Determination of the thermal boundary resistance in the transport approach

We present a new theoretical determination of the thermal boundary resistance at a metal-liquid helium interface. The phonon temperature drops and heat flux densities at the interface are deduced from the numerical solution of the phonon Boltzmann equation inside the metal, with only electron-phonon scattering considered. A calculation of the thermal boundary resistance is performed and a comparison with the Khalatnikov theory is made ; the results differ considerably, the transport approach giving a far smaller resistance, though the phonon boundary conditions in our work are also determined by the classical acoustic theory.Laboratoire associé au Centre National de la Recherche Scientifique.     

Elastic green's function for a bimaterial composite solid containing a crack inclined to the interface

An analytical closed-form expression is derived for the elastic Green's function of a bimaterial composite solid containing a planar interface and a straight crack inclined at an arbitrary angle with the interface. The crack tip is assumed to be at the interface. Both the constituent materials of the composite are assumed to anisotropic. The Green's function satisfies the interfacial boundary conditions of continuous tractions and displacements, and zero tractions at the crack surfaces. The boundary conditions are satisfied by using the virtual force technique. The determination of the virtual forces requires solutions of a Hilbert problem which is obtained by using an orthogonal complex transform. The method is illustrated by applying it to a copper/nickel composite. The Green's function should be useful in the boundary-element method of calculating the stress and the displacement field in the solid.     

An improved generalized particle algorithm that includes boundaries and interfaces

This paper presents an improved generalized particle algorithm (GPA), as well as new boundary and interface algorithms for particle interaction with finite elements and other particles (of different materials). The improved GPA uses a local co‐ordinate system that is aligned with the boundaries and/or interfaces for the determination of the strain rates and forces. This enables the boundary and interface algorithms to be applied in a straightforward manner. It also provides an invariant solution that is independent of the orientation of the global co‐ordinate system. Several examples are presented to illustrate the effects of the various algorithms. Copyright © 2001 John Wiley & Sons, Ltd.     

Macro-elements in the mixed boundary value problems

 The symmetric Galerkin boundary element method (SGBEM), applied to elastostatic problems, is employed in defining a model with BE macro-elements. The model is governed by symmetric operators and it is characterized by a small number of independent variables upon the interface between the macro-elements. The kinematical and mechanical transmission conditions across the interface are imposed in global form, whereas the response of the boundary discretized elastic problem is provided in terms of forces on the interface boundary sides and of displacements at the interface nodes. A variational formulation is presented in which the boundary transmission conditions are derived by Polizzotto's boundary min-max variational principle. Simple numerical applications are shown. Received 8 December 99     

A model of discontinuous precipitation based on the balance and maximum production of the entropy

A model of discontinuous precipitation in supercooled binary polycrystalline alloys at reduced temperatures, taking place as a result of the diffusion-induced grain boundary migration, is constructed with allowance of grain boundary diffusion. The proposed approach allows independent determination of the main parameters, including the interlamellar distance, the maximum velocity of the phase transformation front, and the concentration jump at this boundary. This is achieved by using a set of equations for the (i) mass transfer in the moving interphase boundary, (ii) balance of the entropy fluxes at the phase transformation front, and (iii) maximum rate of the free energy release. The model uses a minimum of thermodynamic information on the two-phase system: the curvature of the Gibbs potential surface in the decomposing phase and the free energy of the interface between the new phases. Theoretical results are compared to the available experimental data.     

Automatic construction of non‐obtuse boundary and/or interface Delaunay triangulations for control volume methods

A Delaunay mesh without triangles having obtuse angles opposite to boundary and interface edges (obtuse boundary/interface triangles) is the basic requirement for problems solved using the control volume method. In this paper we discuss postprocess algorithms that allow the elimination of obtuse boundary/interface triangles of any constrained Delaunay triangulation with minimum angle ε. This is performed by the Delaunay insertion of a finite number of boundary and/or interface points. Techniques for the elimination of two kinds of obtuse boundary/interface triangles are discussed in detail: 1‐edge obtuse triangles, which have a boundary/interface (constrained) longest edge; and 2‐edge obtuse triangles, which have both their longest and second longest edge over the boundary/interface. More complex patterns of obtuse boundary/interface triangles, namely chains of 2‐edge constrained triangles forming a saw diagram and clusters of triangles that have constrained edges sharing a common vertex are managed by using a generalization of the above techniques. Examples of the use of these techniques for semiconductor device applications and a discussion on their generalization to 3‐dimensions (3D) are also included. Copyright © 2002 John Wiley & Sons, Ltd.     

