FE-investigations of micro-polar boundary conditions along interface between soil and structure

The interface between granular bodies and structures is analysed with the finite element method and a micro-polar hypoplastic constitutive model. Quasi-static shearing of an infinitely long and narrow granular strip between two rigid walls of different roughness under conditions of free dilatancy and constant vertical pressure is investigated. The constitutive model can reproduce the essential features of granular bodies during shear localization. To model the different roughness of the interface, micro-polar boundary conditions are proposed taking into account the asperity of the wall roughness and grain diameter. Some emphasis is given to the influence of the wall roughness on the thickness of shear zone and the mobilization of wall friction.     

Ultrasonic wave scattering from rough,imperfect interfaces. Part II. Incoherent and coherent scattered fields

A theoretical model for ultrasonic wave scattering for geometrically irregular and imperfectly bonded interfaces is presented. Part I presents the stochastic interface characterization and a model for its mechanical response based on a micromechanics model of asperity contact. Part II uses this interface representation to write the well used quasi-static boundary conditions for scattering from a.flat imperfect interface¹ directly on the irregular interface profile. The boundary conditions are then expanded in an asymptotic series in the roughness parameter (standard deviation of the surface height) which is small compared to wavelength. The slope of the profile must also be everywhere small. These equations are solved exactly for the zero-th and second order terms, which are the flat coherent solution and its' first coherent correction, and the first order term, which is the first term in the expansion for the incoherently scattered solution. Results for obliquely incident longitudinal and shear waves show a strong dependence on the roughness in both the coherent and incoherent reflected fields, but little if any dependence on the roughness in the transmitted fields. In particular, the reflected coherent fields show markedly increasing attenuation compared to the flat compliant interface with increasing roughness and increasing ultrasonic frequency, the latter result being in qualitative agreement with results for scattering from an inhomogeneous array of individual scatterers.² There is evidence in the incoherent reflected fields for the existence of an incoherent leaky interface disturbance which manifests itself as a bulk incoherent shear wave at a scattering angle equal to the critical longitudinal angle. A coherent true interface wave is also supported by the rough interface which is shown to further attenuate the coherent reflected fields compared to the flat compliant interface solution.     

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.     

Investigation of ultrasonic wave scattering by a randomly rough solid-solid interface

An imperfect interface between two dissimilar materials is modeled by a random interface profile. A theoretical study of the interaction of ultrasonic waves with the rough solid-solid interface is presented. The reflection and transmission coefficients for longitudinal and shear coherent waves are calculated as a function of the angle of incidence within the framework of a second order perturbation theory. The effects of the statistical interface parameters, as well as the interface spectral density on the scattered fields, are investigated. These results are used to determine the roughness-induced attenuation of the coherent fields as a function of the above parameters. In addition, the relation between the incoherent part of the scattering cross-section, and interface roughness is examined.     

Ultrasonic wave scattering from rough,imperfect interfaces. Part I. Stochastic interface models

A theoretical model for ultrasonic wave scattering by geometrically irregular and imperfectly bonded interfaces is presented. In Part I, the normal stiffness of interfaces formed by the partial contact of solids with rough surfaces is estimated for two models of contacting surfaces with random roughness in one dimension only. The first model considers nonconforming surfaces with a single-scale of roughness, while double-scale roughness characterizes the surfaces of the second model, which are conforming at the large scale and nonconforming at the smaller scale. The surfaces' profiles are described by Gaussian probability and spectral densities. The surfaces at each contact are modeled by two cylinders under a compressive load and the normal stiffness per unit area of the interface is evaluated by averaging the stiffness of all the contacts, assuming they do not interact with each other. It is shown that the smaller the roughness, the softer the interface; the larger the autocorrelation length, the softer the interface; and the smaller the initial aperture, the stiffer the interface. Furthermore, interfaces described by the second model appear much stiffer than those described by the first model. The interface characterizations and normal stiffness models developed in Part I will be used in Part II to study the scattering of ultrasonic plane waves by such an interface.     

