Influence of heterogeneities on crack propagation

The influence of material heterogeneities is studied in the context of dynamic failure. We consider a pre-strained plate problem, the homogeneous case of which has been widely studied both experimentally and numerically. This setup is used to isolate the effects of the elastic field resulting from pre-straining and stress wave interactions throughout the crack propagation by adding stiffer and denser regions in the plate. While the crack tip is pushed away by stiffer inclusions, it is attracted to the denser ones. With the presence of denser media, only a portion of the total elastic energy in the system is effectively used to drive crack propagation, leading to a drop in the velocity of its tip in comparison to the homogeneous case. Crack branching is then observed at velocities much lower than the limiting velocity of the material, questioning the validity of crack velocity to be a criterion for crack branching. Instead, we introduce an effective stored energy to analyze the crack velocity and the emergence of crack branching instabilities.     

Computer simulation of forward wave propagation in soft tissue

A method for simulating forward wavefront propagation in heterogeneous tissue is discussed. The intended application of this method is for the study of aberration produced when performing ultrasound imaging through a layer of soft tissue. A one-way wave equation that permits smooth variation in all acoustically important variables is derived. This equation also describes tissue exhibiting nonlinear elasticity and arbitrary frequency-dependent relaxation. A numerical solution to this equation is found by means of operator splitting and propagation along the spatial depth coordinate. The numerical solution is accurate when compared to analytical solutions for special cases, and when compared to numerical solutions of the full wave equation by other methods. The presented implementation provides a fast numerical method for studying the impact of aberration in medical ultrasound imaging through soft tissue--both on the transmitted beam and the nonlinearly generated harmonic beam.     

A k-space method for large-scale models of wave propagation in tissue

Large-scale simulation of ultrasonic pulse propagation in inhomogeneous tissue is important for the study of ultrasound-tissue interaction as well as for development of new imaging methods. Typical scales of interest span hundreds of wavelengths. This paper presents a simplified derivation of the k-space method for a medium of variable sound speed and density; the derivation clearly shows the relationship of this k-space method to both past k-space methods and pseudospectral methods. In the present method, the spatial differential equations are solved by a simple Fourier transform method, and temporal iteration is performed using a k-t space propagator. The temporal iteration procedure is shown to be exact for homogeneous media, unconditionally stable for “slow” (c(x)⩽c₀) media, and highly accurate for general weakly scattering media. The applicability of the k-space method to large-scale soft tissue modeling is shown by simulating two-dimensional propagation of an incident plane wave through several tissue-mimicking cylinders as well as a model chest wall cross section. A three-dimensional implementation of the k-space method is also employed for the example problem of propagation through a tissue-mimicking sphere. Numerical results indicate that the k-space method is accurate for large-scale soft tissue computations with much greater efficiency than that of an analogous leapfrog pseudospectral method or a 2-4 finite difference time-domain method. However, numerical results also indicate that the k-space method is less accurate than the finite-difference method for a high contrast scatterer with bone-like properties, although qualitative results can still be obtained by the k-space method with high efficiency. Possible extensions to the method, including representation of absorption effects, absorbing boundary conditions, elastic-wave propagation, and acoustic nonlinearity, are discussed     

Influence of material microvoids and heterogeneities on fatigue crack propagation

The evaluation of crack initiation, short-crack growth as well as crack path at microscopic scale is a crucial issue for the safety assessment of macroscopically fracture-free structural components. In the present paper, the crack propagation at the material microscale is modeled by taking into account the spatial variability of mechanical characteristics of the material as well as the local multiaxial stress field disturbance induced by inhomogeneities (inclusions or voids). By adopting some crack extension criteria under mixed mode, the short-crack path is determined. A microstructure dependence of the crack path arises in the short-crack regime, while the microstructure of the material does not influence the crack propagation for sufficiently long cracks. A mean weighted equivalent stress-intensity factor (SIF) is computed for kinked short cracks, where the range of such a SIF can be used as a key parameter dictating their fatigue crack growth rate.     

Energetic BEM–FEM coupling for wave propagation in 3D multidomains

Starting from a recently developed energetic space–time weak formulation of boundary integral equations for wave propagation problems, a coupling algorithm is presented, which allows a flexible use of FEMs and BEMs as local discretization techniques. Emphasis is given to theoretical and experimental analysis of the stability of the proposed method. Several numerical results on model problems are presented and discussed, showing that both bounded and unbounded three‐dimensional domains can be efficiently addressed. Copyright © 2013 John Wiley & Sons, Ltd.     

