Wave speeds, shear bands and the second-order work for incrementally nonlinear constitutive models

The paper discusses the consequences of the incremental nonlinearity of a constitutive model of a solid for the analyses of characteristic wave speeds, acceleration waves, the second-order work criterion and shear band formation. Incremental nonlinearity may entail qualitative changes in the results as compared to incrementally linear models. Certain well-known correlations cannot be established if the constitutive equation is assumed to be incrementally nonlinear. In particular, the spectra of the characteristic wave speeds and the acceleration wave speeds become continuous and are described by different equations. The second-order work criterion as a sufficient condition of uniqueness of the incremental boundary value problem loses its applicability in bifurcation analyses, unless the applicability can be proved for a particular type of nonlinearity. The singularity of the acoustic tensor in the general nonlinear case correlates neither with the vanishing of the second-order work nor with the shear band formation.     

Three-dimensional crack problem analysis using boundary element method with finite-part integrals

A set of hypersingular integral equations of a three-dimensional finite elastic solid with an embedded planar crack subjected to arbitrary loads is derived. Then a new numerical method for these equations is proposed by using the boundary element method combined with the finite-part integral method. According to the analytical theory of the hypersingular integral equations of planar crack problems, the square root models of the displacement discontinuities in elements near the crack front are applied, and thus the stress intensity factors can be directly calculated from these. Finally, the stress intensity factor solutions to several typical planar crack problems in a finite body are evaluated. This revised version was published online in August 2006 with corrections to the Cover Date.     

Modified fundamental solutions for the scattering of elastic waves by a cavity: Numerical results

The boundary integral equation method is very often used to solve exterior problems of scattering of waves (elastic waves, acoustic waves, water waves and electromagnetic waves). It is known, however, that this method fails to provide a unique solution at the so-called irregular frequencies. This difficulty is inherent to the method used rather than the nature of the problem. In the context of elastodynamics. we proposed, in a recent work¹, two methods for eliminating these irregular frequencies. Both are based on modifying the fundamental solution. Here we present numerical results pertaining to the solutions of the modified and unmodified integral equations.     

ENERGY DISTRIBUTION AND ASSOCIATED FRACTURE PHENOMENA WHEN EXPLOSIVELY LOADING PARABOLOIDAL-ENDED PERSPEX RODS EMBEDDED IN LEAD AND AIR

Abstract— Fracture damage development in paraboloidal-ended cylindrical rods of Perspex due to stress waves initiated by explosive point loading at the flat end of a rod with a detonator, embedded in surrounding media of solid lead or atmospheric air is discussed. An attempt has been made to explain the form and the location of the terminal internal fractures and the spalls in terms of stress optics considering first and second reflections of the incident waves at the interfacial boundary and the energy distribution of the incident waves when reflected from a boundary or refracted into the surrounding medium.     

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...     

Formulation and validation of Berenger's PML absorbing boundary forthe FDTD simulation of acoustic scattering

Berenger's perfectly matched layer (PML) absorbing boundary condition for electromagnetic (EM) waves is derived to absorb 2-D and 3-D acoustic waves in finite difference time domain (FDTD) simulation of acoustic wave propagation and scattering. A PML medium suitable for acoustic waves is constructed. Plane wave propagation in the PML medium is solved for both 2-D and 3-D cases and explicit FDTD boundary conditions are derived. The equations show that a matched PML medium is a perfect simulation of free space in that a plane wave does not change its direction of propagation or its speed when it propagates from free space into a matched PML medium. FDTD simulation of a pulsed point source propagating in two dimensions is carried out to test the performance of the PML boundary for acoustic waves. Results show that an eight layer PML boundary condition reduces the reflected error 40 dB over Mur's second order boundary condition     

A time domain approach to SH waves on a piezoelectric layer

The propagation of transient shear horizontal waves in a piezoelectric layer with free boundaries is studied within a time domain approach. The layer is modeled as a dissipative electroelastic continuum via linear constitutive equations accounting for memory effects. A separation of space variables is employed to solve the problem for the Laplace transforms of the fields. The pertinent dispersion equations are derived in different cases where the boundary surfaces of the layer are matched with an external potential or are grounded. It is shown that transient wave solutions exist which are compatible with given time-dependent data at the surfaces. The wave amplitude decays along the layer according to the dissipative model and the potential field outside the layer, in the matched case, turns out to vanish as the reciprocal of the distance from the boundaries. Illustrative examples are given for a square pulse applied to the layer's surfaces.     

