A continuum damage model for delaminations in laminated composites

Delamination, a typical mode of interfacial damage in laminated composites, has been considered in the context of continuum damage mechanics in this paper. Interfaces where delaminations could occur are introduced between the constituent layers. A simple but appropriate continuum damage representation is proposed. A single scalar damage parameter is employed and the degradation of the interface stiffness is established. Use has been made of the concept of a damage surface to derive the damage evolution law. The damage surface is constructed so that it combines the conventional stress-based and fracture-mechanics-based failure criteria which take account of mode interaction in mixed-mode delamination problems. The damage surface shrinks as damage develops and leads to a softening interfacial constitutive law. By adjusting the shrinkage rate of the damage surface, various interfacial constitutive laws found in the literature can be reproduced. An incremental interfacial constitutive law is also derived for use in damage analysis of laminated composites, which is a non-linear problem in nature. Numerical predictions for problems involving a DCB specimen under pure mode I delamination and mixed-mode delamination in a split beam are in good agreement with available experimental data or analytical solutions. The model has also been applied to the prediction of the failure strength of overlap ply-blocking specimens. The results have been compared with available experimental and alternative theoretical ones and discussed fully.     

A continuum model for intermittent deformation of single crystal micropillars

Strain bursts are often observed during compression tests of single crystal micropillars. In this work, we formulate a new continuum model that accounts for the strain bursts within the framework of crystal plasticity. The strain bursts are separated from the loading stage (nearly elastic loading) by introducing a dimensionless constant in the continuum model, and are detected by load serrations. The boundary conditions in the context of micropillar compression are studied and they are shown to be changing and unpredictable as plastic deformation proceeds. To evaluate the validity of our model, finite element simulations of the uniaxial compression tests on nickel micropillars are performed. Our simulations produce clearly visible strain bursts during the plastic flow and the produced intermittent flows are comparable with the experimental observations. For the bulk crystal, a series of strain bursts is identified in the course of plastic flow, despite an apparently smooth stress–strain response. We also show that the intermittent flow is intensified in the micrometer-scale due to both increasing numbers of the successive strain bursts and increasing amplitude of the strain burst, when the specimen size decreases. Finally, we show that the occurrences of the strain bursts are always associated with negative values of the second-order work.     

Numerical investigation from rarefied flow to continuum by solving the Boltzmann model equation

Based on the Bhatnagar–Gross–Krook (BGK) Boltzmann model equation, the unified simplified velocity distribution function equation adapted to various flow regimes can be presented. The reduced velocity distribution functions and the discrete velocity ordinate method are developed and applied to remove the velocity space dependency of the distribution function, and then the distribution function equations will be cast into hyperbolic conservation laws form with non‐linear source terms. Based on the unsteady time‐splitting technique and the non‐oscillatory, containing no free parameters, and dissipative (NND) finite‐difference method, the gas kinetic finite‐difference second‐order scheme is constructed for the computation of the discrete velocity distribution functions. The discrete velocity numerical quadrature methods are developed to evaluate the macroscopic flow parameters at each point in the physical space. As a result, a unified simplified gas kinetic algorithm for the gas dynamical problems from various flow regimes is developed. To test the reliability of the present numerical method, the one‐dimensional shock‐tube problems and the flows past two‐dimensional circular cylinder with various Knudsen numbers are simulated. The computations of the related flows indicate that both high resolution of the flow fields and good qualitative agreement with the theoretical, DSMC and experimental results can be obtained. Copyright © 2003 John Wiley & Sons, Ltd.     

A THREE-FLUID MODEL OF THE SAND-DRIVEN FLOW

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A continuum damage model for piezoelectric materials

In this paper, a constitutive model is proposed for piezoelectric material solids containing distributed cracks. The model is formulated in a framework of continuum damage mechanics using second rank tensors as internal variables. The Helrnhotlz free energy of piezoelectric mate- rials with damage is then expressed as a polynomial including the transformed strains, the electric field vector and the tensorial damage variables by using the integrity bases restricted by the initial orthotropic symmetry of the material. By using the Talreja＇s tensor valued internal state damage variables as well as the Helrnhotlz free energy of the piezoelectric material, the constitutive relations of piezoelectric materials with damage are derived. The model is applied to a special case of piezoelectric plate with transverse matrix cracks. With the Kirchhoff hypothesis of plate, the free vibration equations of the piezoelectric rectangular plate considering damage is established. By using Galerkin method, the equations are solved. Numerical results show the effect of the damage on the free vibration of the piezoelectric plate under the close-circuit condition, and the present results are compared with those of the three-dimensional theory.     