Cyclotron wave propagation in silver

Azbel'-Kaner cyclotron resonance in metals is accompanied by electromagnetic waves propagating in a direction perpendicular to the magnetic field. Taking into account the anisotropy of the silver Fermi surface, the dispersion relation for these waves is calculated in the limit where the wavelength is much smaller than the orbit diameter of the electrons. Thus it is shown that a number of previously observed oscillations in the surface impedance of a semiinfinite silver specimen arise from points of zero-group velocity on the dispersion relation. Physically, the oscillations reflect a matching of the electron-orbit diameter with an integer number of wavelengths. They may, therefore, be looked upon as geometric resonances in the surface impedance, complementary to the temporal cyclotron resonances. The surface impedance is calculated under the assumption of specular surface scattering. Satisfactory agreement with experiments is obtained by using an independent-particle model for the electron gas and band parameters based on APW calculations. The influence of the Fermi-surface geometry is demonstrated by comparing with calculations for a cylindrical and a spherical Fermi surface. The electric field in the metal is calculated for selected magnetic fields, and the expected result of a transmission experiment is presented. Finally, the absence of Fermi liquid effects in the experiments is briefly discussed.     

Non-symmetrical wave propagation in arteries

Summary For a better understanding of the effects of initial stress on flow in elastic tubes, the propagation of a harmonic and non-symmetrical wave in an initially stressed thick cylindrical shell filled with an inviscid fluid is studied. Although the blood is known to be a non-Newtonian fluid, for simplicity, it is assumed to be a non-viscous, while the elastic tube is considered to be isotropic and incompressible. Utilizing the theory of small deformations superimposed on large initial static deformation, for a non-symmetrical perturbed motion the governing differential equations are obtained in cylindrical polar coordinates. Due to variability of the coefficients of the resulting differential equations of the solid body, the field equations are solved by truncated power series method. Applying the boundary conditions, the dispersion relation is obtained as a function of inner pressure, axial stretch and the thickness ratio. It is observed that the wave speed of the non-symmetrical wave is large as compared to the axially symmetrical case. Various special cases are also discussed in the paper.     

The Kramers-Kronig relations method and wave propagation in porous elastic media

Waves of an arbitrary frequency in a porous elastic medium are investigated via the Kramers-Kronig relations method. It is shown that some of the widely accepted theories of wave propagation in random composites may violate the causality and/or linearity of the effective medium.Experimentally observed dynamic effects in random media, such as stop bands and complicated behavior of the dispersion curve, are shown to follow from the K-K relations.     

The ultrasonic wave propagation in composite material and its characteristic evaluation

The use of the ultrasonic wave technology was expected as one of important technologies in health monitoring of composite materials and/or structures. However, the propagation of ultrasonic wave becomes very complicated for polymer based composite materials due to reflection, transmission, dispersion and so on, which may occur on the interface of matrix and reinforcements. Therefore, in this paper, elastic wave motion equation was dispersed using the finite element analysis of the PZFlex code; then the propagation of ultrasonic wave in several model composite materials was simulated. Then, the influence of the fiber/matrix interface shape, fiber size and other fiber conditions on wave propagation behavior was clarified. Moreover, the complicated wave propagation resulting from reflection, transmission and refraction on the fiber/matrix interface was visualized and the influence of the fiber arrangements and fiber volume fraction on the ultrasonic wave behavior was investigated for both conditions with and/or without attenuation in matrix.     

Acoustic wave propagation in Laves-phase compounds

We have studied the acoustic wave propagation in the hexagonal structured materials TiCr₂, ZrCr₂ and HfCr₂. In this paper, we have calculated the orientation dependence of three types of acoustic wave velocity and Debye average velocity using second order elastic constants. The six second order elastic constants are calculated for these materials at 300 K using Lenard-Jones Potential. An anomalous behaviour in orientation dependent acoustic wave velocity is obtained which is due to the combined effect of elastic constants and density. These velocity data are important for their structural information and to differentiate them from third group nitrides.     

Aberration in nonlinear acoustic wave propagation

Theory and simulations are presented indicating that imaging at the second-harmonic frequency does not solve the problem of ultrasonic wave aberration. The nonlinearity of acoustic wave propagation in biological tissue is routinely exploited in medical imaging because the improved contrast resolution leads to better image quality in many applications. The major sources of acoustic noise in ultrasound images are aberration and multiple reflections between the transducer and tissue structures (reverberations), both of which are the result of spatial variations in the acoustic properties of the tissue. These variations mainly occur close to the body surface, i.e., the body wall. As a result, the nonlinearly generated, second harmonic is believed to alleviate both reverberation and aberration because it is assumed that the second harmonic is mainly generated after the body wall. However, in the case of aberration, the second harmonic is generated by an aberrated source. Thus the second harmonic experiences considerable aberration at all depths, originating from this source. The results in this paper show that the second harmonic experiences similar aberration as its generating source, the first harmonic.     

