3-dimensional transient wave response in a cracked elastic solid

The three-dimensional transient wave response problem is presented for an infinite elastic medium weakened by a plane crack of infinite length and finite width. Tractions are applied suddenly to the crack, which simulates the case of impact loading. The integral transforms are utilized to reduce the problem to a standard Fredholm integral equation in the Laplace transform variable and sequentially invert the Laplace transforms of the stress components by numerical inversion method. The dynamic mode I stress intensity factors at the crack tip are obtained and some numerical results are presented in graphical form.

Dynamic behavior of a cylindrical crack in a functionally graded interlayer under torsional loading

In this paper the problem of a cylindrical crack located in a functionally graded material (FGM) interlayer between two coaxial elastic dissimilar homogeneous cylinders and subjected to a torsional impact loading is considered. The shear modulus and the mass density of the FGM interlayer are assumed to vary continuously between those of the two coaxial cylinders. This mixed boundary value problem is first reduced to a singular integral equation with a Cauchy type kernel in the Laplace domain by applying Laplace and Fourier integral transforms. The singular integral equation is then solved numerically and the dynamic stress intensity factor (DSIF) is also obtained by a numerical Laplace inversion technique. The DSIF is found to rise rapidly to a peak and then reduce and tend to the static value almost without oscillation. The influences of the crack location, the FGM interlayer thickness and the relative magnitudes of the adjoining material properties are examined. It is found among others that, by increasing the FGM gradient, the DSIF can be greatly reduced.

Torsional impact response of a penny-shaped interface crack in bonded materials with a graded material interlayer

In this paper, the dynamic response of a penny-shaped interface crack in bonded dissimilar homogeneous half-spaces is studied. It is assumed that the two materials are bonded together with such a inhomogeneous interlayer that makes the elastic modulus in the direction perpendicular to the crack surface is continuous throughout the space. The crack surfaces art assumed to be subjected to torsional impact loading. Laplace and Hankel integral transforms are applied combining with a dislocation density,function to reduce the mixed boundary value problem into a singular integral equation with a generalized Cauchy kernel in Laplace domain. By solving the singular integral equation numerically, and using a numerical Laplace inversion technique, the dynamic stress intensity factors art obtained. The influences of material properties and interlayer thickness on the dynamic stress intensity factor are investigated.

关于Young-Laplace公式的吉布斯自由能证明

对于为论证球形液滴附加压强的Young-Laplace公式而设计的一个理想实验,有文献试图借助吉布斯自由能函数进行证明,本文给出符合这一条件的证明方法.

Extended fractional Fourier transforms

The concept of an extended fractional Fourier transform (FRT) is suggested. Previous PBT's and complex FRT's are only its subclasses. Then, through this concept and its method, we explain the physical meaning of any optical Fresnel diffraction through a lens: It is just an extended FRT; a lens-cascaded system can equivalently be simplified to a simple analyzer of the FRT; the two-independent-parameter FRT of an object illuminated with a plane wave can be readily implemented by a lens of arbitrary focal length; when cascading, the Function of each lens unit and the relationship between the adjacent ones are clear and simple; and more parameters and fewer restrictions on cascading make the optical design easy. (C) 1997 Optical Society of America.

黏弹性体界面裂纹的冲击响应

研究两半无限大黏弹性体界面Griffith裂纹在反平面剪切突加载荷下，裂纹尖端动应力强度因子的时间响应。首先，运用积分变换方法将黏弹性混合边值问题化成变换域上的对偶积分方程。通过引入裂纹位错密度函数进一步化成Cauchy型奇异积分方程。运用分片连续函数法数值求解奇异积分方程，得到变换域内的动应力强度因子。再用Laplace积分变换数值反演方法，将变换域的解反演到时间域内，最终求得动应力强度因子的时间响应，并对黏弹性参数的影响进行了分析。

粘弹性力学的对应原理及其数值反演方法

结合国内外的研究成果，就粘弹性力学中存在的各种对应原理及数值反演方法进行了归类和总结。结合在求解粘弹性边值问题中的应用，对各类方法的特点进行了评述，并指出存在的问题及发展新的数值方法的研究重点。

The effect of nucleation time on the growth of a microvoid in a viscoelastic material

In this paper, discussions are focused on the growth of a nucleated void in a viscoelastic material. The in situ tensile tests of specimens made of high-density polyethylene, filled with spherical glass beads (HDPE/GB) are carried out under SEM. The experimental result indicates that the microvoid nucleation is induced by the partially interfacial debonding of particles. By means of the Laplace transform and the Eshelby's equivalent inclusion method, a new analytical expression of the void strain at different nucleation times is derived. It can be seen that the strain of the nucleated void depends not only on the remote strain history, but also on the nucleation time. This expression is also illustrated by numerical examples, and is found to be of great usefulness in the study of damage evolution in viscoelastic materials.

