristics in the beds are measured and compared, and the relative saving in computational cost is weighed against the effectiveness of the coarse grain approach. In general, the method is found perform reasonably well, with a considerable saving of computational time, but to deviate from empirical predictions at large coarse grain ratios.     

相互碰撞的圆粒子在竖直通道中沉降的数值研究

采用格子Boltzmann方法,数值模拟了考虑相互碰撞的两圆粒子的沉降,分析了Re数、初始相对位移及通道宽度对粒子沉降的影响．结果表明,在0.1＜Re＜20范围内, 粒子沉降具有周期性．Re数越大,两圆粒子的相互作用越强,粒子横向位移的幅度也越大．在大Re数时,沉降的过程是两个粒子交替领先;在较小Re数时,当后面的粒子接近的时候,领先的粒子被向右侧推了一段后仍会继续领先;对中等Re数,原先在后面的粒子在第一次加速后将取得领先位置并一直保持下去．粒子的初始分布位置对沉降的形态影响不大．管道宽度变化时,粒子总的沉降特性不变,而周期改变,管道越宽,周期越长．     

Particle simulation of granular media and homogenisation towards continuum quantities

From a microscopic point of view, various natural and engineering materials consist of individual grains, whose motion strongly influence the macroscopic material behaviour. Exemplarily, one may look at the development of shear zones in natural granular materials, such as sand, occurring as a result of local grain dislocations and the transition of the granulate from a denser to a looser packing. The intuitive modelling approach for granular assemblies is consequently the consideration of each grain as a rigid particle. In a numerical framework, this leads to the Discrete Element Method (DEM), wherein the motion of each particle can be obtained solving Newton's equations for each particle. The present contribution discusses the basic fundaments of modelling granular material on the microscopic scale by use of the DEM. Special interest is taken to the constitutive choice of the governing particle-to-particle contact forces, as they have to account for plastic material behaviour as well as for assumptions concerning particle shape, size and distribution. As engineering problems are regularly described on the macroscale by means of continuum mechanics, a homogenisation strategy transfers the information from the microscale towards continuum quantities via volume averaging. Therefore, characteristic Representative Elementary Volumes (REV) are constructed by an ensemble of particles, where each particle can be chosen as the centre of a REV. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Steady state numerical simulation of the particle collection efficiency of a new urban sustainable gravity settler using design of experiments by FVM

The aim of this work is to analyze the efficiency of a new sustainable urban gravity settler to avoid the solid particle transport, to improve the water waste quality and to prevent pollution problems due to rain water harvesting in areas with no drainage pavement. In order to get this objective, it is necessary to solve particle transport equations along with the turbulent fluid flow equations since there are two phases: solid phase (sand particles) and fluid phase (water). In the first place, the turbulent flow is modelled by solving the Reynolds-averaged Navier-Stokes (RANS) equations for incompressible viscous flows through the finite volume method (FVM) and then, once the flow velocity field has been determined, representative particles are tracked using the Lagrangian approach. Within the particle transport models, a particle transport model termed as Lagrangian particle tracking model is used, where particulates are tracked through the flow in a Lagrangian way. The full particulate phase is modelled by just a sample of about 2,000 individual particles. The tracking is carried out by forming a set of ordinary differential equations in time for each particle, consisting of equations for position and velocity. These equations are then integrated using a simple integration method to calculate the behaviour of the particles as they traverse the flow domain. The entire FVM model is built and the design of experiments (DOE) method was used to limit the number of simulations required, saving on the computational time significantly needed to arrive at the optimum configuration of the settler. Finally, conclusions of this work are exposed.     

Effective medium model for flow through beds of porous cylindrical fibres

We have used effective medium model for beds of circular cylindrical porous fibres in order to estimate the overall bed permeability (OBP). It is assumed that a representative circular porous cylindrical fibre is inside a fluid envelope beyond which effective medium is used. Both inside the cylindrical fibre and in the effective medium, Brinkman equation is used, however of different permeabilities and in the fluid envelope Stokes equation is used. The OBP corresponding to the porous fibres is estimated when the flow direction is perpendicular to the axis of the cylindrical fibres as well as parallel to the fibres. This in turn is used to estimate the OBP corresponding to a collection of porous cylindrical fibres that are randomly oriented. We have compared the results with some existing literature.     

