Rayleigh-type wave propagation on a transversely isotropic viscoelastic layer with yielding and rigid foundations

The present study investigates the propagation of Rayleigh-type wave in a transversely isotropic viscoelastic layer in effect of yielding foundation and rigid foundation in two different cases for two considered models. Numerical computation and graphical demonstration have been carried out for the case when layer is comprised of transversely isotropic viscoelastic Mesaverde clay shale material (Model I) and simply isotropic viscoelastic material (Model II). Closed-form expression of phase velocity and damped velocity for both the cases are deduced analytically. Obtained result is found in well agreement to the established standard results existing in the literature. Significant effect of dilatational viscoelasticity, volume viscoelasticity and yielding parameter on phase and damped velocities for both the considered models has been traced out. The comparative study has been performed to unravel the effect of viscoelasticity over elasticity and anisotropy over isotropy in the context of the present problem. Moreover, comparison of phase and damped velocities for the case of layer with stress-free foundation, layer with rigid foundation and layer with yielding foundation serve as a major highlight of the present work.     

Dynamic steady-state crack propagation in a transversely isotropic viscoelastic body

The problem considered herein is the dynamic, subsonic, steady-state propagation of a semi-infinite, generalized plane strain crack in an infinite, transversely isotropic, linear viscoelastic body. The corresponding boundary value problem is considered initially for a general anisotropic, linear viscoelastic body and reduced via transform methods to a matrix Riemann–Hilbert problem. The general problem does not readily yield explicit closed form solutions, so attention is addressed to the special case of a transversely isotropic viscoelastic body whose principal axis of material symmetry is parallel to the crack edge. For this special case, the out-of-plane shear (Mode III), in-plane shear (Mode II) and in-plane opening (Mode I) modes uncouple. Explicit expressions are then constructed for all three Stress Intensity Factors (SIF). The analysis is valid for quite general forms for the relevant viscoelastic relaxation functions subject only to the thermodynamic restriction that work done in closed cycles be non-negative. As a special case, an analytical solution of the Mode I problem for a general isotropic linear viscoelastic material is obtained without the usual assumption of a constant Poissons ratio or exponential decay of the bulk and shear relaxation functions. The Mode I SIF is then calculated for a generalized standard linear solid with unequal mean relaxation times in bulk and shear leading to a non-constant Poissons ratio. Numerical simulations are performed for both point loading on the crack faces and for a uniform traction applied to a compact portion of the crack faces. In both cases, it is observed that the SIF can vanish for crack speeds well below the glassy Rayleigh wave speed. This phenomenon is not seen for Mode I cracks in elastic material or for Mode III cracks in viscoelastic material.     

Three-dimensional fracture analysis in transversely isotropic solids

In this paper a boundary element formulation for three-dimensional crack problems in transversely isotropic bodies is presented. Quarter-point and singular quarter-point elements are implemented in a quadratic isoparametric element context. The point load fundamental solution for transversely isotropic media is implemented. Numerical solutions to several three-dimensional crack problems are obtained. The accuracy and robustness of the present approach for the analysis of fracture mechanics problems in transversely isotropic bodies are shown by comparison of some of the results obtained with existing analytical solutions. The approach is shown to be a simple and useful tool for the evaluation of stress intensity factors in transversely isotropic media.     

Bifurcation of cavitation solutions for incompressible transversely isotropic hyper-elastic materials

In this paper, the bifurcation problem of void formation and growth in a solid circular cylinder, composed of an incompressible, transversely isotropic hyper-elastic material, under a uniform radial tensile boundary dead load and an axial stretch is examined. At first, the deformation of the cylinder, containing an undetermined parameter-the void radius, is given by using the condition of incompressibility of the material. Then the exact analytic formulas to determine the critical load and the bifurcation values for the parameter are obtained by solving the differential equation for the deformation function. Thus, an analytic solution for bifurcation problems in incompressible anisotropic hyper-elastic materials is obtained. The solution depends on the degree of anisotropy of the material. It shows that the bifurcation may occur locally to the right or to the left, depending on the degree of anisotropy, and the condition for the bifurcation to the right or to the left is discussed. The stress distributions subsequent to the cavitation are given and the jumping and concentration of stresses are discussed. The stability of solutions is discussed through comparison of the associated potential energies. The bifurcation to the left is a `snap cavitation'. The growth of a pre-existing void in the cylinder is also observed. The results for a similar problem in three dimensions were obtained by Polignone and Horgan.     

