Stress Singularities at the Apex of a Dissimilar Anisotropic Wedge

1998 ◽  
Vol 65 (2) ◽  
pp. 454-463 ◽  
Author(s):  
Y. Y. Lin ◽  
J. C. Sung
Keyword(s):  
Characteristic Equation ◽  
Complex Form ◽  
Numerical Results ◽  
Orthotropic Materials ◽  
Stress Singularities ◽  
Material Parameters ◽  
Real Forms

The complex form of the characteristic equation for the stress singularities of the order rλ-1(0<Re[λ]<1) for the dissimilar anisotropic wedges is derived. Special attention is then focused on the problems that are composed by two orthotropic materials. For such problems the characteristic equation is expressed in real forms from which the dependence of the singularities on the material parameters and wedge angles is investigated. The case of a single free-fixed wedge problem is particularly studied in detail. Numerical results for several special wedge geometries are also presented.

Singularities at the Tip of a Crack Terminating Normally at an Interface Between Two Orthotropic Media

1996 ◽  
Vol 63 (2) ◽  
pp. 264-270 ◽  
Author(s):  
J. C. Sung ◽  
J. Y. Liou
Keyword(s):  
Characteristic Equation ◽  
Complex Form ◽  
Stress Singularities ◽  
Real Form ◽  
Antisymmetric Mode ◽  
Real Roots ◽  
Complex Roots ◽  
Principal Axes ◽  
Orthotropic Media ◽  
Set Up

The order of stress singularities at the tip of a crack terminating normally at an interface between two orthotropic media is analyzed. Characteristic equation in complex form for the power of singularity s, where 0 < Re{s} < 1, is first set up for two general anisotropic materials. Attention is then focused on the problem that is composed by two orthotropic media where one of them (say, material #2 ) the material principal axes are aligned while the other one (say, material #1) the principal axes can have an angle γ relative to the interface. For such a problem, a real form of the characteristic equation is obtained. The roots are functions of γ in general. Two real roots exist for most values of γ; however, there are possible ranges of γ that the complex roots will occur. The roots s are found to be independent of γ when material #1 has the property that δ(1) = 1. When γ = 0, two roots are always real. Furthermore, each of these two roots is associated with symmetric or antisymmetric mode and they become equal when Δ = 1. Many other features of the effects of the material parameters on the behaviors of the roots s are further investigated in the present work, where the six generalized Dundurs’ constants, expressed in terms of Krenk’s parameters, play an important role in the analysis.

Some Phenomena of Cracks Perpendicular to an Interface Between Dissimilar Orthotropic Materials

1996 ◽  
Vol 63 (1) ◽  
pp. 190-203 ◽  
Author(s):  
J. C. Sung ◽  
J. Y. Liou ◽  
Y. Y. Lin
Keyword(s):  
Stress Intensity ◽  
Characteristic Equation ◽  
Stress Intensity Factors ◽  
Dissimilar Materials ◽  
Singular Integral Equations ◽  
Kernel Functions ◽  
Orthotropic Materials ◽  
Intensity Factors ◽  
Present Context ◽  
Real Forms

The problem of two aligned orthotropic materials bonded perfectly along the interface with cracks embedded in either one or both of the materials while their directions being perpendicular to the interface is considered. A system of singular integral equations for general anisotropic materials is derived. Employing four effective material parameters proposed by Krenk and introducing four generalized Dundurs’ constants, the kernel functions appearing in the integrals are converted into real forms for the present problem which are keys to the present study. The kernel functions for isotropic dissimilar materials can be deduced from the present results directly, no any limiting process is needed. These kernel functions are then employed to investigate the singular behaviors for stresses at the point on the interface. Characteristic equation which determines the power of singularity for stresses is given in real forms for the case of cracks that are going through the interface. Studies of the characteristic equation reveal that the singular nature for the stresses could vanish for some material combinations and the singular nature for the stresses is found to be independent of the replacement of the material parameter Δ by Δ-1. The kernel functions developed are further used to explore analytically some interesting phenomena for the stress intensity factors, which are discussed in detail in the present context. Some numerical results for the stress intensity factors for a typical dissimilar materials are also given.

