General Solution to Two-Dimensional Nonslipping JKR Model with a Pulling Force in an Arbitrary Direction

In this paper, a generalized JKR model is investigated, in which an elastic cylinder adhesively contacts with an elastic half space and the contact region is assumed to be perfect bonding. An external pulling force is acted on the cylinder in an arbitrary direction. The contact area changes during the pull-off process, which can be predicted using the dynamic Griffith energy balance criterion as the contact edge shifts. Full coupled solution with an oscillatory singularity is obtained and analyzed by numerical calculations. The effect of Dundurs' parameter on the pull-off process is analyzed, which shows that a nonoscillatory solution can approximate the general one under some conditions, i.e., larger pulling angle (pi/2 is the maximum value), smaller a/R or larger nondimensional parameter value of Delta gamma/E*R. Relations among the contact half width, the external pulling force and the pulling angle are used to determine the pull-off force and pull-off contact half width explicitly. All the results in the present paper as basic solutions are helpful and applicable for experimenters and engineers.

Analytical Study of Idealized Two-Dimensional Cellular Detonations

In this study, the idealized two-dimensional detonation cells were decomposed into the primary units referred to as sub-cells. Based on the theory of oblique shock waves, an analytical formula was derived to describe the relation between the Mach number ratio through triple-shock collision and the geometric properties of the cell. By applying a modified blast wave theory, an analytical model was developed to predict the propagation of detonation waves along the cell. The calculated results show that detonation wave is, first, strengthened at the beginning of the cell after triple-shock collision, and then decays till reaching the cell end. The analytical results were compared with experimental data and previous numerical results; the agreement between them appears to be good, in general.

Three-Dimensional Propagation of the Transmitted Shock Wave in a Square Cross-Sectional Chamber

An investigation into the three-dimensional propagation of the transmitted shock wave in a square cross-section chamber was described in this paper, and the work was carried out numerically by solving the Euler equations with a dispersion-controlled scheme. Computational images were constructed from the density distribution of the transmitted shock wave discharging from the open end of the square shock tube and compared directly with holographic interferograms available for CFD validation. Two cases of the transmitted shock wave propagating at different Mach numbers in the same geometry were simulated. A special shock reflection system near the corner of the square cross-section chamber was observed, consisting of four shock waves: the transmitted shock wave, two reflection shock waves and a Mach stem. A contact surface may appear in the four-shock system when the transmitted shock wave becomes stronger. Both the secondary shock wave and the primary vortex loop are three-dimensional in the present case due to the non-uniform flow expansion behind the transmitted shock.

Effective elastic moduli of two-dimensional solids with multiple cracks

An accurate method which directly accounts for the interactions between different microcracks is used for analyzing the elastic problem of multiple cracks solids. The effective elastic moduli for randomly oriented cracks and parallel cracks are evaluated for the representative volume element (RVE) with microcracks in infinite media. The numerical results are compared with those from various micromechanics models and experimental data. These results show that the present method is simple and provides a direct and efficient approach to dealing with elastic solids containing multiple cracks.

Evolution of three-dimensional coherent structures in compressible axisymmetric jet

A high order difference scheme is used to simulate the spatially developing compressible axisymmetric jet. The results show that the Kelvin-Helmholtz instability appears first when the jet loses its stability, and then with development of jet the increase in nonlinear effects leads to the secondary instability and the formation of the streamwise vortices. The evolution of the three-dimensional coherent structure is presented. The computed results verify that in axisymmetric jet the secondary instability and formation of the streamwise vortices are the important physical mechanism of enhancing the flow mixing and transition occurring.

A New Designed Two-Dimensional Bifurcation Parallel-Plate Flow Chamber

解决平行平板流槽每次实验只能观测壁面培养细胞受一种剪应力作用的问题。作者在平行平板流槽的基础上,首次提出了一种改进后的流槽--二维平板分叉流槽。通过数值模拟,给出了流体作定常流动时,流速和壁面剪应力的分布。结果发现,利用这种二维平板分叉流槽可以研究壁面培养的细胞在不同大小剪应力作用下的力学行为。该研究结果为流槽的合理设计和使用,并分析剪应力空间分布对内皮细胞的影响有重要实际意义。

Three-dimensional instability of an oscillating viscous flow past a circular cylinder

A systematically numerical study of the sinusoidally oscillating viscous flow around a circular cylinder was performed to investigate vortical instability by solving the three-dimensional incompressible Navier-Stokes equations. The transition from two- to three-dimensional flow structures along the axial direction due to the vortical instability appears, and the three-dimensional structures lie alternatively on the two sides of the cylinder. Numerical study has been taken for the Keulegan-Carpenter( KC) numbers from 1 to 3.2 and frequency parameters from 100 to 600. The force behaviors are also studied by solving the Morison equation. Calculated results agree well with experimental data and theoretical prediction.

Two-Dimensional Flood Simulation of the Lower Yellow River from Huayuankou to Jiahetan

黄河下游花园口至夹河滩河段系典型的游荡型河段.在该河段,黄河大堤内范围宽广,一般洪水频率年份,水流主要限制在主槽内,因此大堤内分布有不少居民点以及纵横交错的保护居民点的生产堤和不少高于地面的灌溉渠堤和公路,使洪水行洪范围受到了很大的限制.当洪峰流量很大时,洪水将造成生产堤溃决,极大地危害滩区居民的生活.因此,设计模拟模型计算网格时需要考虑大堤、生产堤、明显高于地面的道路等阻水建筑物的影响,使这些堤及公路成为计算格网的边.不规则四边形网格能够很好地拟合黄河这种复杂的计算域.数值模拟时采用有限体积法,为确保通量的单向性,文中使用Osher格式计算通量.通过对1982年洪水的模拟,模拟结果表明了模型的合理性.

