Static friction between elastic solids due to random asperities

Several workers have established that the Larkin domains for two three-dimensional nonmetallic elastic solids in contact with each other at a disordered but atomically flat interface are enormously large, implying that there should be negligible static friction per unit area in the macroscopic solid limit. In contrast, the present Letter argues that when the Larkin domains are calculated for disorder on the multiasperity scale, they are much smaller than the interface size. This can account for the virtual universal occurrence of static friction.     

Predicting the Mechanical Properties of Binary Blends of Immiscible Polymers

We couple a morphological study of an immiscible binary AB mixture with a micromechanical simulation to determine how the spatial distribution of the A and B domains and the interfacial region (interphase) affects the mechanical behavior of the blend. The morphological studies are conducted through a three-dimensional Cahn-Hilliard (CH) simulation. Through the CH calculations, we obtain the size and structure of the domains for different blend compositions. The output of the CH model serves as the input to the Lattice Spring Model (LSM), which consists of a three-dimensional network of springs. In particular, the location of the different phases is mapped onto the LSM lattice and the appropriate force constants are assigned to the LSM sites. A stress is applied to the LSM lattice and we calculate the elastic response of the material. We find that the local stress and strain fields are highly dependent on the morphology of the system. By integrating the morphological and mechanical models, we can isolate how modifications in the composition of the mixture affect the macroscopic behavior. Thus, we can establish how choices made in the components affect the ultimate performance of the material.     

Stability diagram for elastic domains in epitaxial ferroelectric thin films

The statics of isolated elastic domains (twins) in epitaxial thin tetragonal films grown on a cubic substrate is investigated theoretically. Different possible variants of the geometric shape of a domain are studied: plate, trapezoidal, and triangular. The nonuniform internal stresses, which also exist in polydomain epitaxial systems, are calculated by the effective-dislocation method. Hence the elastic energies stored in heterostructures with different domains are determined. The equilibrium width of a domain is calculated by minimizing the total internal energy of the heterostructure. Next, the stability diagram for isolated domains in epitaxial films is constructed from energy considerations. It is shown that in a large part of this diagram trapezoidal domains are energetically more advantageous than plate-shaped domains. The effect of an external electric field on the stability of 90° domains in epitaxial ferroelectric films is investigated. Fiz. Tverd. Tela (St. Petersburg) 39, 127–134 (January 1997)     

Strain at junctions in multidomain configurations

This article deals with the determination of multidomain configurations in ferroics taking into account the elastic compatibility of the neighbouring domains. The proposed method is based on transformation matrices, which describe the spacial relationship of two crystal lattice bases for coherent domain pairs. The matrices are calculated using the symmetry operations between domains and lattice parameters. The principle point of this method is the comparison of the product of transformation matrices and the unity matrix. For example, by using this method it was shown that the junction of three and five orientation domains is strained whereas the encounter of four domains is strain free in three different ferroelastic perovskite phases. The derived allowed four-domain configurations are confirmed by experimental data.     

PERTURBATION METHOD SOLVING ELASTIC PROBLEMS OF ICOSAHEDRAL QUASICRYSTALS CONTAINING A CIRCULAR CRACK

Perturbation method for solving elastic three-dimensional (3D) problems for 3D icosahedral quasicrystals is proposed. Considering an infinite 3D icosahedral quasicrystal weakened by a circular crack, we obtain the uniformly valid asymptotic solutions up to O(R²) for the mode I loading, where R is the elastic constant of phonon-phason coupling.     