Effect of surface roughness on gas flow in microchannels by molecular dynamics simulation

Understanding the effect of surface roughness on gas flow in microchannels is highly desirable in microfluidic devices. Non-equilibrium molecular dynamics simulation is applied to investigate the effect of the surface roughness on slip flow of gaseous argon in submicron platinum channels. The geometries of the surface roughness are modeled by triangular, rectangular, sinusoidal and randomly triangular waves respectively. The results show that the boundary conditions of velocity slip, including slip, no-slip and negative slip, depend not only on the Knudsen number but also on the surface roughness. Induced by the roughness, the slip length of gas microflow over a rough surface is less than that predicted by the Maxwell model and shows a non-linear relationship with the Knudsen number. The friction coefficient increases not only with decreasing the Knudsen number but also with increasing the surface roughness. The impacts of the surface roughness and the gas rarefaction on the friction coefficient of gas microflow are strongly coupled. The roughness geometry also shows significant effects on the boundary conditions and the friction characteristics. The distortion of the streamlines and the enhancement of the penetrability near the rough surface are demonstrated to be responsible for the roughness effect.     

Reflection and refraction of plane waves at interface between two piezoelectric media

This paper analyses reflection and refraction of plane waves at a perfect interface between two anisotropic piezoelectric media. The equations of elastic waves, quasi-static electric field, and constitutive relationships for the piezoelectric media are derived. A solution based on the inhomogeneous wave theory is developed to address the inconsistency between the numbers of independent wave modes in the media and the numbers of interfacial boundary conditions to obtain accurate reflection and refraction coefficients in case of strong piezoelectric media, where all the elastic and electric continuity conditions across the interface are satisfied simultaneously. The study shows that there exist independent and zero energy wave modes satisfying the general Snell’s law and propagating along the interface for any incident wave angle. These waves can be treated as pseudo surface waves. It is further found that all the reflection/refraction waves including the pseudo surface waves obey the energy conservation law at the interface boundary. In addition, the analysis also reveals that the reflection and refraction elastic waves can turn into pseudo surface waves at some critical incident angles.     

Acoustic reflection from the boundary of anisotropic thermoviscoelastic solid with fluid

Vertical slownesses of waves at a boundary of an anisotropic thermoviscoelastic medium are calculated as roots of a polynomial equation of degree eight. Out of the corresponding eight waves, the four, which travel towards the boundary are identified as upgoing waves. Remaining four waves travel away from the boundary and are termed as downgoing waves. Reflection and refraction of plane harmonic acoustic waves are studied at a plane boundary between anisotropic thermoviscoelastic solid and a non-viscous fluid. At this fluid-solid interface, an incident acoustic wave through the fluid reflects back as an attenuated acoustic wave and refracts as four attenuating waves into the anisotropic base. Slowness vectors of all the waves in two media differ only in vertical components. Complex values of vertical slowness define inhomogeneous refracted waves with a fixed direction of attenuation, i.e. perpendicular to the interface. Energy partition is calculated at the interface to find energy shares of reflected and refracted waves. A part of incident energy dissipates due to interaction among the attenuated refracted waves. Numerical examples are considered to study the variations in energy shares with the direction of incident wave. For each incidence, the conservation of incident energy is verified in the presence of interaction energy. Energy partition at the interface seems to be changing very slightly with the azimuthal variations of the incident direction. Effects of anisotropy, elastic relaxation and thermal parameters on the variations in energy partition are discussed. The acoustic wave reflected from isothermal interface is much significant for incidence around some critical directions, which are analogous to the critical angles in a non-dissipative medium. The changes in thermal relaxation times and uniform temperature of the thermoviscoelastic medium do not show any significant effect on the reflected energy.     

Ballistic FET modeling using QDAME: quantum device analysis by modal evaluation

We present an algorithm for self-consistent solution of the Poisson and Schrodinger equations in two spatial dimensions with open-boundary conditions to permit current flow. The algorithm works by discretely sampling a device's density of states using standing wave boundary conditions, decomposing the standing waves into traveling waves injected from the contacts to assign occupancies, and iterating the quantum charge with the potential to self-consistency using a novel hybrid Newton-Broyden method. A double-gate FET is simulated as an example, with applications focused on surface roughness and contact geometry.     