Wave Propagation in a Green–Naghdi Thermoelastic Solid with Diffusion

The Green and Naghdi theory of thermoelasticity is applied to study plane-wave propagation in an elastic solid with thermo-diffusion. The governing equations of an elastic solid with generalized thermo-diffusion are solved to show the existence of three coupled longitudinal waves and a shear vertical (SV) wave in a two-dimensional model of the solid with thermo-diffusion. The reflection of plane waves from a thermally insulated stress-free surface of an elastic solid with thermo-diffusion is also studied. A non-homogeneous system of four equations in reflection coefficients is obtained. The speeds of the plane waves are computed numerically and plotted against frequency for a particular range. The complex absolute values of the reflection coefficients of all reflected waves are computed numerically and plotted against the angle of incidence of the striking wave at the free surface. The effects of diffusion parameters are shown graphically for speeds and reflection coefficients of plane waves.     

Disturbance due to Thermal and Mass Loads in Generalized Elasto-thermodiffusive Solids

The one-dimensional problem of a generalized elasto-thermodiffusive solid half-space, whose surface is maintained traction free but subjected to the action of thermal or mass concentration loads, has been investigated. The model, composed of basic governing equations and boundary conditions, has been solved by using the Laplace transform technique. As we know that the ‘second sound’ effects are short lived, thus, short-time approximations of solutions for dilatation, chemical potential, and stress functions have been obtained. The short-time solutions for each considered function consist of three waves, namely, elasto-diffusive, mass-diffusive, and thermo-diffusive waves traveling with distinct speeds. The discontinuities at the wave fronts of various considered physical quantities have also been discussed. To obtain the dilatation, chemical potential, and stress in the physical domain due to instantaneous, continuous, and periodic loads, the transformed solutions of these functions have been inverted by employing a numerical technique. Finally, the dilatation, chemical potential, and stress functions have been computed numerically for copper and brass materials. The computer-simulated results so obtained have been presented graphically to illustrate the analytical developments.     

Shock front analysis for axial shear wave propagation in a hyperelastic incompressible solid

Summary A wavefront analysis is employed to study the propagation of axial shear waves in an incompressible hyperelastic solid, whose strain energy function is expressible as a truncated power series in terms of the basic invariants of the left Cauchy-Green tensor. Waves are generated by the application of an axial shear stress at the surface of a cylindrical cavity in an unbounded medium. Depending on the nature of the boundary condition, an acceleration front or a shock front propagates from the boundary of the cavity. For an acceleration front, the coefficients in the wavefront expansion satisfy a sequence of transport equations which can be solved analytically. For a shock front, a wavefront analysis gives approximate formulas for the wave speed, shock front and intensity of the various field variables at the front. As well, our shock front analysis is used to devise a method of estimating the breaking distance of a shock front. In order to test the validity of the results of our wavefront analysis, numerical solutions are obtained for waves initiated by a step function or by a finite duration pulse at the boundary. Our numerical solutions are found by using a recently proposed relaxation scheme for systems of conservation laws.     

A coupled ES-FEM/BEM method for fluid–structure interaction problems

The edge-based smoothed finite element method (ES-FEM) developed recently shows some excellent features in solving solid mechanics problems using triangular mesh. In this paper, a coupled ES-FEM/BEM method is proposed to analyze acoustic fluid–structure interaction problems, where the ES-FEM is used to model the structure, while the acoustic fluid is represented by boundary element method (BEM). Three-node triangular elements are used to discretize the structural and acoustic fluid domains for the important adaptability to complicated geometries. The smoothed Galerkin weak form is adopted to formulate the discretized equations for the structure, and the gradient smoothing operation is applied over the edge-based smoothing domains. The global equations of acoustic fluid–structure interaction problems are then established by coupling the ES-FEM for the structure and the BEM for the fluid. The gradient smoothing technique applied in the structural domain can provide the important and right amount of softening effects to the “overly-stiff” FEM model and thus improve the accuracy of the solutions of coupled system. Numerical examples of acoustic fluid–structure interaction problems have been used to assess the present formulation, and the results show that the accuracy of present method is very good and even higher than those obtained using the coupled FEM/BEM with quadrilateral mesh.     

光弹法研究固体圆柱横截面上的脉冲声场

为了研究超声脉冲波在钢、铁、铝等金属棒内的传播规律。检验已有的声学理论,采用和金属声速接近的光学玻璃为样品,当超声垂直于样品侧壁入射时,利用研制的动态光弹成像系统研究了玻璃园棒内超声脉冲纵波、横波、瑞利波声场的传播特性。自动记录了0—99．9μs时间内各种超声波声场在玻璃园棒横截面上的传播图像（时间间隔0．1μs）,由此来模拟超声脉冲波在金属棒横截面中的传播行为。     

风浪谱模型在高度计风速反演中的应用

依据粗糙海面电磁波镜面散射理论,将根据全波数范围内的风浪谱模型计算的标准化雷达后向散射截面与T/P卫星高度计测得的雷达后向散射截面(Ku波段)进行比较,实现了对高度计风速的反演.研究表明,在所选浮标附近海域,波龄因子对高度计风速反演存在较大影响.与目前高度计业务化算法相比,考虑波龄因子影响后,根据谱模型反演获得的风速与中国近海浮标风速之间均方根误差和平均偏差更小.由于波龄因子可以根据高度计测得有效波高以及业务化算法获得的风速得到,因此根据风浪谱模型反演获得的风速具有广泛的适用性.     

