Stress singularity analysis of anisotropic multi-material wedges under antiplane shear deformation using the symplectic approach

Symplectic approach has emerged a popular tool in dealing with elasticity problems especially for those with stress singularities. However, anisotropic material problem under polar coordinate system is still a bottleneck. This paper presents a subfield method coupled with the symplectic approach to study the anisotropic material under antiplane shear deformation. Anisotropic material around wedge tip is considered to be consisted of many subfields with constant material properties which can be handled by the symplectic approach individually. In this way, approximate solutions of the stress and displacement can be obtained. Numerical examples show that the present method is very accurate and efficient for such wedge problems. Besides, this paper has extended the application of the symplectic approach and provides a new idea for wedge problems of anisotropic material.

Determination of stress intensity factor with direct stress approach using finite element analysis

In this article, a direct stress approach based on finite element analysis to determine the stress intensity factor is improved. Firstly, by comparing the rigorous solution against the asymptotic solution for a problem of an infinite plate embedded a central crack, we found that the stresses in a restrictive interval near the crack tip given by the rigorous solution can be used to determine the stress intensity factor, which is nearly equal to the stress intensity factor given by the asymptotic solution. Secondly, the crack problem is solved numerically by the finite element method. Depending on the modeling capability of the software, we designed an adaptive mesh model to simulate the stress singularity. Thus, the stress result in an appropriate interval near the crack tip is fairly approximated to the rigorous solution of the corresponding crack problem. Therefore, the stress intensity factor may be calculated from the stress distribution in the appropriate interval, with a high accuracy.

On the pressure and stress singularities induced by steady flows of incompressible viscous fluids

Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, to date there has been relatively little explicit identification of stress singularities caused by fluid flows. In this study, stress and pressure singularities induced by steady flows of viscous incompressible fluids are asymptotically identified. This is done by taking advantage of an earlier result that the Navier-Stokes equations are locally governed by Stokes flow in angular corners. Findings for power singularities are confirmed by developing and using an analogy with solid mechanics. This analogy also facilitates the identification of flow-induced log singularities. Both types of singularity are further confirmed for two global configurations by applying convergence-divergence checks to numerical results. Even though these flow-induced stress singularities are analogous to singularities in solid mechanics, they nonetheless render a number of structural configurations singular that were not previously appreciated as such from identifications within solid mechanics alone.

On the pressure and stress singularities induced by steady flows of a pair of nonmiscible,incompressible,viscous fluids in contact with a wall

Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, only of late has there been much in the way of corresponding identifications of flow-induced stress singularities in fluid mechanics. These recent asymptotic identifications are for a single incompressible viscous fluid： Here the asymptotic approach is extended to apply to a configuration entailing two such fluids, For this configuration, various specifications leading to power or log singularities are determined. These results demonstrate that flow-induced stress singularities can occur in a structural container at a location where no singularities are identified within solid mechanics alone.

ANALYSIS OF THE SINGULARITY FOR THE VERTICAL CONTACT PROBLEM OF LINE CRACK-INCLUSION

Taking the short-fiber composite materials as engineering back-ground, utilizing the existing basic solutions of single inclusion and single crack, the plane problem of vertical contact interactions between line crack and rigid line inclusion in infinite plane (matrix) from the viewpoint of crack fracture mechanics is studied. According to boundary conditions, a set of standard Cauchy-type singular integral equations of the problem is obtainable. Besides, singular indexes, stresses and stress intensity factors around the contact point are expressed. Numerical examples are given to provide references to engineering.

The Expression of Stress and Strain at the Tip of Three-Dimensional Notch

The singularity of stress and strain at the tip of three-dimensional notch isanalysed by the power expansion method .the eigenquation of the notch is gainedthrough the boundary conditions of the notch, the eigenvalues under different innerangles of the notch are obtained, the expression of stress and strain at the tip of thenotch is finally derived .

Anti-plane pull-out of a rigid line inclusion from an elastic medium

The transient and static anti-plane problem of a rigid line inclusion pulled out from an elastic medium is studied.The singular integral equation method is used to solve the stress field.Under the static load,the stress intensity factor(SIF)at the inclusion tips increases with the medium length.The problem becomes equivalent to an inclusion in a medium with an infinite length when the length of the medium is 3.5times longer than that of the inclusion.However,under the transient load,the maximum value of the SIF occurs when the medium length is about two times the inclusion length.Besides,the relation between the pull-out force and the anti-plane displacement is given.The conclusions are useful in guiding the design of fiber reinforced composite materials.