Interface waves along an anisotropic imperfect interface between anisotropic solids

First and second order asymptotic boundary conditions are introduced to model a thin anisotropic layer between two generally anisotropic solids. Such boundary conditions can be used to describe wave interaction with a solid-solid imperfect anisotropic interface. The wave solutions for the second order boundary conditions satisfy energy balance and give zero scattering from a homogeneous substrate/layer/substrate system. They couple the in-plane and out-of-plane stresses and displacements on the interface even for isotropic substrates. Interface imperfections are modeled by an interfacial multiphase orthotropic layer with effective elastic properties. This model determines the transfer matrix which includes interfacial stiffness and inertial and coupling terms. The present results are a generalization of previous work valid for either an isotropic viscoelastic layer or an orthotropic layer with a plane of symmetry coinciding with the wave incident plane. The problem of localization of interface waves is considered. It is shown that the conditions for the existence of such interface waves are less restrictive than those for Stoneley waves. The results are illustrated by calculation of the interface wave velocity as a function of normalized layer thickness and angle of propagation. The applicability of the asymptotic boundary conditions is analyzed by comparison with an exact solution for an interfacial anisotropic layer. It is shown that the asymptotic boundary conditions are applicable not only for small thickness-to-wavelength ratios, but for much broader frequency ranges than one might expect. The existence of symmetric and SH-type interface waves is also discussed.     

BIFURCATIONS AND INSTABILITIES IN FRACTURE OF COHESIVE-SOFTENING STRUCTURES: A BOUNDARY ELEMENT ANALYSIS†

The “cohesive-crack model” is adopted, together with the hypotheses of small deformations and linear elasticity outside the process zone or “craze”, for the simulation of fracture processes in structures of concrete-like materials. A “direct”, collocation, multidomain boundary element method is employed and shown to be computationally effective in the considered situations, which are characterized by non-linearity on interfaces only. Iterative algorithms for the direction search and interface adjustment in propagation analysis and for the determination of the response to a craze-tip advancement are developed and numerically tested. Softening as an instabilizing factor embodied in the cohesive-crack model may give rise to path bifurcations (“equilibrium branching”), instability under load control and intrinsic (“snapback”) instability. These phenomena are analysed by the proposed boundary element procedure and discussed.     

Thermal loading of a thin layer with circular debonding over a substrate

By using techniques appropriate to mixed boundary value problems, this study addresses the determination of stress intensity factors for a circular interface debonding between a thin layer and a substrate subjected to nearly uniform temperature change. The solution method involves three-dimensional equilibrium equations of thermo-elasticity under axisymmetry conditions. The stress intensity factors are obtained by solving the resulting pair of coupled singular integral equations numerically. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermoelastic stress field in a piecewise homogeneous domain under non‐uniform temperature using a coupled boundary and finite element method

This study concerns the development of a coupled finite element–boundary element analysis method for the solution of thermoelastic stresses in a domain composed of dissimilar materials with geometric discontinuities. The continuity of displacement and traction components is enforced directly along the interfaces between different material regions of the domain. The presence of material and geometric discontinuities are included in the formulation explicitly. The unknown interface traction components are expressed in terms of unknown interface displacement components by using the boundary element method for each material region of the domain. Enforcing the continuity conditions leads to a final system of equations containing unknown interface displacement components only. With the solution of interface displacement components, each region has a complete set of boundary conditions, thus leading to the solution of the remaining unknown boundary quantities. The concepts developed for the BEM formulation of a domain with dissimilar regions is employed in the finite element–boundary element coupling procedure. Along the common boundaries of FEM–BEM regions, stresses from specific BEM regions are first expressed in terms of interface displacements, then integrated and lumped at the nodal points of the common FEM–BEM boundary so that they are treated as boundary conditions in the analysis of FEM regions along the common FEM–BEM boundary. Copyright © 2002 John Wiley & Sons, Ltd.     