Transformation Media in Acoustics with Constant Bulk Modulus or Constant Density Tensor

2015 ◽  
Vol 32 (3) ◽  
pp. 313-323
Author(s):  
Y.-L. Tsai ◽  
T. Chen
Keyword(s):  
Bulk Modulus ◽  
Numerical Results ◽  
Practical Implementation ◽  
Constant Density ◽  
Density Tensor ◽  
Material Parameters

AbstractThis work is to present a formulation of cloaking or concentrating device in acoustics in which the transformed material could be either having uniform bulk modulus or having homogeneous density tensor. The transformed material parameters, depending on the mapping of physical and virtual coordinates, are often position-varying and anisotropic. This often adds substantial complexity in practical implementation. Here we present a theoretical algorithm that allows us to design a transformation field that could have either uniform bulk modulus or constant density tensor. For cloaking devices with constant bulk modulus, analytical and numerical results are presented for circular as well as for non-circular cloaking devices. Specifically, elliptical and twin-cloak devices are exemplified. To achieve the effect of constant density tensor, we consider only circular geometry. Devices with cloaking or concentrating effects can be exactly formulated. We note, however, that it seems unlikely at this moment to have a transformation device that has constant bulk modulus and constant density tensor at the same time. Nevertheless, we remark the present results are of still sufficient merit in that the uniform material parameters, in either set of material parameters, indeed greatly simplify the practice in real implementations.

Plane Solutions for the Displacement and Traction-Displacement Problems for Anisotropic Elastic Wedges

1974 ◽  
Vol 41 (1) ◽  
pp. 197-202 ◽  
Author(s):  
M. C. Kuo ◽  
D. B. Bogy
Keyword(s):  
Mellin Transform ◽  
Symmetry Axis ◽  
Wedge Angle ◽  
Complex Function ◽  
Material Symmetry ◽  
Stress Singularities ◽  
Material Parameters ◽  
Plane Solution ◽  
Anisotropic Elastic ◽  
Plane Displacement

The plane displacement and traction-displacement problems for anisotropic elastic wedges are solved by use of the complex function representation of the plane solution in conjunction with the Mellin transform. The special forms of the solutions pertinent to orthotropic wedges with a material symmetry axis along the wedge bisector is also presented and the dependence of the order of the stress singularities at the apex on the wedge angle and material parameters is shown graphically for this case.

Temperature Distributions in CW Laser Induced Pyrolytic Deposition

1983 ◽  
Vol 29 ◽  
Author(s):  
Klaus Piglmayer ◽  
Josef Doppelbauer ◽  
Dieter BÄuerle
Keyword(s):  
Experimental Data ◽  
Chemical Vapor Deposition ◽  
Laser Radiation ◽  
Vapor Deposition ◽  
Chemical Vapor ◽  
Numerical Results ◽  
Infinite Plane ◽  
Material Parameters ◽  
Temperature Distributions ◽  
Cw Laser

ABSTRACTTemperature distributions induced by cw laser radiation absorbed on the surface of combined structures, consisting of discs or of stripes on semi - infinite plane substrates, are calculated for different material parameters and different geometries. The relevance of the numerical results is demonstrated by comparison with earlier experimental data obtained in pyrolytic laser-induced chemical vapor deposition.

On the Inclined Surface Crack Terminating at the Orthotropic Bimaterial Interface

2008 ◽  
Vol 385-387 ◽  
pp. 541-544
Author(s):  
Tomáš Profant ◽  
Michal Kotoul
Keyword(s):  
Stress Intensity Factor ◽  
Surface Crack ◽  
Reciprocal Theorem ◽  
Orthotropic Materials ◽  
Bimaterial Interface ◽  
Stress Singularities ◽  
Singular Stress ◽  
Singular Stress Field ◽  
The Reciprocal Theorem ◽  
Inclined Surface

The evaluation of the stress singularities and generalised stress intensity factor (GSIF) for the case of an inclined surface crack terminating perpendicular to the interface between two orthotropic materials is considered. The knowledge of the regular and auxiliary solution allows evaluating the GSIF using the reciprocal theorem (Ψ-integral). A co-operating effect of a stronger and a weaker singular stress field for a crack impinging a bimaterial interface is investigated.