Dynamics of Spreading of Liquid on Solid Surface

Based on assuming that there is the precursor film in the front of the apparent contact line （ACL）, a model was proposed to understand the dynamic wetting process and associated dynamic contact angle. The present model indicated that a new dimensionless characteristic parameter, 2, attects the dynamic wetting process and associated dynamic contact angle as well. However, the previous model suggested that the dynamic contact angle is dependent＇on the capillary number and static contact angle only. An experimental investigation was conducted to measure the dynamic wetting behavior of silicon oil moving over glass, aluminum and stainless steel surfaces. It concluded that when the value of 2 was selected as 0.07, 0.16 and 0.35 for glass, aluminum and stainless steel, respectively, the experimental results were in good accordance with the prediction of the model. Furthermore, the comparison of the model with Strom＇s experimental data showed that 2 is independent on the species of liquids. Apparently, 2 should be interpreted as the effect of the solid surface properties on the dynamic wetting process.Meanwhile, it is found in the present experiment that the Hoffman-Voinov-Tanner law, which is valid at very low capillary number （Ca 〈〈 1 or 80〈 10°） recommend by Cazabat, still holds for higher contact angles, even up to 70°-80°. This is explained by （he present model very well.

SIF-based fracture criterion for interface cracks

The complex stress intensity factor K governing the stress field of an interface crack tip may be split into two parts, i.e.,■ and s^（-iε）, so that K = ■ s^（-iε）, s is a characteristic length and ε is the oscillatory index. ■ has the same dimension as the classical stress intensity factor and characterizes the interface crack tip field. That means a criterion for interface cracks may be formulated directly with■, as Irwin（ASME J. Appl. Mech. 24：361–364, 1957） did in 1957 for the classical fracture mechanics. Then, for an interface crack,it is demonstrated that the quasi Mode I and Mode II tip fields can be defined and distinguished from the coupled mode tip fields. Built upon SIF-based fracture criteria for quasi Mode I and Mode II, the stress intensity factor（SIF）-based fracture criterion for mixed mode interface cracks is proposed and validated against existing experimental results.

THE INTERACTION BETWEEN MULTIPLE CURVED RIGID LINE AND ANTIPLANE CIRCULAR INCLUSION

The interaction between multiple curved rigid line and circular inclusion in antiplane loading condition is considered in this paper. By utilizing the point force elementary solutions and taking density function of traction difference along curved rigid lines, a group of weakly singular integral equations with logarithmic kernels can be obtained. After the numerical solution of the integral equations, the discrete values of density functions of traction difference are obtainable. So the stress singularity coefficient at rigid line tips can be calculated, and two numerical examples are given.

ELASTOSTATIC SOLUTOINS FOR SEMI-INFINITE ORTHOTROPIC CANTILEVERED STRIPS

The elastostatic solutions of semi-infinite orthotropic cantilevered strips with traction free edges and loading at infinity are governed by the differential equationφ,■+(2+δ_(0))φ,■+φ,■=0 withδ_(0)>-4 with Based on the work of[10]forδ_(0)>0 case,.this paper completes the caseδ_(0)=0 for isotropic materials and the case 0>δ_(0)>-4 for orthotropic materials.The solutions of the above problems have important application in the properly formulated boundary conditions of plate theories for prescribed displacement edge data.

Analysis of mode Ⅲ crack perpendicular to the interface between two dissimilar strips

The present work is concerned with the problem of mode Ⅲ crack perpendicular to the interface of a bi-strip composite. One of these strips is made of a functionally graded material and the other of an isotropic material, which contains an edge crack perpendicular to and terminating at the interface. Fourier transforms and asymptotic analysis are employed to reduce the problem to a singular integral equation which is numerically solved using Gauss-Chebyshev quadrature formulae. Furthermore, a parametric study is carried out to investigate the effects of elastic and geometric characteristics of the composite on the values of stress intensity factor.

A reined global-local approach for evaluation of singular stress ield based on scaled boundary inite element method

A reined global-local approach based on the scaled boundary inite element method（SBFEM） is proposed to improve the accuracy of predicted singular stress ield. The proposed approach is carried out in conjunction with two steps. First, the entire structure is analyzed by employing an arbitrary numerical method. Then, the interested region, which contains stress singularity, is re-solved using the SBFEM by placing the scaling center right at the singular stress point with the boundary conditions evaluated from the irst step imposed along the whole boundary including the side-faces. Beneiting from the semi-analytical nature of the SBFEM, the singular stress ield can be predicted accurately without highly reined meshes. It provides the FEM or other numerical methods with a rather simple and convenient way to improve the accuracy of stress analysis. Numerical examples validate the effectiveness of the proposed approach in dealing with various kinds of problems.

On the pressure and stress singularities induced by steady flows of a pair of nonmiscible,incompressible,viscous fluids contacting a wall with slip

An earlier asymptotic analysis identified the flow-induced power and log singularities present when two nonmiscible,incompressible,viscous fluids contact a wall with no slip permitted.Here a parallel asymptotic analysis identifies such singularities in pressures and stresses when slip is admitted.While the singularity exponents for the two types of contact conditions are similar,the angles of interface impingement that have either power or log singularities are usually quite distinct.