超声吸收体边界条件的分析

超声吸收体的边界条件分析对于求解超声吸收体表面温升与入射波声强的函数关系至关重要。通过分析在超声吸收体与水和与空气界面处超声辐照的物理过程,分别得到超声吸收体与水界面处的平均传热系数与焦点声强之间的函数关系式和超声吸收体与空气界面处的复合传热表面系数与温差的函数关系式。通过仿真分析了不同条件下两个界面处的传热系数对超声吸收体与空气界面温升的影响。实验结果表明,当辐照时间较短时,对于超声吸收体与空气界面的温度变化,超声吸收体与水界面可以认为是一个无限远且温度恒定的边界,超声吸收体与空气界面可以认为是一个符合第一类边界条件的连续热传导。     

Load transfer at imperfect interfaces--dislocation-like model

A dislocation-like model describing the boundary conditions of a partially debonded interface is verified experimentally. The effect of the imperfect interface on the load transfer is studied by photoelastically measuring the elastic deformation in bimaterials due to an inclusion with dilatational misfit strain. The boundary conditions to be modeled are that the radial and the tangential tractions are continuous across the interface and the displacements may be discontinuous from one solid to another. The discontinuity of displacement across the interface is assumed linearly proportional to the displacement at the interface of the constituent where the stress source is. The maximum shear stress distributions measured from the isochromatic fringe patterns are in good agreement with the theoretical calculations. The results show that an imperfect interface could be viewed as a continuum entity with interface rigidity as proposed by the dislocation-like model.     

Crystal interface and high-resolution electron microscopy—the best partner

Several contributions of HRTEM on the interface science are reviewed in chronological order. The first contribution of HRTEM is the observation of gold (113)S°11 boundary, giving experimental proof of the CSL model. An observation of the asymmetric (112)S°3 boundary follows. A SiC grain boundary is effectively assessed not by the density of CSL point but the number of dangling bonds in the boundary. A ZnO/Pd interface provides an example that a misfit dislocation does not necessarily accommodate the lattice mismatch. Segregated interface shows characteristic HRTEM image contrast, suggesting change in atomic bonding. An atomic height step in the semiconductor hetero interface is observed by the Chemical Lattice Image technique. In the diamond grain boundary a dangling bond may not elevate the boundary energy, being contradictory of the least dangling bond rule. Super–high resolution of the HVHRTEM enable us to determine atomic species in the grain boundary. Combined use of HRTEM and EELSE allows us to discuss the correlation between atomic structure and nature of the corresponding interface. It is not exaggeration to say that modern interface science does not exist witout HRTEM. On the other hand, many complicated interfaces found by HRTEM remained as unaswered questions. An innovative structural model is requested to appear on the scene.     

Iterative calculation of reflected and transmitted acoustic wavesat a rough interface

A rigorous iterative technique is described for calculating the acoustic wave reflection and transmission at an irregular interface between two different media. The method is based upon a plane-wave expansion technique in which the acoustic field equations and the radiation condition are satisfied analytically, while the boundary conditions at the interface are satisfied numerically. The latter is accomplished by an iterative minimization of the integrated squared error in the boundary conditions by a conjugate gradient technique, leading to a converging and relatively simple scheme. The plane interface result can be used as starting value. Although in principle the method is rigorous, numerical examples show that in practice there is a lower bound on the error in the boundary conditions which can be achieved     

Boundary element analysis of thermal stress intensity factors for interface griffith and cusp cracks

The thermal stress intensity factors for interface cracks of Griffith and symmetric lip cusp types under vertical uniform heat flow in a finite body are calculated by the boundary element method. The boundary conditions on the crack surfaces are insulated or fixed to constant temperature. The relationship between the stress intensity factors and the displacements on the nodal point of a crack-tip element is derived. The numerical values of the thermal stress intensity factors for an interface Griffith crack in an infinite body are compared with the previous solutions. The thermal stress intensity factors for a symmetric lip cusp interface crack in a finite body are calculated with respect to various effective crack lengths, configuration parameters, material property ratios and the thermal boundary conditions on the crack surfaces. Under the same outer boundary conditions, there are no appreciable differences in the distribution of thermal stress intensity factors with respect to each material property. However, the effect of crack surface thermal boundary conditions on the thermal stress intensity factors is considerable.     