Passive muscle behaviour – experimental and numerical investigations

The material behaviour of skeletal muscles can be decomposed into two parts: an active part, describing the contractile mechanisms, and a passive one, characterising the passive components such as the connective tissue. Computational models are used to support the understanding of complex mechanism inside a muscle. In the present work, we focus on the three-dimensional passive tissue behaviour from the experimental as well as modelling point of view. Therefore, quasi-static experiments have been performed on specimens with regular geometry. By using a three-dimensional optical measurement system the shape of the specimens has been reconstructed at different deformation states. On the modelling side a hyperelastic model with transversal isotropic fibre orientation has been used to describe non-linear stress responses. The model has been validated by performing analyses for different fibre orientations. In summary, it figures out that the proposed modelling approach is able to reflect the experimental results in a satisfying manner. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On existence of solutions for a system of Boltzmann transport equations

We consider a linear system of Boltzmann transport equations. The system models charged particle transport in tissue, for example. Although only one species of particles, say photons, is invasing these particles mobilize electrons and positrons. Hence in realistic modelling of particle transport one needs a coupled system of three Boltzmann transport equations. The solution of this system must satisfy the inflow boundary condition. We show existence and uniqueness result of the solution applying coercitivity of the underlying linear operator and its adjoint operator. In addition, we consider existence of continuous solutions by iterative methods. Copyright © 2008 John Wiley & Sons, Ltd.     

Estimation for jump processes in the tangent bundle of a Riemann manifold

A stochastic process is formulated in the tangent bundle of a Riemann manifold where the vector fibre portion of the process is a jump process. Since the tangent spaces change as the process in the base manifold evolves, it is necessary to define a jump process in the fibres of the tangent bundle with respect to the process in the base manifold. An estimation problem is formulated and solved for a process obtained from the jump process in the fibres of the tangent bundle where the observations include the process in the base manifold and the jump times. Since each fibre of the tangent bundle is a linear space, a suitable modification of some results for estimation in linear spaces can be used to solve the aforementioned estimation problem.Research supported by NSF Grants ENG 75-06562 and MCS 76-01695 and AFOSR Grant 77-3177.     

On coupled Boltzmann transport equation related to radiation therapy

We consider a system of Boltzmann transport equations which models the charged particle evolution in media. The system is related to the dose calculation in radiation therapy. Although only one species of particles, say photons is invasing these particles mobilize other type of particles (electrons and positrons). Hence in realistic modelling of particle transport one needs a coupled system of three Boltzmann transport equations. The solution of this system must satisfy the inflow boundary condition. We show existence and uniqueness result of the solution applying generalized Lax-Milgram Theorem. In addition, we verify that (in the case of external therapy) under certain assumptions the “incoming flux to dose operator” D₁ is compact. Also the adjoint is analyzed. Finally we consider the inverse planning problem as an optimal control problem. Its solution can be used as an initial solution of the actual inverse planning problem.     

Slow viscous flow through a membrane built up from porous cylindrical particles with an impermeable core

This paper concerns the slow viscous flow through an aggregate of concentric clusters of porous cylindrical particles with Happel boundary condition. An aggregate of clusters of porous cylindrical particles is considered as a hydro-dynamically equivalent to solid cylindrical core with concentric porous cylindrical shell. The Brinkman equation inside the porous cylindrical shell and the Stokes equation outside the porous cylindrical shell in their stream function formulations are used. The drag force acting on each porous cylindrical particle in a cell is evaluated. In certain limiting cases, drag force converges to pre-existing analytical results, such as, the drag on a porous circular cylinder and the drag on a solid cylinder in a Happel unit cell. Representative results are then discussed and presented in graphical forms. The hydrodynamic permeability of the membrane built up from porous particles is evaluated. The variation of hydrodynamic permeability with different parameters is graphically presented. Some new results are reported for flow pattern in the porous region. Being in resemblance with the model of colloid particles with a coating of porous layers due to adsorption phenomenon, results obtained through this model can be useful to study the membrane filtration process.     

CFD modelling of the flow and reactions in the Olympic Dam flash furnace smelter reaction shaft

The performance of flash furnace burners can be evaluated quickly and efficiently using CFD modelling. Gas flows are modelled using the conventional Eulerian approach, while Lagrangian particle tracking is used to model the flow of solid feed through the burner and into the reaction shaft. A composite particle model has been developed that considers the solid feed to be made up of single particles containing appropriate quantities of concentrate, flux and dust. Solid fuels (such as coal) can also be included in the composite particle. Reactions between the solids and gas are then modelled using standard heat and mass transfer relationships. Results from the modelling process are shown for BHP-Billiton’s Olympic Dam copper flash smelter with the burner that was used from 1998–2003. Flow patterns, temperature and gas composition distributions, particle dispersion and residence time, and overall extent of sulphur removal are predicted and used to evaluate furnace performance. However, results are sensitive to the assumed size of the composite particles, and plant measurements are required to determine the appropriate composite particle size to predict quantitative data.     