Study on micronozzle flow and propulsion performance using DSMC and continuum methods

In this paper, both DSMC and Navier–Stokes computational approaches were applied to study micronozzle flow. The effects of inlet condition, wall boundary condition, Reynolds number, micronozzle geometry and Knudsen number on the micronozzle flow field and propulsion performance were studied in detail. It is found that within the Knudsen number range under consideration, both the methods work to predict flow characteristics inside micronozzles. The continuum method with slip boundary conditions has shown good performance in simulating the formation of a boundary layer inside the nozzle. However, in the nozzle exit lip region, the DSMC method is better due to gas rapid expansion. It is found that with decreasing the inlet pressure, the difference between the continuum model and DSMC results increases due to the enhanced rarefaction effect. The coefficient of discharge and the thrust efficiency increase with increasing the Reynolds number. Thrust is almost proportional to the nozzle width. With dimension enlarged, the nozzle performance becomes better while the rarefaction effects would be somewhat weakened.The project supported by the National Natural Science Foundation of China (10372099). The English text was polished by Boyi Wang     

Optimal flow conditions of a tracheobronchial model to reengineer lung structures

The high demand for lung transplants cannot be matched by an adequate number of lungs from donors. Since fully ex-novo lungs are far from being feasible, tissue engi-neering is actively considering implantation of engineered lungs where the devitalized structure of a donor is used as scaffold to be repopulated by stem cells of the receiv-ing patient. A decellularized donated lung is treated inside a bioreactor where transport through the tracheobronchial tree (TBT) will allow for both deposition of stem cells and nour-ishment for their subsequent growth, thus developing new lung tissue. The key concern is to set optimally the boundary conditions to utilize in the bioreactor. We propose a pre-dictive model of slow liquid ventilation, which combines a one-dimensional (1-D) mathematical model of the TBT and a solute deposition model strongly dependent on fluid velocity across the tree. With it, we were able to track and drive the concentration of a generic solute across the airways, look-ing for its optimal distribution. This was given by properly adjusting the pumps' regime serving the bioreactor. A feed-back system, created by coupling the two models, allowed us to derive the optimal pattern. The TBT model can be easily invertible, thus yielding a straightforward flow/pressure law at the inlet to optimize the efficiency of the bioreactor.     

A two-fluid model for pulsatile flow in catheterized blood vessels

The pulsatile flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the peripheral region of plasma as a Newtonian fluid. The resulting non-linear implicit system of partial differential equations is solved using perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio, amplitude, pulsatile Reynolds number ratio and peripheral layer thickness are discussed. It is observed that the velocity distribution and flow rate decrease, while, the wall shear, width of the plug flow region and longitudinal impedance increase when the yield stress increases. It is also found that the velocity increases, but, the longitudinal impedance decreases when the thickness of the peripheral layer increases. The wall shear stress decreases non-linearly, while, the longitudinal impedance increases non-linearly when the catheter radius ratio increases. The estimates of the increase in the longitudinal impedance are considerably lower for the present two-fluid model than those of the single-fluid model.     

Assessment of the kinetic-frictional model for dense granular flow

This paper aims to quantitatively assess the application of kinetic-frictional model to simulate the motion of dry granular materials in dense condition, in particular, the annular shearing in Couette configuration. The weight of frictional stress was varied to study the contribution of the frictional stress in dense granular flows. The results show that the pure kinetic-theory-based computational fluid dynamics （CFD） model （without frictional stress） over-predicts the dominant solids motion of dense granular flow while adding frictional stress [Schaeffer, D. G. （1987）. Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations, 66（1）, 19-50] with the solids pressure of [Lun, C. NTK., Savage, S. B., Jeffrey, D. J., ＆ Chepurniy, N. （1984）. Kinetic theories for granular flow： Inelastic particles in Couette flow and slightly inelastic particles in a general flow field. Journal of Fluid Mechanics, 140, 223-256] in the CFD model improves the simulation to better conform available experimental results. The results also suggest that frictional stress transmission plays an important role in dense granular flow and should not be neglected in granular flow simulations. Compatible simulation results to the experimental data are seen by increasing the weight of frictional stress to a factor of 1.25-1.5. These improved simulation results suggest the current constitutive relations （kinetic-frictional model） need to be improved in order to better reflect the real dense granular flow.     

Two-phase non-linear model for blood flow in asymmetric and axisymmetric stenosed arteries

The pulsatile flow of a two-phase model for blood flow through axisymmetric and asymmetric stenosed narrow arteries is analyzed, treating blood as a two-phase model with the suspension of all the erythrocytes in the core region as the Herschel-Bulkley material and plasma in the peripheral layer as the Newtonian fluid. The perturbation method is applied to solve the resulting non-linear implicit system of partial differential equations. The expressions for various flow quantities are obtained. It is found that the pressure drop, plug core radius, wall shear stress increase as the yield stress or stenosis height increases. It is noted that the velocity increases, longitudinal impedance decreases as the amplitude increases. For asymmetric stenosis, the wall shear stress increases non-linearly with the increase of the axial distance. The estimates of the increase in longitudinal impedance to flow of the two-phase Herschel-Bulkley material are significantly lower than those of the single-phase Herschel-Bulkley material. The results show the advantages of two-phase flow over single-phase flow in small diameter arteries with stenosis.     