BEM analysis of wave scattering in transversely isotropic solids

A boundary element approach for wave propagation problems in transversely isotropic solids is developed in this paper. The procedure is based on the well‐known formulation for time‐harmonic elasticity and a new version of a recently obtained fundamental solution for transversely isotropic media. The fundamental solution is transformed to obtain new expressions which can be efficiently evaluated at any point. This fact allows for a drastic reduction of the computation time and makes possible the implementation of a general purpose three‐dimensional quadratic element code. To show the simplicity and accuracy of the approach, the diffraction of waves by a spherical cavity and the interaction between two cavities in a boundless domain are studied. The computed results show a very good agreement with the analytical solution in the simple case where such solution exists. Other geometries can be studied without difficulty. Copyright © 1999 John Wiley & Sons, Ltd.     

Axisymmetric crack terminating at the interface of transversely isotropic dissimilar media

In this paper, the axisymmetric elasticity problem of an infinitely long transversely isotropic solid cylinder imbedded in a transversely isotropic medium is considered. The cylinder contains an annular or a penny shaped crack subjected to uniform pressure on its surfaces. It is assumed that the cylinder is perfectly bonded to the medium. A singular integral equation of the first kind (whose unknown is the derivative of crack surface displacement) is derived by using Fourier and Hankel transforms. By performing an asymptotic analysis of the Fredholm kernel, the generalized Cauchy kernel associated with the case of `crack terminating at the interface' is derived. The stress singularity associated with this case is obtained. The singular integral equation is solved numerically for sample cases. Stress intensity factors are given for various crack geometries (internal annular and penny-shaped cracks, annular cracks and penny-shaped cracks terminating at the interface) for sample material pairs.     

Smooth moving punch in an initially stressed transversely isotropic magnetoelastic medium due to shear wave

This study investigates the effect of a semi-infinite smooth moving punch due to shear wave propagation in initially stressed, magnetoelastic, transversely isotropic material. The Wiener–Hopf technique has been employed to determine the closed form expression of dynamic stress concentration due to punch with a load of constant intensity. The substantial effects of magnetoelastic coupling parameters, horizontal and vertical compressive/tensile initial stress, and anisotropy on dynamic stress concentrations has been remarkably traced out. Numerical computations and graphical illustrations, along with comparative study, have been executed for three distinct models: when the strip is comprised of Zinc, Beryl material having hexagonal symmetry, and simply isotropic material.     

横观各向同性饱和土中单桩竖向振动的简化模型求解

基于饱和多孔介质理论,将土体视为横观各向同性饱和两相介质,利用分离变量法求解了横观各向同性饱和土层的竖向振动,在此基础上建立横观各向同性饱和土中单桩竖向振动的控制方程,借助桩端边界条件和三角函数的正交性对桩竖向振动问题进行了求解,并分析了相关参数对竖向振动的影响。研究表明:桩-土系统存在共振现象,复刚度的变化受激振频率的影响较大;在高频和低频时,各向异性参数对动刚度的影响不同,各向异性参数越大,复刚度的峰值越小。     

A solution method for finding dynamic stress intensity factors for arbitrarily oriented cracks in transversely isotropic materials