A deterministic Lagrangian particle separation-based method for advective-diffusion problems

A simple and robust Lagrangian particle scheme is proposed to solve the advective-diffusion transport problem. The scheme is based on relative diffusion concepts and simulates diffusion by regulating particle separation. This new approach generates a deterministic result and requires far less number of particles than the random walk method. For the advection process, particles are simply moved according to their velocity. The general scheme is mass conservative and is free from numerical diffusion. It can be applied to a wide variety of advective-diffusion problems, but is particularly suited for ecological and water quality modelling when definition of particle attributes (e.g., cell status for modelling algal blooms or red tides) is a necessity. The basic derivation, numerical stability and practical implementation of the NEighborhood Separation Technique (NEST) are presented. The accuracy of the method is demonstrated through a series of test cases which embrace realistic features of coastal environmental transport problems. Two field application examples on the tidal flushing of a fish farm and the dynamics of vertically migrating marine algae are also presented.     

Direct numerical simulation of bi-disperse particle-laden gravity currents in the channel configuration

We present a numerical investigation of bi-disperse particle-laden gravity currents in the lock-exchange configuration. Previous results, based on numerical simulation and laboratory experiments, are used to establish comparisons. Our discussion focuses on explaining how the presence of more than one particle diameter influences the main features of the flow, such as deposit profile, the evolution of the front location and suspended mass. We develop the complete energy budget equation for bi-disperse flows. A set of two and three-dimensional direct numerical simulations (DNS), with different initial compositions of coarse and fine particles, are carried out for Reynolds number equal to 4000. Such simulations show that the energy terms are strongly affected by varying the initial particle fractions. The addition of a small amount of fine particles into a current predominantly composed of coarse particles increases its run-out distance. In particular, it is shown that higher amounts of coarse particles have a dumping effect on the current development. Comparisons show that the two-dimensional simulation does not reproduce the intense turbulence generated in 3D cases accurately, which results in a significant difference in the suspended mass, front position as well as the dissipation term due to the advective motion.     

Advanced comminution modelling: Part 1 – Crushers

Particle scale modelling of comminution processes can provide significant insight into the flow of particles, their breakage, the effect of slurry, wear and energy utilisation within these machines. The ability to use such models to assist in faster and lower cost design of new comminution devices and in the improvement of existing ones will be critical to the ability of industry to respond to the substantive challenges facing mineral processing in the next decade. These challenges are reviewed and drivers for change are discussed. Understanding individual unit process performance needs to be in the context of the flowsheets in which they are used so this is also reviewed. Advances in particle based comminution modelling are presented with this work divided into two parts. This first part focuses on recent advances in particle based modelling of crushing. Three crusher types are used to demonstrate these capabilities:1. Twin roll crusher2. Cone crusher3. Vertical Shaft Impactor (VSI)These show the nature and level of fidelity that is now possible to include in particle scale crusher models including breakage of non-spherical particles and prediction of the product size distribution and throughput.     

Finite element analysis of multi-particle impact on erosion in abrasive water jet machining of titanium alloy

Abrasive water jets (AWJs) are finding growing applications for machining a wide range of difficult-to-machine materials such as titanium alloys, stainless steel, metal matrix and fibre reinforced composites, etc. Current applications of AWJs include machining of Titanium alloys for aircraft components and bio-medical implants to removal of aircraft engine coatings. This paper presents the application of an elasto-plastic model based explicit finite element analysis (FEA) to model the erosion behaviour in abrasive water jet machining (AWJM). The novelty of this work includes FE modelling of the effect of multiple (twenty) particle impact on erosion of Grade 5 Titanium alloy (Ti-6Al-4V). The influence of abrasive particle impact angle and velocity on the crater sphericity and depth, and erosion rate has been investigated. The FE model has been validated for stainless steel and yields largely improved results. Further, the same FEA approach has been extended to model the multi-particle impact erosion behaviour of Titanium alloy.