Scattering of anti-plane shear waves by a partially debonded piezoelectric circular cylindrical inclusion

Summary This paper presents an analysis of the scattering of anti-plane shear waves by a single piezo-electric cylindrical inclusion partially bonded to an unbounded matrix. The anti-plane governing equations for piezoelectric materials are reduced to Helmholtz and Laplacian equations. The fields of scattered waves are obtained by means of the wave function expansion method when the bonded interface is perfect. When the interface is partially debonded, the region of the debonding is modeled as an interface crack with non-contacting faces. The electric permeable boundary conditions are adopted, i.e. the normal electric displacement and electric potential are continuous across the crack faces. The crack opening displacement is represented by Chebyshev polynomials and a system of equations is derived and solved for the unknown coefficients.     

Effect of surface/interface on the dynamic stress of two interacting cylindrical nano-inhomogeneities under compressional waves

Based on the surface/interface elasticity theory, the effect of surface/interface on the dynamic stress of two interacting cylindrical nano-inhomogeneities under compressional waves is considered. The analytical solutions of displacement potentials are expressed by employing wave function expansion method and the expanded mode coefficients are determined by satisfying the boundary conditions at the interfaces. The addition theorem for cylindrical wave function is used to accomplish the superposition of wave fields in different coordinate systems. Analyses show that the effect of the interface properties on the dynamic stress is significantly related to the wave frequency of incident waves, the shear modulus ratio of the nano-inhomogeneities to matrix, and the relative position and distance between the two nano-inhomogeneities.     

Experimental and numerical study of granular medium-rough wall interface friction

Wall roughness plays a crucial role in granular medium - rough wall interface friction. In this study, an experimental device has been designed to study the influence of boundary conditions, more specifically wall roughness, on the behavior of sheared granular medium. The study is based on use of an analog model, and consists of simulating roughness by means of notches and grains in the medium by monodisperse beads and on use of a numerical model based on the discrete element method. The test protocol entails displacing at fixed speed notched rods under confined granular medium. Movement of the beads layer near the rods as well as friction of the beads against the rods are both studied herein. Results indicate that the parameter controlling friction at the granular medium - rough wall interface is primarily the depth of beads embedment in surface asperities. The objective of the associated numerical modeling is to supplement the experimental results.     

弱粘接界面固-固界面波特性及与界面粘接性质关系数值研究

根据两固体粘接结构在不同粘接强度下的弹簧模型边界条件,通过傅里叶积分变换方法进行波动方程求解,理论分析和数值计算了相近横波速度的两种固体间界面波的频散及衰减特性.计算结果表明,当切向弹簧劲度系数从滑移粘接界面向完好粘接界面逐渐变化时,界面波的频散特性随之变化.在此基础上进一步计算了不同界面粘接条件下法向线源脉冲激发的界...     

Acoustic microscopy and dispersion of leaky Rayleigh waves onrandomly rough surfaces: a theoretical study

A theoretical investigation of the dispersion of leaky Rayleigh waves propagating along one-dimensional (1-D) rough fluid-solid interfaces was carried out by simulating the measurement process of a line-focus beam acoustic microscope. The interface profiles were described in terms of their rms, also known as the roughness of the profile, autocorrelation length, and autocorrelation function. The reflectivity of the interfaces was calculated by using a second-order perturbation approach in the profile roughness. Theoretical V(z) curves were generated and analyzed to yield values of the phase velocity of the Rayleigh waves. The dependence of the Rayleigh wave velocity on the profile and material parameters was examined. Significant variations of the phase velocity were found for values of the roughness which are small compared to the shortest of the wavelengths involved in the scattering. The dispersion relations also showed considerable sensitivity to changes in mechanical properties typical of materials of engineering interest. In the low-frequency range, simulations indicated the dispersion of Rayleigh waves to be rather insensitive to the spectral content of the profile     