Finite deformation continuum model for single-walled carbon nanotubes

A continuum-based model for computing strain energies and estimating Young’s modulus of single-walled carbon nanotubes (SWCNTs) is developed by using an energy equivalence-based multi-scale approach. A SWCNT is viewed as a continuum hollow cylinder formed by rolling up a flat graphite sheet that is treated as an isotropic continuum plate. Kinematic analysis is performed on the continuum level, with the Hencky (true) strain and the Cauchy (true) stress being employed to account for finite deformations. Based on the equivalence of the strain energy and the molecular potential energy, a formula for calculating Young’s modulus of SWCNTs is derived. This formula, containing both the molecular and continuum scale parameters, directly links macroscopic responses of nanotubes to their molecular structures. Sample numerical results show that the predictions by the new model compare favorably with those by several existing continuum and molecular dynamics models.     

Two-fluid non-linear model for flow in catheterized blood vessels

Blood flow through a catheterized artery is analyzed, assuming the flow is steady and blood is treated as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the plasma in the peripheral region as a Newtonian fluid. The expressions for velocity, flow rate, wall shear stress and frictional resistance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio and peripheral layer thickness are discussed. It is noticed that the velocity and flow rate decrease while the wall shear stress and resistance to flow increase when the yield stress or the catheter radius ratio increases while all the other parameters were held fixed. It is found that the velocity and flow rate increase while the wall shear stress and frictional resistance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the frictional resistance are significantly very small for the present two-fluid model than those of the single-fluid Casson model.     

A continuum traffic flow model with the consideration of coupling effect for two-lane freeways

A new higher-order continuum model is proposed by considering the coupling and lane changing effects of the vehicles on two adjacent lanes. A stability analysis of the proposed model provides the conditions that ensure its linear stability. Issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are also investigated with numerical experiments. The simulation results show that the proposed model is capable of providing explanations to some particular traffic phenomena commonly observable in real traffic flows.     

明渠气二相流的双流体模型

从解决平均二相流基本方程的封闭问题出发,分析了水利工程中气水二相流的特点,介绍了据此提出的可用于水利工程稀疏气泡流计算的双流体模型,并对明渠气水二相流进行了算例验证。     

Numerical simulation of pedestrian flow past a circular obstruction

In this paper, a revisiting Hughes' dynamic continuum model is used to investigate and predict the essential macroscopic characteristics of pedestrian flow, such as flow, density and average speed, in a two dimensional continuous walking facility scattered with a circular obstruction. It is assumed that pedestrians prefer to walk a path with the lowest instantaneous travel cost from origin to destination, under the consideration of the current traffic conditions and the tendency to avoid a high-density region and an obstruction. An algorithm for the pedestrian flow model is based on a cellcentered finite volume method for a scalar conservation law equation, a fast sweeping method for an Eikonal-type equation and a second-order TVD Runge-Kutta method for the time integration on unstructured meshes. Numerical results demonstrate the effectiveness of the algorithm. It is verified that density distribution of pedestrian flow is influenced by the position of the obstruction and the path-choice behavior of pedestrians.     

A LGA model for fluid flow in heterogeneous porous media

A lattice gas automaton (LGA) model is proposed to simulate fluid flow in heterogeneous porous media. Permeability fields are created by distributing scatterers (solids, grains) within the fluid flow field. These scatterers act as obstacles to flow. The loss in momentum of the fluid is directly related to the permeability of the lattice gas model. It is shown that by varying the probability of occurrence of solid nodes, the permeability of the porous medium can be changed over several orders of magnitude. To simulate fluid flow in heterogeneous permeability fields, isotropic, anisotropic, random, and correlated permeability fields are generated. The lattice gas model developed here is then used to obtain the effective permeability as well as the local fluid flow field. The method presented here can be used to simulate fluid flow in arbitrarily complex heterogeneous porous media.     

Development and experimental validation of a continuum micromechanics model for the elasticity of wood

This contribution covers the development and validation of a microelastic model for wood, based on a four-step homogenization scheme. At a length scale of several tens of nanometers, hemicellulose, lignin, and water are intimately mixed, and build up a polymer (polycrystal-type) network. At a length scale of around one micron, fiberlike aggregates of crystalline and amorphous cellulose are embedded in an contiguous polymer matrix, constituting the so-called cell wall material. At a length scale of about one hundred microns, the material softwood is defined, comprising cylindrical pores (lumen) in the cell wall material of the preceding homogenization step. Finally, at a length scale of several millimeters, hardwood comprises larger cylindrical pores (vessels) embedded in the softwood-type material homogenized before. Model validation rests on statistically and physically independent experiments: The macroscopic stiffness values (of hardwood or softwood) predicted by the micromechanical model on the basis of tissue-independent (‘universal’) phase stiffness properties of hemicellulose, amorphous cellulose, crystalline cellulose, lignin, and water (experimental set I) for tissue-specific composition data (experimental set IIb) are compared to corresponding experimentally determined tissue-specific stiffness values (experimental set IIa).