Two Analytical Models to Determine the Stress Singularities in Elastic-Viscoelastic Joints

2013 ◽  
Vol 834-836 ◽  
pp. 1391-1394
Author(s):  
Zhi Xu Gu ◽  
Jian Zheng ◽  
Wei Peng ◽  
Xi Nan Tang
Keyword(s):  
Elastic Material ◽  
The Other ◽  
Analytical Models ◽  
Stress Singularities ◽  
Material Parameters ◽  
Elastic Joints ◽  
The Difference

The stress singularities are obtained by two methods in elastic-viscoelastic joints, one is extending the corresponding solutions for elastic-elastic joints by using elastic-viscoelastic correspondence principles and the other is replacing the elastic material parameters with viscoelastic ones in Dundurs parameters directly. The difference between the two methods and the validity are discussed.

Mathematical Simulation of Cloaking Metamaterial Structures

2012 ◽  
Vol 4 (1) ◽  
pp. 93-101 ◽  
Author(s):  
Jichun Li ◽  
Yunqing Huang
Keyword(s):  
Mathematical Simulation ◽  
Numerical Results ◽  
Rigorous Derivation ◽  
Material Parameters

AbstractIn this paper we present a rigorous derivation of the material parameters for both the cylinder and rectangle cloaking structures. Numerical results using these material parameters are presented to demonstrate the cloaking effect.

The Brittle Strength of Orthotropic Materials

1967 ◽  
Vol 1 (2) ◽  
pp. 200-206 ◽  
Author(s):  
Oscar Hoffman
Keyword(s):  
Yield Condition ◽  
Orthotropic Materials ◽  
Brittle Strength ◽  
Material Parameters ◽  
Reinforced Composite ◽  
Fracture Condition ◽  
Physical Phenomena ◽  
Yield Conditions ◽  
Good Agreement ◽  
Reinforced Composite Material

A phenomenological fracture condition is proposed for ortho tropic brittle materials. It contains nine material parameters and can account for widely differing compressive and tensile strengths in various directions. The proposed fracture condition is devel oped, purely on formal grounds, by borrowing features of the Mises-Schleicher isotropic yield condition and Hill's orthotropic yield condition. Comparison with experimental data on a fiber- reinforced composite material shows good agreement. The reader is reminded repeatedly that, despite formal similarities, yield conditions and brittle-fracture conditions pertain to unrelated physical phenomena.

Identification of Elastic Orthotropic Material Parameters by the Singular Boundary Method

2016 ◽  
Vol 8 (5) ◽  
pp. 810-826 ◽  
Author(s):  
Bin Chen ◽  
Wen Chen ◽  
Xing Wei
Keyword(s):  
Inverse Problem ◽  
Optimization Problem ◽  
Orthotropic Materials ◽  
Singular Boundary ◽  
Material Parameters ◽  
Boundary Method ◽  
Residual Functional ◽  
The Stability ◽  
Singular Boundary Method ◽  
Different Levels

AbstractThis article addresses the resolution of the inverse problem for the parameter identification in orthotropic materials with a number of measurements merely on the boundaries. The inverse problem is formulated as an optimization problem of a residual functional which evaluates the differences between the experimental and predicted displacements. The singular boundary method, an integration-free, mathematically simple and boundary-only meshless method, is employed to numerically determine the predicted displacements. The residual functional is minimized by the Levenberg-Marquardt method. Three numerical examples are carried out to illustrate the robustness, efficiency, and accuracy of the proposed scheme. In addition, different levels of noise are added into the boundary conditions to verify the stability of the present methodology.

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