The scattering and transmission of elastic waves in quasi-two-dimensional planar waveguides with linear defect boundaries

The influence of linear defect boundaries on the transmission and scattering of elastic waves in quasi-two-dimensional wave-guides is studied using the matching method. A linear defect boundary separating two wave-guide crystalline lattice domains is characterised here by a linear chain of defect masses and by modified elastic constants in the boundary, different from their values in the bulk of the domains. In particular a square lattice is considered to model the domains of the two-dimensional planar wave-guide containing the linear defect. The reflection and transmission probabilities, and the total transmission probabilities are calculated numerically and presented for the scattering processes in a variety of cases. We show that the interaction between the localised modes introduced by the defect boundary and the propagating modes of the system leads to Fano resonances. These resonances shift to higher (lower) frequencies for smaller (larger) defect masses, and for the same mass as function of the angle of the incident wave. Other spectral features shown to exist are due to interference effects especially at oblique incidence and when modifying the boundary elastic constants. Received 8 November 1999 and Received in final form 14 January 2000     

Material property estimation in thin plates using focused,synthetic-aperture acoustic beams

The method developed here exploits the wide angular range of focused acoustic probes and the large synthetic aperture of scanned transducers to permit a rapid and reliable estimation of material properties in thin plates. It is found in several tests with various materials that estimates of elastic behavior using this method agree with contact measurements to within less than 5%. The method utilizes transmission (or reflection) coefficient reconstruction for an infinite thin plate, across a wide range of frequency and wave number, from which elastic property estimates are made. Data collected over a large synthetic acoustic aperture are processed with temporal and spatial Fourier transforms applied to change the acquired data from the coordinate and time domains to the wave number and frequency domains. Extrinsic real-beam effects on the data are accounted for with a complex transducer point analysis. Transmission measurements yield reconstructed data extending to the mode cutoffs, permitting easy and nearly unambiguous estimation of a subset of the elastic stiffnesses. For anisotropic plates, elastic stiffnesses are estimated with an inversion procedure that uses only limited data carefully selected from different portions of the measured scattering coefficient. Estimates are made by reconstructing in a stepwise fashion, based on sensitivity studies, where only one stiffness is estimated from the data at any one time, restricting the optimization to a robust one-dimensional search.     

Basic ideas and applications of the method of reduction of dimensionality in contact mechanics

The method of reduction of dimensionality in contact mechanics is based on a mapping of some classes of three-dimensional contact problems onto one-dimensional contacts with elastic foundations. Recently, a rigorous mathematical proof of the method has been provided for contacts of arbitrary bodies of revolution with and without adhesion. The method of reduction of dimensionality has been further verified for randomly rough surfaces. The present paper gives an overview of the physical foundations of the method and of its applications to elastic and viscoelastic contacts with adhesion and friction. Both normal and tangential contact problems are discussed.     

Coherency stresses in multilayers

The determination of the elastic state of coherently matched layers is important in a wide range of domains, including epitaxial films on a substrate with different crystal structures, deformation of a lamella welded on a substrate and lamellar crystals. It is shown that the elastic state of coherently matched multilayers depends on two coupled field quantities: the stress (or equivalently the elastic strain) and the curvature. A general method is derived to determine these fields and the contribution of curvature on stress relaxation is emphasized. Detailed applications are given for the case of stress-free dilatation and pure shear.     

Investigation of interface properties by nanoscale elastic modulus mapping

We present a method for investigating the spatial changes of elastic moduli in a nm-scale vicinity of interfaces. The method is demonstrated on twin walls in PbTiO(3) single crystals. It is revealed that the region near the twin wall is significantly softer than the two domains surrounding it. A comparison with finite element simulations relates this effect to an anelastic relaxation due to point defect accumulation around the twin wall. Local softening around the twin wall can affect the overall elastic modulus in thin films and nanostructured ferroelectric materials, in which the average distance between twin walls is smaller than the thickness of the softer region.     