Explosive collapse of vapor film under conditions of intensive heat fluxes

The stability is investigated (linear and nonlinear analysis) of the interface between a thin vapor film and a layer of liquid in the presence of a steady heat flux from a metal surface heated to a high temperature to the vapor film and then from vapor to subcooled liquid. In view of thermal disequilibrium which takes into account the temperature dependence of saturation pressure, boundary conditions on the vapor-liquid interface are derived, which generalize the known correlations on the free surface of liquid in the gravity field. A number of new effects arise in the problem under consideration, as distinct from the classical problem. The thermal processes, which occur on the phase boundary and are possible in the absence of the force of gravity as well, lead to the generation of weakly decaying periodic waves of low amplitude, whose velocity may exceed significantly that of gravity waves. The heat flux through the interface may cause on this surface periodic waves of small length (ripple) which are not capillary. The processes of phase transition on the interface are capable of providing for the stability of vapor film under the layer of liquid in the gravity field. Along with periodic waves and solitons, the mode of explosive instability may arise in the nonlinear stage because of a weak variation of the film thickness, where the amplitude of an initially low-amplitude plane wave rises to infinity during a finite period of time.     

Boundary integral equations for the scattering of elastic waves by elastic inclusions with thin interface layers

Elastic waves are scattered by an elastic inclusion. The interface between the inclusion and the surrounding material is imperfect: the displacement and traction vectors on one side of the interface are assumed to be linearly related to both the displacement vector and the traction vector on the other side of the interface. The literature on such inclusion problems is reviewed, with special emphasis on the development of interface conditions modeling different types of interface layer. Inclusion problems are formulated mathematically, and uniqueness theorems are proved. Finally, various systems of boundary integral equations over the interface are derived.     

液体-压电晶片界面上电边界条件对兰姆波激发的影响

本文对液体-压电晶片结构中,不同电边界条件下叉指换能器所激发的兰姆波传播特性进行了分析研究,给出了不同电边界条件下兰姆波的相速度、叉指换能器激发兰姆波的机电耦合系数与压电晶片的归一化厚度、晶体切向之间的关系曲线,为实际设计中电边界条件的正确选择提供了理论基础。     

Interface acoustic waves properties in some common crystal cuts

Interface acoustic waves (IAWs), also termed boundary waves, propagate at the interface between two solids. We present two IAW numerical analysis tools, inspired from well established surface acoustic wave (SAW) methods. First, the interface effective permittivity is derived for arbitrary piezoelectric solids and is used to estimate some basic parameters of IAWs. The harmonic admittance for an interface excitation is then derived from the interface effective permittivity, in much the same way the harmonic admittance for surface excitation is obtained from the (surface) effective permittivity. The finite electrode thickness is neglected in this problem analysis. The harmonic admittance is used to model propagation in the case when an infinite periodic interdigital transducer is located at the interface. Simulation results are commented upon for some usual piezoelectric material cuts and the paper outlines a modal selection specific to IAWs as compared with SAWs. The temperature dependence of the resonance frequency is also estimated.     

Surface roughness induced attenuation and changes in the propagation velocity of long Rayleigh-type waves

Summary The propagation of long Rayleigh waves on a rough surface is studied theoretically by Rayleigh method and for the free rough surface of a homogeneous and isotropic elastic half-space. The frequency dependence of the propagation velocity and attenuation is analysed under the assumption that the frequency is real. Moreover, the changes in the propagation velocity induced by the surface roughness are expressed in terms of the square of the ratio of the root-mean-square departure of the surface from flatness to the correlation length of the distance between successive peaks and valleys in the rough-surface profile.     

Phase Conjugation in Degenerate Four-wave Mixing with Finite Apertures

The phase-conjugate field fidelity in backward-going four-wave mixing, based on the diffraction model solvable analytically, is investigated. The method assumes interaction of the non-depleted infinite plane pump waves with the spatially limited probe and signal waves inside the nonlinear medium. Solutions are obtained applying the Fourier transformation and the Green function technique under various boundary conditions for coupled wave equations. The probe and its phase-conjugate waves are defined by using a complex phase formulation including both the phase variation and amplitude modulation. It is shown that the analysed approach can involve assumptions leading to the ideal or distorted phase conjugation.