Transient heat conduction analysis in a piecewise homogeneous domain by a coupled boundary and finite element method

A coupled finite element–boundary element analysis method for the solution of transient two‐dimensional heat conduction equations involving dissimilar materials and geometric discontinuities is developed. Along the interfaces between different material regions of the domain, temperature continuity and energy balance are enforced directly. Also, a special algorithm is implemented in the boundary element method (BEM) to treat the existence of corners of arbitrary angles along the boundary of the domain. Unknown interface fluxes are expressed in terms of unknown interface temperatures by using the boundary element method for each material region of the domain. Energy balance and temperature continuity are used for the solution of unknown interface temperatures leading to a complete set of boundary conditions in each region, thus allowing the solution of the remaining unknown boundary quantities. The concepts developed for the BEM formulation of a domain with dissimilar regions is employed in the finite element–boundary element coupling procedure. Along the common boundaries of FEM–BEM regions, fluxes from specific BEM regions are expressed in terms of common boundary (interface) temperatures, then integrated and lumped at the nodal points of the common FEM–BEM boundary so that they are treated as boundary conditions in the analysis of finite element method (FEM) regions along the common FEM–BEM boundary. Copyright © 2002 John Wiley & Sons, Ltd.     

Boundary integral equation formulation for Interface cracks in anisotropic materials

We present a boundary integral formulation for anisotropic interface crack problems based on an exact Green's function. The fundamental displacement and traction solutions needed for the boundary integral equations are obtained from the Green's function. The traction-free boundary conditions on the crack faces are satisfied exactly with the Green's function so no discretization of the crack surfaces is necessary. The analytic forms of the interface crack displacement and stress fields are contained in the exact Green's function thereby offering advantage over modeling strategies for the crack. The Green's function contains both the inverse square root and oscillatory singularities associated with the elastic, anisotropic interface crack problem. The integral equations for a boundary element analysis are presented and an example problem given for interface cracking in a copper-nickel bimaterial.     

A set of interface cracks with contact zones in a combined tension-shear field

Summary. A set of cracks lying along the interface of two dissimilar isotropic materials under a mixed-mode loading is considered. The interface cracks are assumed to be fully open, partially closed with frictionless contact zones and fully closed. The problem is reduced to a homogeneous combined Dirichlet-Riemann boundary value problem, which is solved in closed form. A set of transcendental equations for the determination of the contact zone lengths for an arbitrary number of cracks and the closed-form expressions for the stresses and the displacement jumps on the material interface are obtained. A single crack with one and two contact zones has been considered in details. An explicit set of two transcendental equations for the relative contact zone length and closed-form expressions for the stress intensity factors at the crack tips are obtained for both cases. The contact zone lengths and the stress intensity factors are investigated numerically for different material pairs under different values of the loading, and a comparison of the results for a crack with one and two contact zones is carried out.     

A Chain Approach of Boundary Element Row-Subdomains for Simulating the Failure Processes in Heterogeneous Brittle Materials

To improve the effectiveness of the lattice model for simulating the failure processes of heterogeneous brittle materials, each lattice element is refined as a subdomain with homogenous material, and is modeled by the boundary element method in this paper. For simplicity, each subdomain is modeled with constant boundary elements. To enhance the efficiency, a row of sub-domains is formed, and then a chain structure of such row-subdomain is constructed. The row-equation systems are solved one by one, and then back substituted, to obtain the final solution. Such a chain subdomain approach of the boundary element method not only reduces the operations, but also the memory requirements. By ``failure' of the heterogeneous brittle material is meant to be the debonding of the interface of subdomains, and each homogeneous subdomain remains to be linear elastic. For the simulation of the failure process, a quasi-static approach is adopted. The criterion of interface strength is used to determine the element wherein the interface debonding will occur, and then the interface continuity condition is replaced by the interface debonding condition for the next computation. The simulation of the failure process is controlled by the sequential debonding of the boundary elements. Some results are given to show the applicability of the presented BEM scheme, and the complexity of the failure process of heterogeneous material.     

Interface integral BEM for solving multi-medium heat conduction problems

In this paper, a new and simple boundary element method, called interface integral boundary element method (IIBEM), is presented for solving heat conduction problems consisting of multiple media. In the method, the boundary integral equation is derived by a degeneration technique from domain integrals involved in varying heat conductivity problems into interface integrals in multi-medium problems. The main feature of the presented technique is that only a single boundary integral equation is used to solve heat conduction problems with different material properties. The effect of nonhomogeneity between adjacent materials is embodied in the interface integrals including the material property difference between the two adjacent materials. Comparing with conventional multi-domain boundary integral equation techniques, the presented method is more efficient in computational time, data preparing, and program coding. Numerical examples are given to verify the correctness of the presented technique.