Structural-acoustic modeling for three-dimensional freefield and littoral environments with verification and validation

This paper describes a high-order, finite-element-based, three-dimensional time-harmonic model for large-scale exterior structural-acoustics problems. It is applicable to both freefield and littoral environments. For the freefield case, the infinite exterior is treated as a homogeneous linear acoustic medium. For littoral applications, the water or air and the sediment domains are each treated as linear homogeneous, semi-infinite half-spaces with piecewise-constant properties. Both domains admit complex-valued wave speeds to enable the inclusion of damping. The finite element formulation uses a variational statement which naturally incorporates the transmission-condition at the water or air-sediment interface. The truncation of the infinite exterior is realized using an infinite-element for the freefield case, and the perfectly-matched-layer approximation for littoral applications. Computation of the farfield quantities is done based on an integral representation which, for the littoral cases, uses efficient approximations for the appropriate Green's function. Numerical computations are presented for a series of progressively more complex problems, and are used to verify the model against analytic and other numerical solutions and validate it based on the experimental data for scattering from elastic scatterers as measured in freefield and sediment pool laboratory facilities.     

Simultaneous measurement of atmospheric temperature,humidity, and aerosol extinction and backscatter coefficients by a combined vibrational–pure-rotational Raman lidar

Implementation of the pure-rotational Raman (PRR) lidar method for simultaneous measurement of atmospheric temperature, humidity, and aerosol extinction and backscatter coefficients is reported. The isolation of two wavelength domains of the PRR spectrum and the suppression of the elastically scattered light is carried out by a double-grating polychromator. Experiments involving elastic backscatter from dense clouds and a solid target confirm the high level of suppression of the elastic light in the corresponding acquisition channels of the two selected PRR domains. Calibration of the temperature channel was done both by comparison with an experimentally verified atmospheric temperature model profile and by inter-comparison with radiosondes. Night-time temperature profiles with high vertical resolution were obtained up to the lower stratosphere. The PRR temperature profile combined with the water vapor mixing ratio obtained from the ro-vibrational Raman channel is used to estimate the relative humidity. PACS 42.68.Wt; 42.68.Mj; 33.20.Fb     

Constantes élastiques des phases cristallographiques ordonnées et désordonnées de PtCo

The elastic constants of the PtCo (1:1) alloy in the ordered and disordered states have been measured between 298 and 4.2 K by the superposition method. The Debye temperatures have been deduced. The influence of the magnetic domains on the absolute values of the elastic constants has been also studied. The room temperature values of the magnetoelastic constants of the disordered phase have been determined from the elastic constants and the magnetostriction coefficients.     

Computer simulations of the Stranski-Krastanov growth of heteroepitaxial films with elastic anisotropy

A three-dimensional finite element method is developed to simulate the surface morphological evolution during the Stranski-Krastanov heteroepitaxial growth. In the formulation, the surface evolves through surface diffusion driven by the gradient of the surface chemical potential, which includes the elastic strain energy, elastic anisotropy and surface energy. Surface condensation rate is assumed to depend on the difference between the surface chemical potential and the chemical potential of the vapor phase. Our simulations reveal that the self-assembly of quantum dots are strongly dependent on the variation of growth rate and elastic anisotropy strength. With appropriate choice of growth rate and elastic anisotropy strength, a relatively more uniform and regular quantum dot array can be obtained.     

Diffraction of sound pulses on an elastic spherical shell submerged in an oceanic waveguide

The paper is devoted to simulating an acoustic field scattered by an elastic spherical shell placed in a waveguide with a fluid attenuating bottom. The emitted signal is a wideband pulse with a Gaussian envelope. The normal wave method is used in the frequency domain for calculating the field of a point source in a free waveguide and the shell scattering coefficients. Movement of the receiver along a vertical straight line located behind the shell makes it possible to obtain a “three-dimensional” image of the field scattered by the shell. In this representation, the horizontal axis is time; the vertical axis is the submersion depth of the receiver; the intensity shows the amplitude of the received signal. Such three-dimensional structures make it possible to analyze the dependence of the complex diffraction structure of the acoustic field on receiver depth. In the considered numerical example, a thin, elastic, spherical shell is located near the attenuating fluid bottom.     

