Dynamic Stress Concentration Factor Research Articles

Interface stress around a nanosized spherical inhomogeneity under asymmetric dynamic loads

In the design and optimization of nanocomposites, the surface/interface stress arising at the inhomogeneity-matrix boundary plays an important role in determining the strength of structures. In this paper, the effect of surface/interface stress on the dynamic stress around a spherical inhomogeneity subjected to asymmetric dynamic loads is investigated. The surface/interface stress effects are taken into account by introducing Gurtin-Murdoch surface/interface elasticity model. The analytical solutions to displacement potentials are expressed by spherical wave function and associated Legendre function. The dynamic stress concentration factors around the spherical nano-inhomogeneity are illustrated and analyzed. The effects of the incident wave number, and the material properties of the interface and inhomogeneity on the dynamic stress around the inhomogeneity are examined.

Dynamic response of twin closely-spaced circular tunnels to harmonic plane waves in a full space

An analytical solution for dynamic stress concentration of twin closely-spaced circular tunnels to plane P and SV waves in a full space is derived by the complex variable method in elastodynamics. Using the Helmholtz decomposition, the scattered wave fields by two circular cavities are expressed by wave function expansions. The complex variable method, the conformal transformation and the pertinent boundary conditions are jointly employed to develop an exact mathematical solution of the corresponding boundary value problem. The convergence of the present method is verified by the variation of the amplitude of the dynamic stress concentration factor of the cavities with the truncation of the series number. The influences of the space between two tunnels and the frequency of the incident waves on the dynamic stress concentration along the cavity walls are examined by the proposed solution. Numerical results show that they have considerable influence on the dynamic responses of the tunnel walls.

Effects of interface energy on scattering of plane elastic wave by a nano-sized coated fiber

In the framework of surface elasticity theory, the scattering of plane compressional and shear waves by a single nano-sized coated fiber embedded in an elastic matrix is studied using the method of eigenfunction expansion. The dynamic stress concentration factors along the interface between the coated fiber and the matrix induced by the plane elastic wave and scattering cross section are derived and numerically evaluated. The interface stress, inhomogeneous material constants and thickness of the coated layer on the scattering of the elastic wave become much more important when the radius of the coated-fiber is reduced to the nanometer scale. These were confirmed by the use of numerical results. Our results can aid in understanding the dynamic mechanical properties of nano-composites. The proposed method has potential applications in the characterization of the interfacial layer that links reinforced fibers to their matrix.

Dynamic Stress Concentration of a Cylindrical Cavity in Half-Plane Excited by Standing Goodier-Bishop Stress Wave

AbstractBased on expansion technique, the dynamic stress concentration of a cylindrical cavity buried in an elastic half-plane is studied in the paper. The cavity and the half-plane are excited by a harmonic standing Goodier-Bishop stress wave which, as a result of taking the normalized frequency tends to zero, is equivalent to a simple uniform static tension parallel to the ground surface. In the formulation, the scattered waves are represented by a series expansion, and their associated modal fields of the expansion satisfy the boundary conditions on the ground surface as well as the radiation condition at infinity. As a consequence, the scattering problem is reduced to the determination of the expansion coefficients by matching the boundary conditions on the cavity. The numerical technique based on the steepest descent method is used to calculate the integral representation of potential functions in wave-number domain. Numerical results for the dynamic hoop stresses around the wall of the cavity and the dynamic stress concentration factors with various buried depth and excitation frequencies are presented.

Dynamic analysis for circular inclusions of arbitrary positions near interfacial crack impacted by SH-wave in half-space

Abstract The diffraction of time harmonic anti-plane shear waves by arbitrary positions of inclusions and a finite length interfacial crack embedded in an elastic half-space is considered by using Green's function and complex function methods. With the aid of image method, the expression of scattering wave as well as the Green's function are constructed. A series of Fredholm integral equations containing unknown forces at the linking sections are obtained via the interface “conjunction” technique. The integral equations are reduced to a system of linear algebraic equations by using the effective truncation. Steady-state responses for some parameters are calculated and discussed. Numerical results demonstrate that the geometry under consideration is indeed capable of causing a localized high concentration of wave energy underground. Graphical results for the dynamic stress concentration factors are presented.

