Finite Boundary Effects in Problem of a Crack Perpendicular to and Terminating at a Bimaterial Interface

In this paper, the problem of a crack perpendicular to and terminating at an interface in bimaterial structure with finite boundaries is investigated. The dislocation simulation method and boundary collocation approach are used to derive and solve the basic equations. Two kinds of loading form are considered when the crack lies in a softer or a stiffer material, one is an ideal loading and the other one fits to the practical experiment loading. Complete solutions of the stress field including the T stress are obtained as well as the stress intensity factors. Influences of T stress on the stress field ahead of the crack tip are studied. Finite boundary effects on the stress intensity factors are emphasized. Comparisons with the problem presented by Chen et al. (Int. J. Solids and Structure, 2003, 40, 2731-2755) are discussed also.

A Molecular Dynamics Simulation: the Effect of Finite Size on the Thermal Conductivity in a Single Crystal Silicon

Non-equilibrium molecular dynamics (NEMD) simulations are performed to calculate thermal conductivity. The environment-dependent interatomic potential (EDIP) potential on crystal silicon is adopted as a model system. The issues are related to nonlinear response, local thermal equilibrium and statistical averaging. The simulation results by non-equilibrium molecular dynamics show that the calculated thermal conductivity decreases almost linearly as the film thickness reduced at the nanometre scale. The effect of size on the thermal conductivity is also obtained by a theoretic analysis of the kinetic theory and formulas of the heat capacity. The analysis reveals that the contributions of phonon mean free path (MFP) and phonon number in a finite cell to thermal conductivity are very important.

Characterization Of Crystal Structure In Binary Mixtures Of Latex Globules

Colloidal crystals formed by two types of polystyrene particles of different sizes (94 and 141 nm) at various number ratios (94:141 nm) are studied. Experiments showed that the formation time of crystals lengthens as the number ratio of the two components approaches 1:1. The dependence of the mean interparticle distance (D-0), crystal structure and alloy structure on the number ratio of the two types of particles was Studied by means of Kossel diffraction technique and reflection spectra. The results showed that as the number ratio decreased, the mean interparticle distance (D-0) became larger. And the colloidal crystal in binary mixtures is more preferably to form the bcc structure. This study found that binary systems form the substitutional solid solution (sss)-type alloy structure in all cases except when the number ratio of two types of particles is 5:1, which results instead in the superlattice structure. (C) 2008 Elsevier Inc. All rights reserved.

A Multimoment Finite-Volume Shallow-Water Model On The Yin-Yang Overset Spherical Grid

A numerical model for shallow-water equations has been built and tested on the Yin-Yang overset spherical grid. A high-order multimoment finite-volume method is used for the spatial discretization in which two kinds of so-called moments of the physical field [i.e., the volume integrated average ( VIA) and the point value (PV)] are treated as the model variables and updated separately in time. In the present model, the PV is computed by the semi-implicit semi-Lagrangian formulation, whereas the VIA is predicted in time via a flux-based finite-volume method and is numerically conserved on each component grid. The concept of including an extra moment (i.e., the volume-integrated value) to enforce the numerical conservativeness provides a general methodology and applies to the existing semi-implicit semi-Lagrangian formulations. Based on both VIA and PV, the high-order interpolation reconstruction can only be done over a single grid cell, which then minimizes the overlapping zone between the Yin and Yang components and effectively reduces the numerical errors introduced in the interpolation required to communicate the data between the two components. The present model completely gets around the singularity and grid convergence in the polar regions of the conventional longitude-latitude grid. Being an issue demanding further investigation, the high-order interpolation across the overlapping region of the Yin-Yang grid in the current model does not rigorously guarantee the numerical conservativeness. Nevertheless, these numerical tests show that the global conservation error in the present model is negligibly small. The model has competitive accuracy and efficiency.

Tensionless Contact Of A Finite Beam Resting On Reissner Foundation

A more generalized model of a beam resting on a tensionless Reissner foundation is presented. Compared with the Winkler foundation model, the Reissner foundation model is a much improved one. In the Winkler foundation model, there is no shear stress inside the foundation layer and the foundation is assumed to consist of closely spaced, independent springs. The presence of shear stress inside Reissner foundation makes the springs no longer independent and the foundation to deform as a whole. Mathematically, the governing equation of a beam on Reissner foundation is sixth order differential equation compared with fourth order of Winkler one. Because of this order change of the governing equation, new boundary conditions are needed and related discussion is presented. The presence of the shear stress inside the tensionless Reissner foundation together with the unknown feature of contact area/length makes the problem much more difficult than that of Winkler foundation. In the model presented here, the effects of beam dimension, gap distance, loading asymmetry and foundation shear stress on the contact length are all incorporated and studied. As the beam length increases, the results of a finite beam with zero gap distance converge asymptotically to those obtained by the previous model for an infinitely long beam. (C) 2008 Elsevier Ltd. All rights reserved.