The transient elastodynamic response of a transversely isotropic material containing a semi-infinite crack under uniform impact loading on the faces is examined. The crack lies in a principle plane of the material, but the crack front does not coincide with a principle direction. Rather, the crack front is at an angle to a principle direction and thus the problem becomes more three-dimensional in nature. Three loading modes are considered, i.e., opening, in-plane shear and anti-plane shear. The solutions for the stress intensity factor history around the crack tip are found. Laplace and Fourier transforms together with the Wiener-Hopf technique are employed to solve the equations of motion directly. The asymptotic expression of stress near the crack tip leads to a closed-form solution for the dynamic stress intensity factor for each loading mode. It is found that the stress intensity factors are proportional to the square root of time as expected. Results given here converge to known solutions in transversely isotropic materials with a crack oriented along a principle direction and isotropic materials as special cases. The results of this analysis are used to find approximate strain energy release rates for dynamically loaded penny shaped cracks.     

Effect of surface stress and irregularity of the interface on the propagation of SH-waves in the magneto-elastic crustal layer based on a solid semi space

The object of the present paper is to investigate plane SH waves through a magneto-elastic crustal layer based over an elastic, solid semi space under the influence of surface stress on the free surface of the crustal layer and irregularity of the interface. Two types of irregularities of the interface namely, rectangular and parabolic have been considered. Modulations of wave velocity due to the presence of surface stress, irregularity and the magnetic field have been studied separately. Their combined effect has also been investigated. Graphs are drawn to highlight some important peculiarities. It is observed that surface stress, irregularity and magnetic field have their respective role to play in the propagation of SH waves in the crustal layer. Further modulation of wave velocity occurs due to their combined effect.     

Boundary integral equation solution of three‐dimensional elastostatic problems in transversely isotropic solids using closed‐form displacement fundamental solutions

The boundary integral equation method is used for the solution of three‐dimensional elastostatic problems in transversely isotropic solids using closed‐form fundamental solutions. The previously published point force solutions for such solids were modified and are presented in a convenient form, especially suitable for use in the boundary integral equation method. The new presentations are used as a basis for accurate numerical computations of all Green's functions necessary in the BEM process without inaccuracy and redundant computations. The validity of the new presentation is shown through three numerical examples. Copyright © 2000 John Wiley & Sons, Ltd.     

Thermal effect on gravity waves in a compressible liquid layer over a solid half-space under initial hydrostatic stress

This paper deals with the effect of temperature on gravity waves in a compressible liquid layer over a solid half-space. It has been assumed that the liquid layer is under the action of gravity, while the solid half-space is under the influence of initial compressive hydrostatic stress. When the temperature of the half-space is altered, gravity waves propagate through the liquid layer along with sub-oceanic Rayleigh waves in the system. A new frequency equation has been derived here for gravity waves and sub-oceanic Rayleigh waves. It has been shown graphically that the phase velocity of gravity waves is influenced significantly by the initial compressive hydrostatic stress present in the solid half-space, for a particular value of the phase velocity of sub-oceanic Rayleigh waves and different coupling co-efficients of the temperature.     

带覆盖层半空间内SH波对浅埋圆孔及夹杂散射与地震动

采用大圆弧假定法将具有地表覆盖层的半空间直边界问题转化为曲面边界问题。借助Helmholtz定理预先给出问题波函数的一般形式解,再利用复变函数法及边界条件将问题化为求解波函数未知系数的无穷线性代数方程组,截断该方程组即可求解带地表覆盖层的半空间内浅埋圆孔及夹杂对SH波散射问题,并给出地面运动数值结果。定性分析入射波数、入射角度、埋深、夹杂刚度及覆盖层刚度等对地面运动影响。研究表明,浅埋圆孔及夹杂与地表覆盖层间存在强烈的相互作用,地震动会受较大影响。     

Effect of voids on the propagation of waves in an elastic layer

The present paper investigates the propagation of waves in an elastic layer containing voids. Numerical calculations and discussions indicate that the velocity of the propagation of waves decreases due to the presence of voids in the material medium of the layer and the voids cause dispersion of the general waveform.     