Dynamic Analysis for Circular Inclusion Near Interfacial Crack Impacted by SH-Wave in Half Space

ABSTRACTComplex method and Green's function method are used here to investigate the dynamic analysis for circular inclusion near interfacial crack impacted by SH-wave in bi-material half-space. Firstly, the displacement expression of the scattering wave was constructed which satisfied the free boundary conditions, then Green's function could be constructed, which was an essential solution to the displacement field for an elastic right-angle space with a circular inclusion impacted by out-plane harmonic line source loading at vertical surface. Secondly, crack was made out with “crack-division” technique. Meanwhile, the bi-material media was divided into two parts along the bi-material interface based on the idea of interface “conjunction”, and then the vertical surfaces of the two right-angle spaces were loaded with undetermined anti-plane forces in order to satisfy displacement continuity and stress continuity conditions at linking section. So a series of algebraic equations for determining the unknown forces could be set up through continuity conditions and the Green's function. Finally, some examples and results for dynamic stress concentration factor of the circular elastic inclusion were given. Numerical results show that they are influenced by interfacial crack, the incident wave number and the free boundary in some degree.

Dynamic strength around two interacting piezoelectric nano-fibers with surfaces/interfaces in solid under electro-elastic waves

Considerable efforts have been devoted to the characterization of the strength at the surfaces/interfaces of piezoelectric nanocomposites. In this paper, the multiple scattering of electro-elastic waves from two piezoelectric nano-fibers in piezoelectric matrix is considered and the dynamic stress at the interface is obtained. A decoupling function is introduced to solve the governing equation in piezoelectric materials. The displacement and electric potential are described by a wave function expansion method. The addition theorem for cylindrical wave function is used to obtain the total coupling wave field. The conventional surface/interface model of Gurtin and Murdoch is extended to the case of coupling stress and electric displacement. The dynamic stress concentration factor around two nano-fibers is obtained. Through numerical analysis, it is found that the interaction between the two nano-fibers has a significant effect on the coupling of stress and electric displacement at the interface, especially in the region of high frequency. The interacting effect of the two piezoelectric interfaces is also related to the properties of the nano-fibers and interface. To show the validity of the dynamic model, comparison with existing results is also given.

Dynamic Stress Concentration of Underground Lined Cavities in Different Distance under Incident Plane SV Wave

A series solution for dynamic stress concentration of underground lined cavities in different distance under incident plane SV waves is given by wave function expansion method. The infinite series is cut and calculated under the required precision. The lining includes rigid lining, unlined cavities, flexible lining. The numerical results show that the distance between cavities has an important impact on the dynamic stress concentration factor and the interaction between two cavities greatly amplifies the dynamic stress concentration. With the distance increases the dynamic stress concentration factor turn smaller gradually and tend to the distribution case of one cavity; The rigidity of lining also has great effect on the dynamic stress concentration which is highest for the rigid lining, second for unlined cavities and is lowest for the flexible lining.

Dynamic Stress Concentration of Underground Lined Cavities in Different Distance under Incident Plane SV Wave

A series solution for dynamic stress concentration of underground lined cavities in different distance under incident plane SV waves is given by wave function expansion method. The infinite series is cut and calculated under the required precision. The lining includes rigid lining, unlined cavities, flexible lining. The numerical results show that the distance between cavities has an important impact on the dynamic stress concentration factor and the interaction between two cavities greatly amplifies the dynamic stress concentration. With the distance increases the dynamic stress concentration factor turn smaller gradually and tend to the distribution case of one cavity; The rigidity of lining also has great effect on the dynamic stress concentration which is highest for the rigid lining, second for unlined cavities and is lowest for the flexible lining.

Dynamic Antiplane Behavior for a Quarter Infinite Piezoelectric Medium with a Subsurface Circular Inclusion

Dynamic antiplane behaviors are investigated theoretically in this paper for a quarter infinite piezoelectric medium with a subsurface circular inclusion. Based on complex variable and mirror image method, the expressions are obtained on dynamic stress concentration factor (DSCF) and electric field intensity concentration factor (EFICF) at the inclusion’s edge caused by the interaction between the inclusion and the right angle edge under time-harmonic anti-plane shearing. While some calculating cases are plotted, so as to show how the frequencies of incident wave, the piezoelectric material’s parameters and the structure’s geometry influence on DSCF and EFICF. The calculating results indicate that dynamic analyses are important to a quarter-infinite piezoelectric medium with defects at the surface vicinity.