Pulse propagation and windowed wave functions

Abstract

We apply quasi-distribution methods developed for quantum mechanics to the propagation of pulses in dispersive media with attenuation. We show that a Schrödinger type equation follows for propagation of the pulse for each mode. One then transforms the equation to obtain an equation of evolution in the phase space of position and wavenumber. In this paper we emphasize windowed wave functions and their corresponding phase space quasi-distributions. We obtain the time evolution equation, discuss possible approximations, and compare to the Wigner distribution approximation previously derived by Loughlin and Cohen by different methods.     

Computer-aided instruction in wave propagation phenomena

A `virtual laboratory' which uses computer simulation and visualisation techniques is proposed for the training of high school and college students in the study of wave propagation phenomena. Physical laboratory experiments are replaced by numerical experiments based on a mathematical model and its numerical simulation on a computer. Simple experiments that can be performed in a water tank with simple tools are simulated in the `virtual laboratory' using the wave equation as a mathematical model. As an example the interference between the waves generated by two time harmonic point sources is studied and Bragg's law observed. In the `virtual laboratory' students can design their own experiments and observe the results of the numerical simulations via animation techniques     

Ultrasonic wave propagation in temperature gradients

Ultrasonic methods are being developed for sensing and control of high temperature material processes such as welding and solidification. One of the problems in these methods is the distortion of the sound field caused by the change in material properties due to temperature gradients. This paper describes a ray-tracing method for calculating the effects of temperature on ultrasonic propagation in such systems. In the ray-tracing method, the material is conceptually divided into a number of plane layers. The refraction at each layer boundary is calculated from Snell's law using the sound speeds determined from the temperatures of the adjacent layers. The time required for an ultrasonic pulse to traverse each layer is also calculated, allowing the determination of the total time along a particular path. The method is applied to calculating the time of arrival of echoes from various interfaces around a molten weld pool.     

在含气孔粘弹媒质中非线性声传播特性

1引言: 共振型消声是实现水下吸声的一种基本形式.结构共振消声是通过在基底粘弹(通常为橡胶类粘弹材料)材料中嵌入声学结构--各种类型和大小的空腔,利用空腔的共振吸收增加损耗.本文运用等效媒质法,着重对含气孔粘弹材料的二阶非线性声场做了研究.     

狭缝空腔间粘弹性体中弹性波传播特性的研究

利用笛卡尔坐标下的Kelvin-Voigt线性粘弹性模型,研究了无限长粘弹性狭缝通道中波的传播和衰减。利用自适应绕数求根方法,针对具有狭缝形空腔周期性分布覆盖层的吸声问题,求得频散方程的根,并且得到无限长狭缝空腔中相速度频散曲线和衰减曲线。分析了各阶模式对无限长粘弹性狭缝结构中波传播的相速度和衰减的影响。通过引入复粘弹性模量,粘弹性波动方程具有弹性波动方程相对应的形式,计算中可用复值粘弹性模量代替相应的弹性模量。粘弹性狭缝结构中所有波传播模式均存在衰减,高阶波在某个频率以下衰减非常大,而在该频率以上逐渐减小;最低阶模式的相速度与材料无损耗的情况非常接近。粘弹性狭缝结构中波传播的衰减特性不仅与狭缝的结构参数有关,还与粘弹性材料本身的复弹性模量有关。     

Elastic wave and energy propagation in angled beams

This investigation comprises an experimental and numerical study of elastic wave propagation in angled beams. Axial impact by two strikers of different lengths was applied to three steel beams, each bent to incorporate a “V” section of different angle in the middle. Finite element simulation using ABAQUS was employed to examine details of the elastic waves generated in the impact tests. The numerical results correlated well with experimental data, and computational simulation was utilized to analyse the propagation of energy associated with the elastic waves. This demonstrated that after several reflections from and transmission across the bends energy is progressively smeared throughout the entire beam and does not concentrate at any particular segment; the bulk of the energy is conveyed via flexural waves. Numerical simulation of wave propagation in a beam with a single angle was also undertaken to study the energy associated with waves reflected from and transmitted across the bend, and how these are affected by the bend angle. The effects of input pulse duration, beam thickness and beam material properties on energy reflection and transmission at a bend are also discussed; this leads to the conclusion that when a longitudinal pulse of a particular frequency impinges on a bend, the ratio between its wavelength and the beam thickness governs the energy reflected from and transmitted across the bend. Moreover, the bend junction geometry (curvature) is found to have a significant influence on the energy reflected and transmitted, especially for obtuse bend angles.     

Light propagation in biological tissue

Biological tissue scatters light mainly in the forward direction where the scattering phase function has a narrow peak. This peak makes it difficult to solve the radiative transport equation. However, it is just for forward-peaked scattering that the Fokker-Planck equation provides a good approximation, and it is easier to solve than the transport equation. Furthermore, the modification of the Fokker-Planck equation by Leakeas and Larsen provides an even better approximation and is also easier to solve. We demonstrate the accuracy of these two approximations by solving the problem of reflection and transmission of a plane wave normally incident on a slab composed of a uniform scattering medium.