Interactions of Penny-Shaped Cracks in Three-Dimensional Solids

The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is developed in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.

Pressure Controlled Self-Assembly of High Quality Three-Dimensional Colloidal Photonic Crystals

A concise pressure controlled isothermal heating vertical deposition (PCIHVD) method is developed, which provides an optimal growing condition with better stability and reproducibility for fabricating photonic crystals (PCs) without the limitation of colloidal sphere materials and sizes. High quality PCs are fabricated with PCIHVD from polystyrene spheres with diameters ranging from 200 nm to 1 mu m. The deep photonic band gap and steep photonic band edge of the samples are most favorable for realizing ultrafast optical devices, photonic chips, and communications. This method makes a meaningful advance in the quality and diversity of PCs and greatly promotes their wide applications.

Embedded cell model of three-dimensional two-phase composites

An embedded cell model is presented to obtain the effective elastic moduli and the elastic-plastic stress-strain relations of three-dimensional two-phase particulate composites. Each cell consists of an ellipsoidal inclusion surrounded by a finite ellipsoidal matrix that embedded in an infinite matrix. When both matrix and particle are elastic, the effective elastic moduli are derived which is an exact analytic formula without any simplified approximation that can be expressed in an explicit form. Further, the elastic-plastic stress-strain relations are obtained for spherical cells and oblate spheroid cells, in which the matrix is elastic and the particle is elastic-plastic. In addition, the macroscopic elastic-plastic constitutive relation of particle reinforced composites (PRC) is investigated by a systematic approach [1] in which the matrix is elastic-plastic and the particle is elastic.

Analysis of two-dimensional finite solids with microcracks

A general method is presented for solving the plane elasticity problem of finite plates with multiple microcracks. The method directly accounts for the interactions between different microcracks and the effect of outer boundary of a finite plate. Analysis is based on a superposition scheme and series expansions of the complex potentials. By using the traction-free conditions on each crack surface and resultant forces relations along outer boundary, a set of governing equations is formulated. The governing equations are solved numerically on the basis of a boundary collocation procedure. The effective Young's moduli for randomly oriented cracks and parallel cracks are evaluated for rectangular plates with microcracks. The numerical results are compared with those from various micromechanics models and experimental data. These results show that the present method provides a direct and efficient approach to deal with finite solids containing multiple microcracks.

Scaling, Dimensional Analysis, and Indentation Measurements

We provide an overview of the basic concepts of scaling and dimensional analysis, followed by a review of some of the recent work on applying these concepts to modeling instrumented indentation measurements. Specifically, we examine conical and pyramidal indentation in elastic-plastic solids with power-law work-hardening, in power-law creep solids, and in linear viscoelastic materials. We show that the scaling approach to indentation modeling provides new insights into several basic questions in instrumented indentation, including, what information is contained in the indentation load-displacement curves? How does hardness depend on the mechanical properties and indenter geometry? What are the factors determining piling-up and sinking-in of surface profiles around indents? Can stress-strain relationships be obtained from indentation load-displacement curves? How to measure time dependent mechanical properties from indentation? How to detect or confirm indentation size effects? The scaling approach also helps organize knowledge and provides a framework for bridging micro- and macroscales. We hope that this review will accomplish two purposes: (1) introducing the basic concepts of scaling and dimensional analysis to materials scientists and engineers, and (2) providing a better understanding of instrumented indentation measurements.

Seismic Responses of a Hemispherical Alluvial Valley to SV Waves: A Three-Dimensional Analytical Approximation

An analytical solution to the three-dimensional scattering and diffraction of plane SV-waves by a saturated hemispherical alluvial valley in elastic half-space is obtained by using Fourier-Bessel series expansion technique. The hemispherical alluvial valley with saturated soil deposits is simulated with Biot's dynamic theory for saturated porous media. The following conclusions based on numerical results can be drawn: (1) there are a significant differences in the seismic response simulation between the previous single-phase models and the present two-phase model; (2) the normalized displacements on the free surface of the alluvial valley depend mainly on the incident wave angles, the dimensionless frequency of the incident SV waves and the porosity of sediments; (3) with the increase of the incident angle, the displacement distributions become more complicated; and the displacements on the free surface of the alluvial valley increase as the porosity of sediments increases.

Reliable Validation Based on Optical Flow Visualization for CFD Simulations

A reliable validation based on the optical flow visualization for numerical simulations of complex flowfields is addressed in this paper. Several test cases, including two-dimensional, axisymmetric and three-dimensional flowfields, were presented to demonstrate the effectiveness of the validation and gain credibility of numerical solutions of complex flowfields. In the validation, images of these flowfields were constructed from numerical results based on the principle of the optical flow visualization, and compared directly with experimental interferograms. Because both experimental and numerical results are of identical physical representation, the agreement between them can be evaluated effectively by examining flow structures as well as checking discrepancies in density. The study shows that the reliable validation can be achieved by using the direct comparison between numerical and experiment results without any loss of accuracy in either of them.