The Scattering of SH-Wave Caused by Subsurface Circular Cavities in a Layered Half-Space

The scattering of SH-wave caused by the subsurface circular cavities in an elastic half-space covered with an elastic layer was discussed, which was based on the complex function method ,wave functions expansion method and big circular arc postulation method in which the circular boundary of large radius was used to approximate straight boundary of surface elastic layer. By the theory of Helmholtz, the general solution of the Biot’s wave function was achieved. Utilizing the complex series expansion technology and the boundary conditions, we could transform the present problem into the problem in which we needed to solve the infinite linear algebraic equations with unknown coefficients in wave functions. Finally, the dynamic stress concentration factors around the circular cavities were discussed in numerical examples.

Dynamic Stresses Concentrations of SH Wave by Circular Tunnel with Lining

Based on the scattering theory of elastic waves, employing the wave function expansion method, the scattering and the dynamic stresses concentration of SH wave by circular tunnel with lining are investigated. The analytical solution of the problem is derived, and the numerical solution of the dynamic stress concentration factors around the lining is presented. The effects of the shear elasticity of the surrounding rock and the lining, the wave number on the dynamic stress concentration factors are analyzed. Analysis has shown that the shear elasticity of the surrounding rock and the wave number are factors that influence dynamic stress concentration factor, and provide important theoretical foundation for the earthquake evaluation of lining.

Dynamic Response of Out-Plane Line Loads by a Shallow-Embedded Circular Lining Structure

The dynamic response problems of out-plane line loads by a shallow-embedded circular lining structure were investigated here by using the method of Green’s Function. Firstly a suitable Green’s function was constructed, which is an essential solution to the displacement field possessing a shallow-embedded circular lining structure while bearing out-plane harmonic line loads at an arbitrary point. Then we obtained a series of algebraic equations to solve this problem after constructing scattering waves that satisfied the zero-stress condition on the ground surface. Lastly, some numerical examples are given to show the effects that different parameters influence dynamic stress concentration factor (DSCF) by out-plane line source loads.

Anti-plane dynamic hole–crack interaction in a functionally graded piezoelectric media

The anti-plane dynamic problem of a functionally graded piezoelectric plane containing a hole–crack system is treated by a non-hypersingular traction-based boundary integral equation method. The material parameters vary exponentially in the same manner in an arbitrary direction. The system is loaded by an incident SH-type wave, and impermeable boundary conditions are assumed. Using a frequency-dependent fundamental solution of the wave equation, the boundary value problem is transformed into a system of integro-differential equations along the boundary of the hole and on the crack line. Its numerical solution yields the dynamic stress intensity factors and stress concentration factors. A parametric study reveals their dependence on the hole–crack scenario and its geometry, characteristics of the dynamic load and magnitude and direction of material inhomogeneity.

Research of Dynamic Stress Concentration of Lined Cavities under Incident Plane SV Waves in Different Angles

AbstractAn analytical series solution for dynamic stress concentration of lined cavities in a half space under incident plane SV waves was given by using wave function expansion method. The infinite series was cut and calculated under the required precision. The linings includes rigid lining, unlined cavities, flexible lining. The numerical result shows that (1) incident angle has great effect on the dynamic stress concentration factor; (2) the distance between two cavities has great effect on the dynamic stress concentration factor too, and the interaction between two cavities can greatly amplify the dynamic stress concentration when the distance between cavities is closer; (3) the rigidity of lining also has great effect on the dynamic stress concentration which is highest for the rigid lining second for unlined cavities and lowest for the flexible lining.