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.     

Thermoelastic wave propagation in a random medium and some related problems

The mean waves in a medium with random inhomogeneities are studied within the theory of linear thermoelasticity. Under the assumption of small random fluctuations approximate integro-differential equations governing the mean displacement and temperature fields are derived. For the elastic case the material behaves effectively as a viscoelastic body with memory. The dispersion equation is obtained for the thermoelastic case. This equation is analyzed for some special cases. The random effects introduce attenuation and change of phase speeds for the compressional and shear waves. For weak thermoelastic coupling, the shear wave is not affected by the random thermal properties. Explicit results are obtained for general and special cases. In general the mean fields are coupled in a complicated way. Therefore an uncoupled theory is presented. Then the problems with random boundary conditions or a randomly varying boundary are discussed. Different perturbation methods are given. Two examples are provided respectively by the heat conduction across a rough surface and the hydrodynamic theory of lubrication under a random loading.     

Numerical method of crack analysis in 2D finite magnetoelectroelastic media

The present paper extends the hybrid extended displacement discontinuity fundamental solution method (HEDD-FSM) (Eng Anal Bound Elem 33:592–600, 2009) to analysis of cracks in 2D finite magnetoelectroelastic media. The solution of the crack is expressed approximately by a linear combination of fundamental solutions of the governing equations, which includes the extended point force fundamental solutions with sources placed at chosen points outside the domain of the problem under consideration, and the extended Crouch fundamental solutions with extended displacement discontinuities placed on the crack. The coefficients of the fundamental solutions are determined by letting the approximated solution satisfy the prescribed boundary conditions on the boundary of the domain and on the crack face. The Crouch fundamental solution for a parabolic element at the crack tip is derived to model the square root variations of near tip fields. The extended stress intensity factors are calculated under different electric and magnetic boundary conditions.     

Non-reflecting boundary conditions for plane waves in anisotropic elasticity and poroelasticity

The paper presents exact non-reflecting boundary conditions for transient plane waves in an anisotropic elastic solid for oblique incidence. The boundary conditions are expressed through the eigenvectors of the acoustic tensor and are written in impedance form as a relation between the velocity vector and the traction vector. The approach is extended to anisotropic fluid-saturated porous solids. Exact plane-wave non-reflecting boundary conditions are derived for transient non-dissipative waves in a medium with infinite or zero permeability, and for steady-state dissipative waves.     

Mass sensitivity of thin rod acoustic wave sensors

Theoretical and experimental investigations of mass sensitivities of thin rod acoustic wave sensor are presented. From the low-frequency approximation of the dispersion equations, explicit forms of the relation describing the mass sensitivity are derived with the consideration of the effects due to elasticity and inertia of the loading layer. The three lowest thin rod acoustic modes are presented. Mass sensing experiments are based on the electrodeposition of loading material on a thin metallic fiber (the thin rod). Copper has been used to load the propagation of acoustic waves in gold fibers. The mass of copper deposited and the phase shift of the acoustical thin rod delay line were monitored simultaneously by a computer. Mass response curves showing the variation in phase due to the mass deposited per unit surface area were then obtained in order to determine the mass sensitivity. Both flexural and extensional wave modes have been excited. Theoretical and experimental results were found to be consistent in both sign and magnitude     

Measurement of material anisotropy by dual-probe laser interferometer

A novel dual-probe laser interferometer, which has the advantage that it measures the surface displacements of the same surface wave at two locations, has been used to measure the speeds of surface waves and pseudo-surface waves on a silicon single crystal. Two configurations have been investigated. When the distance between the two points of detection is large relative to the length of the acoustic wave, the two signals detected by the probes are separated in the time domain. Hence the signal travel time can be found by the autocorrelation method. When the distance between the two points of detection is short relative to the acoustic wave, a composite signal is obtained consisting of two overlapping signals. Then the power cepstrum method is employed to extract the signal travel time between the probe points. The speeds for both types of surface waves are shown as functions of direction relative to the [001] crystal axis. The results have been compared with theoretical calculations and line-focus acoustic microscopy measurements.