Effect of magnetic field and initial stress on the propagation of interface waves in transversely isotropic perfectly conducting media

Elasto-dynamical equations for transversely isotropic solids have been employed to investigate the general theory of transversely isotropic magneto-elastic interface waves in conducting media under initial hydrostatic tension or compression. Particular cases of interface waves such as Rayleigh, Love and Stoneley waves have been investigated in details. In all cases, the wave velocity equations have been deduced which are in complete agreement with the corresponding results of classical surface waves of the same types where magnetic fields and initial stresses are absent. Results obtained in this paper may be considered as more general and important in the sense that the corresponding results of classical surface waves due to Rayleigh, Love and Stoneley can readily be deduced from our results as special cases. Numerical calculations and graphs have been presented in the case of Love waves and conclusions are drawn.     

防护层对爆炸焊接质量的影响

为了研究防护层在炸药爆轰过程中对复板表面的保护作用,依据实验数据,分析了复板在焊接完成后的表面平整度、是否发生熔融现象以及金属结合界面的波状纹理的变化情况。防护层隔绝高温的炸药爆轰产物对复板侵蚀,同时在爆轰初始阶段对于应力波透过防护层作用在复板上的应力有明显的增强效应。最终确定在爆炸焊接过程中对复板厚度为0.2cm时,在其表面均匀覆盖一层0.05⁰.15cm的黄油可以较好地保护复板不受高温的爆轰产物侵蚀。实验过程中,选取不同种类炸药进行了对比实验,发现粉状硝铵炸药更加容易装药和控制爆轰速度,本实验选用硝铵炸药完成。     

防护层对爆炸焊接质量的影响

为了研究防护层在炸药爆轰过程中对复板表面的保护作用,依据实验数据,分析了复板在焊接完成后的表面平整度、是否发生熔融现象以及金属结合界面的波状纹理的变化情况。防护层隔绝高温的炸药爆轰产物对复板侵蚀,同时在爆轰初始阶段对于应力波透过防护层作用在复板上的应力有明显的增强效应。最终确定在爆炸焊接过程中对复板厚度为0.2cm时,在其表面均匀覆盖一层0.05~0.15cm的黄油可以较好地保护复板不受高温的爆轰产物侵蚀。实验过程中,选取不同种类炸药进行了对比实验,发现粉状硝铵炸药更加容易装药和控制爆轰速度,本实验选用硝铵炸药完成。     

Influence of principal material directions of thin orthotropic structures on Rayleigh-edge wave velocity

The paper is concerned with Rayleigh-edge wave propagation in thin panels made of two types of materials. The first one is a long-fiber-reinforced composite and second one is a cubic crystallic structure. The influence of principal material directions on Rayleigh-edge wave velocity is studied theoretically and experimentally. Theoretical solution is based on finite element approach. The propagation in the principal material directions is also investigated analytically. Experimental solution utilizes for non-contact measurements a laser vibrometer. The measurements are carried out on the composite panels. It has been found that Rayleigh wave velocity depends significantly on the directions of material axes. It has been also ascertain that the Rayleigh-edge wave propagation exhibits no geometric dispersion from point of view of the precision and frequency range of computational model.     

Solution of a three-dimensional problem of the elasticity theory in terms of displacements for an isotropic elastic layer

A new method is proposed for solving a three-dimensional problem of the elasticity theory for a layer in terms of displacements. It is much easier to satisfy the boundary conditions within the framework of this approach than with the known methods. An example brought to numerical results is considered. __________ Translated from Problemy Prochnosti, No. 3, pp. 38–46, May–June, 2008.     

Effect of interface layer on fatigue crack growth in an aluminium laminate

In order to study the effect of an interface layer on fatigue crack growth, a thin pure Al layer was sandwiched between two LY12 plates using explosive bonding. Experiment shows that as a fatigue crack approaches the interface a remote plastic zone appears in the soft Al layer. Energy dissipation in the interface leads to significant deceleration of crack growth rate. FEM analysis shows that crack arrest is associated with load and distance between the crack tip and the interface. The size of the plastic zone can be calculated and used to predict the reduction in crack growth rate. The predictions agree well with the experimental results.