Scattering of Sh-Wave by Cylindrical Inclusion Near Interface in Bi-Material Half-Space

ABSTRACTGreen's function and complex function methods are used here to investigate the problem of the scattering of SH-wave by a cylindrical inclusion near interface in bi-material half-space. Firstly, Green's function was constructed which was an essential solution of displacement field for an elastic right-angle space possessing a cylindrical inclusion while bearing out-of-plane harmonic line source load at any point of its vertical boundary. Secondly, the bi-material media was divided into two parts along the vertical interface using the idea of interface “conjunction”, then undetermined anti-plane forces were loaded at the linking sections respectively to satisfy continuity conditions, and a series of Fredholm integral equations of first kind for determining the unknown forces could be set up through continuity conditions on surface. Finally, some examples for dynamic stress concentration factor of the cylindrical elastic inclusion are given. Numerical results show that dynamic stress concentration factor is influenced by interfaces, free boundary and combination of different media parameters.

The Effect on Scattering of SH-Wave in a Layered Half-Space with the Subsurface Circular Cavities

The scattering of SH-wave caused by the subsurface circular cavities in an elastic half-space covered with an elastic layer was discussed, which was based on the complex function method and wave functions expansion method. The solution of scattering of SH-wave was given by using circular boundary of large radius to approximate straight boundary of surface elastic layer. According to boundary conditions, we needed to solve the infinite linear algebraic equations with unknown coefficients in wave functions. Finally, the dynamic stress concentration factors around circular cavities were discussed in numerical examples.

Dynamic Analysis for a Subsurface Elastic Cylindrical Inclusion with a Semi- Cylindrical Hill Impacted by SH-Wave

An analytic method is developed for dynamic stress concentration of a subsurface elastic cylindrical inclusion below a semi-cylindrical hill under SH-wave. And the dynamic stress concentration factor (DSCF) is given by complex variable function. During the solution, a standing wave and scattered wave displacement functions are constructed in different parts respectively. All of these displacement functions should satisfy the boundary conditions of each part. Employed to the boundary conditions around the elastic cylindrical inclusion, a series of infinite algebraic equations about the problem can be obtained. The calculating results of DSCF around the elastic cylindrical inclusion are plotted to show the effects of some parameters on DSCF.

Dynamic Stress Concentration – a Hybrid Analysis

Dynamic Stress Concentrations are being increasing critical in variety of micro-fluidic channels and other devices with sharp corners and edges. The Finite Element Method (FEM) is widely used as a numerical simulation system. Additional Photoelasticity is one of the more widely used experimental methods for verification of the FEM models. This has been done widely for static loading situations. In this paper dynamic Stress Concentration Factors are determined numerically using FEM and experimental using a novel dynamic photoelastic system. It is found that the results from the finite element analysis resemble closely the experimental patterns recorded.

Far Field Solution of Circular Inclusion and Linear Crack by SH-Wave

Circular inclusion exists widely in natural media, engineering materials and structures, and defects are usually found around the inclusion. When a composite material with circular inclusion and cracks is impacted by the dynamic load, on the one hand, the scattering field produced by the circular inclusion and cracks determines the dynamic stress concentration factor around the circular inclusion, and therefore determines whether the material is damaged or not; on the other hand, the scattering field also presents many characteristic parameters of the inclusion and cracks such as defect composition, location and shape, so the research on the scattering far-field is important to the geological prospects, seismological investigation, non-destruction evaluation and the other fields. In the ocean acoustics, the scattering far-field of the acoustic wave is also used in the under-water survey, object distinguishing and so on. In theory, the scattering solution of elastic waves is one of the basic topics of reverse problems on elastic wave. On the basis of literature, few paper concentrates on the scattering far-field solution of SH-wave by a circular inclusion and a linear crack around the inclusion. In the paper a new model and a new method are presented in order to investigate deeply on this kind problem. The paper uses the Green’s function to study the scattering far-field of an elastic wave by a circular inclusion and a linear crack. The Green’s function should be a fundamental solution of displacement field for an elastic space possessing a circular inclusion while bearing out-of-plane harmonic line source force at any point. In terms of the solution of SH-wave’s scattering by an elastic space with a circular inclusion, anti-plane stresses which are the same in quantity but opposite in direction to those mentioned before, are loaded at the region where the linear crack is in existent actually; Then, the expressions of the displacement and stresses are given when the circular inclusion and linear crack exist at the same time. When the special Green’s function has been constructed and close field solution has been illustrated, the far field of scattered wave is studied. The displacement mode of scattered wave at far field and scattering cross-section are given. At last, an example is given and its numerical results are discussed.