Peeling Experiments Of Ductile Thin Films Along Ceramic Substrates - Critical Assessment Of Analytical Models

Two types of peeling experiments are performed in the present research. One is for the Al film/Al2O3 substrate system with an adhesive layer between the film and the substrate. The other one is for the Cu film/Al2O3 substrate system without adhesive layer between the film and the substrate, and the Cu films are electroplated onto the Al2O3 substrates. For the case with adhesive layer, two kinds of adhesives are selected, which are all the mixtures of epoxy and polyimide with mass ratios 1:1.5 and 1:1, respectively. The relationships between energy release rate, the film thickness and the adhesive layer thickness are measured during the steady-state peeling process. The effects of the adhesive layer on the energy release rate are analyzed. Using the experimental results, several analytical criteria for the steady-state peeling based on the bending model and on the two-dimensional finite element analysis model are critically assessed. Through assessment of analytical models, we find that the cohesive zone criterion based on the beam bend model is suitable for a weak interface strength case and it describes a macroscale fracture process zone case, while the two-dimensional finite element model is effective to both the strong interface and weak interface, and it describes a small-scale fracture process zone case. (C) 2007 Elsevier Ltd. All rights reserved.

Molecular/Cluster Statistical Thermodynamics Methods To Simulate Quasi-Static Deformations At Finite Temperature

The rapid evolution of nanotechnology appeals for the understanding of global response of nanoscale systems based on atomic interactions, hence necessitates novel, sophisticated, and physically based approaches to bridge the gaps between various length and time scales. In this paper, we propose a group of statistical thermodynamics methods for the simulations of nanoscale systems under quasi-static loading at finite temperature, that is, molecular statistical thermodynamics (MST) method, cluster statistical thermodynamics (CST) method, and the hybrid molecular/cluster statistical thermodynamics (HMCST) method. These methods, by treating atoms as oscillators and particles simultaneously, as well as clusters, comprise different spatial and temporal scales in a unified framework. One appealing feature of these methods is their "seamlessness" or consistency in the same underlying atomistic model in all regions consisting of atoms and clusters, and hence can avoid the ghost force in the simulation. On the other hand, compared with conventional MD simulations, their high computational efficiency appears very attractive, as manifested by the simulations of uniaxial compression and nanoindenation. (C) 2008 Elsevier Ltd. All rights reserved.

Shallow Water Model On Cubed-Sphere By Multi-Moment Finite Volume Method

A global numerical model for shallow water flows on the cubed-sphere grid is proposed in this paper. The model is constructed by using the constrained interpolation profile/multi-moment finite volume method (CIP/MM FVM). Two kinds of moments, i.e. the point value (PV) and the volume-integrated average (VIA) are defined and independently updated in the present model by different numerical formulations. The Lax-Friedrichs upwind splitting is used to update the PV moment in terms of a derivative Riemann problem, and a finite volume formulation derived by integrating the governing equations over each mesh element is used to predict the VIA moment. The cubed-sphere grid is applied to get around the polar singularity and to obtain uniform grid spacing for a spherical geometry. Highly localized reconstruction in CIP/MM FVM is well suited for the cubed-sphere grid, especially in dealing with the discontinuity in the coordinates between different patches. The mass conservation is completely achieved over the whole globe. The numerical model has been verified by Williamson's standard test set for shallow water equation model on sphere. The results reveal that the present model is competitive to most existing ones. (C) 2008 Elsevier Inc. All rights reserved.

A Cip/Multi-Moment Finite Volume Method For Shallow Water Equations With Source Terms

A novel finite volume method has been presented to solve the shallow water equations. In addition to the volume-integrated average (VIA) for each mesh cell, the surface-integrated average (SIA) is also treated as the model variable and is independently predicted. The numerical reconstruction is conducted based on both the VIA and the SIA. Different approaches are used to update VIA and SIA separately. The SIA is updated by a semi-Lagrangian scheme in terms of the Riemann invariants of the shallow water equations, while the VIA is computed by a flux-based finite volume formulation and is thus exactly conserved. Numerical oscillation can be effectively avoided through the use of a non-oscillatory interpolation function. The numerical formulations for both SIA and VIA moments maintain exactly the balance between the fluxes and the source terms. 1D and 2D numerical formulations are validated with numerical experiments. Copyright (c) 2007 John Wiley & Sons, Ltd.

Threshold diversity and trans-scales sensitivity in a finite nonlinear evolution model of materials failure

We present a slice-sampling method and study the ensemble evolution of a large finite nonlinear system in order to model materials failure. There is a transitional region of failure probability. Its size effect is expressed by a slowly decaying scaling law. In a meso-macroscopic range (similar to 10(5)) in realistic failure, the diversity cannot be ignored. Sensitivity to mesoscopic details governs the phenomena. (C) 1997 Published by Elsevier Science B.V.

Saturated duration of rectangular pressure pulse applied to rectangular plates with finite-deflections

The inequities in health care and housing access experienced by low-income women in the United States are a continuing concern. This article addresses the interrelationships between housing and health as experienced by low-income clients so that health care practitioners can begin to build active and effective health-promoting partnerships with clients, their families, and their communities. A case study is presented that describes the actual experience of a woman living in a low-income housing development and its effect on her health and access to health care. The importance of the role of midwives in addressing the health care and advocacy needs of women in substandard housing is highlighted.