Nonlocal three-dimensional theory of elasticity with application to free vibration of functionally graded nanoplates on elastic foundations

In the present work, a three-dimensional (3D) elastic plate model capturing the small scale effects is developed for the free vibration of functionally graded (FG) nanoplates resting on elastic foundations. The theoretical model is formulated employing the nonlocal differential constitutive relations of Eringen in conjunction with the 3D equations of motion of elasticity.The material properties are assumed to vary continuously along the thickness of the nanoplate in accordance with the power law formulation. Through extending the generalized differential quadrature (GDQ) method to the three-dimensional case, the governing equations are simultaneously discretized in every three coordinate directions and are then recast to the standard form of an eigen value problem. Solving the acquired problem, the natural frequencies of the nanoplates with different boundary conditions are calculated. The convergence behavior of the numerical results is checked out and comparison studies are conducted to make sure of the accuracy and reliability of the present model. Finally, the dependence of the vibration behavior of the nanoplate on edge conditions, elastic coefficients of the foundation, scale coefficient, mode number, material and geometric parameters are discussed.     

Influence of domain boundary width on the statics of 90° domains in epitaxial ferroelectric thin films

The influence of the domain boundary width on the statics of single 90° elastic domains (twins) in epitaxial ferroelectric tetragonal films grown on a cubic substrate is theoretically investigated. The inhomogeneous internal stresses arising in polydomain epitaxial systems are calculated by the effective dislocation method. The elastic energy stored in the heterostructure is determined. The equilibrium domain size is found and the stability diagram for single domains at different wall widths is constructed by minimizing the total internal energy of the system. It is demonstrated that, as the domain boundary width 2w increases, the stability region of 90° domains increases and qualitatively changes for ultrathin films when the parameter 2w exceeds the specific critical value 2w _cr. The equilibrium width 2w* of domain walls in thin films is predicted to be larger compared to the width 2w ₀ of domain boundaries in a macroscopic crystal.     

A meshless Galerkin method with moving least square approximations for infinite elastic solids

Combining moving least square approximations and boundary integral equations, a meshless Galerkin method, which is the Galerkin boundary node method （GBNM）, for twoand three-dimensional infinite elastic solid mechanics problems with traction boundary conditions is discussed. In this numerical method, the resulting formulation inherits the symmetry and positive definiteness of variational problems, and boundary conditions can be applied directly and easily. A rigorous error analysis and convergence study for both displacement and stress is presented in Sobolev spaces. The capability of this method is illustrated and assessed by some numerical examples.     

A composite grid solver for conjugate heat transfer in fluid–structure systems

We describe a numerical method for modeling temperature-dependent fluid flow coupled to heat transfer in solids. This approach to conjugate heat transfer can be used to compute transient and steady state solutions to a wide range of fluid–solid systems in complex two- and three-dimensional geometry. Fluids are modeled with the temperature-dependent incompressible Navier–Stokes equations using the Boussinesq approximation. Solids with heat transfer are modeled with the heat equation. Appropriate interface equations are applied to couple the solutions across different domains. The computational region is divided into a number of sub-domains corresponding to fluid domains and solid domains. There may be multiple fluid domains and multiple solid domains. Each fluid or solid sub-domain is discretized with an overlapping grid. The entire region is associated with a composite grid which is the union of the overlapping grids for the sub-domains. A different physics solver (fluid solver or solid solver) is associated with each sub-domain. A higher-level multi-domain solver manages the entire solution process.     

水下目标弹性声散射信号分离

水下目标弹性声散射与其他声散射成分在时域和频域上均存在混叠, 现有信号处理方法受分辨力限制无法在混叠状态下识别目标弹性声散射特征. 针对这个问题, 提出了一种目标弹性声散射信号分离方法. 以目标回波亮点模型为基础, 分析了线性调频信号入射时目标声散射成分的信号特性, 提出了一种目标声散射成分向单频信号的映射方法, 并理论推导出了目标声散射结构与映射结果之间的线性对应关系, 实现了通过窄带滤波分离出目标弹性声散射成分. 仿真与消声水池实验数据处理结果表明, 该方法基本可以完全分离出目标回波信号中的弹性声散射成分, 分离出的弹性声散射具有与理论一致的信号特征, 验证了该分离方法的有效性.