Diffusive Wave Solutions for Open Channel Flows with Uniform and Concentrated Lateral Inflow

The diffusive wave equation with inhomogeneous terms representing hydraulics with uniform or concentrated lateral inflow intoa river is theoretically investigated in the current paper. All the solutions have been systematically expressed in a unified form interms of response function or so called K-function. The integration of K-function obtained by using Laplace transform becomesS-function, which is examined in detail to improve the understanding of flood routing characters. The backwater effects usuallyresulting in the discharge reductions and water surface elevations upstream due to both the downstream boundary and lateral infloware analyzed. With a pulse discharge in upstream boundary inflow, downstream boundary outflow and lateral inflow respectively,hydrographs of a channel are routed by using the S-functions. Moreover, the comparisons of hydrographs in infinite, semi-infiniteand finite channels are pursued to exhibit the different backwater effects due to a concentrated lateral inflow for various channeltypes.

Torsional impact of transversely isotropic solid with functionally graded shear moduli and a penny-shaped crack

The torsional impact response of a penny-shaped crack in an unbounded transversely isotropic solid is considered. The shear moduli are assumed to be functionally graded such that the mathematics is tractable. Laplace transform and Hankel transform are used to reduce the problem to solving a Fredholm integral equation. The crack tip stress fields are obtained. Investigated are the influence of material nonhomogeneity and orthotropy on the dynamic stress intensity factor. The peak value of the dynamic stress intensity factor can be suppressed by increasing the shear moduli's gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface.

Dynamic stress intensity factor of a functionally graded material under antiplane shear loading

The dynamic response of a finite crack in an unbounded Functionally Graded Material (FGM) subjected to an antiplane shear loading is studied in this paper. The variation of the shear modulus of the functionally graded material is modeled by a quadratic increase along the direction perpendicular to the crack surface. The dynamic stress intensity factor is extracted from the asymptotic expansion of the stresses around the crack tip in the Laplace transform plane and obtained in the time domain by a numerical Laplace inversion technique. The influence of graded material property on the dynamic intensity factor is investigated. It is observed that the magnitude of dynamic stress intensity factor for a finite crack in such a functionally graded material is less than in the homogeneous material with a property identical to that of the FGM crack plane.

功能梯度材料裂纹尖端动态应力场

研究受反平面剪切作用的功能梯度材料动态裂纹问题,通过积分变换-对偶积分方程方法推出了裂纹尖端动态应力场。时间域内的动态应力强度因子由Laplace数值反演获得。研究结果表明功能梯度材料的梯度越大,相应的裂纹问题的动态应力强度因子值越低。

Molecular Dynamics Study Of The Mechanical Behavior Of Nickel Nanowire: Strain Rate Effects

We present the analysis of uniaxial deformation of nickel nanowires using molecular dynamics simulations, and address the strain rate effects on mechanical responses and deformation behavior. The applied strain rate is ranging from 1 x 10(8) s(-1) to 1.4 x 10(11) s(-1). The results show that two critical strain rates, i.e., 5 x 10(9) s(-1) and 8 x 10(10) s(-1), are observed to play a pivotal role in switching between plastic deformation modes. At strain rate below 5 x 10(9) s(-1), Ni nanowire maintains its crystalline structure with neck occurring at the end of loading, and the plastic deformation is characterized by {111} slippages associated with Shockley partial dislocations and rearrangements of atoms close to necking region. At strain rate above 8x10(10) s(-1), Ni nanowire transforms from a fcc crystal into a completely amorphous state once beyond the yield point, and hereafter it deforms uniformly without obvious necking until the end of simulation. For strain rate between 5 x 10(9) s(-1) and 8 x 10(10) s(-1), only part of the nanowire exhibits amorphous state after yielding while the other part remains crystalline state. Both the {111} slippages in ordered region and homogenous deformation in amorphous region contribute to the plastic deformation. (C) 2007 Published by Elsevier B.V.

Stress intensity factor histories of a steadily propagating crack under 3-D combined mode traction

Elastodynamic stress intensity factor histories of an unbounded solid containing a semi-infinite plane crack that propagates at a constant velocity under 3-D time-independent combined mode loading are considered. The fundamental solution, which is the response of point loading, is obtained. Then, stress intensity factor histories of a general loading system are written out in terms of superposition integrals. The methods used here are the Laplace transform methods in conjunction with the Wiener-Hopf technique.