Dynamic Stress Concentration Research Articles

Scattering of SH Waves by a Partially Debonded Cylindrical Inclusion in the Covering Layer

This article presents analytical solutions to the problem of dynamic stress concentration and the surface displacement of a partially debonded cylindrical inclusion in the covering layer under the action of a steady-state horizontally polarized shear wave (SH wave); these solutions are using the complex function method and wave function expansion method. By applying the large-arc assumption method, the straight line boundary of the half-space covering layer is transformed into a curved boundary. The wave field of the debonded inclusion is constructed utilizing a Fourier series and boundary conditions of continuity. The impact of debonding upon the dynamic stress concentration and surface displacement around the cylindrical concrete or steel inclusion is analyzed through numerical examples of the SH waves that are incident at normal angles, from a harder medium to a softer medium and from a softer medium to a harder medium. The examples show that various factors (including the medium parameters of the soil layers and the inclusion, the frequency of the incident waves, and the debonding situations) jointly affect the dynamic stress concentration factor and the surface displacement around the structure.

Dynamic Stress Concentration Factors and Damage Mode of Horseshoe Tunnels Crossing Fault Fracture Zone

A series of uniaxial compression tests are carried out firstly to confirm the reasonable surrounding rock parameters. Then building up the finite element analysis models of the horseshoe tunnel subjected to the seismic loads. The tunnel buried in different geological conditions, like the different plane angles between tunnel and fault fracture zone (e.g. 0°, 30°, 60° and 90°), different width of the fault zone (e.g. 1 m, 0.5D, 1.0D, 1.5D, 2.0D) (D is the tunnel width). The paper mainly discusses the dynamic stress concentration factors and damage mode on the horseshoe tunnel. Based on the experimental and numerical results, analyzing the distribution of dynamic stress concentration and damage mode on the tunnel, it can be concluded that the tunnel crossing fault fracture zone with the plane angle of 60° and the width of 1.0D are more hazardous, whose vertical convergent deformation, equivalent plastic strain (tensile), tensile damage and the slipping displacement of the fault are in the high level, when compared with other geological conditions simulated in the numerical analysis.

Dynamic analysis of SH wave by a three-layer inclusion near interface in bi-material half space

In this paper, the scattering of SH waves by a three-layer inclusion near the bi-material interface has been studied. A complex function method is employed to solve a two-dimensional wave propagation problem. The displacement fields in the bi-material half space and inside the linings of the inclusion are constructed, satisfying the governing equation, and unknown coefficients are solved from boundary conditions. The bi-material half space is separated into two quarter spaces, and the region matching method is used to determine the extra-forces on the interface. With the aid of the Green function method, the displacement fields owing to the forces are obtained. Then, the dynamic stress concentration factors (DSCFs) around the inner and outer surfaces of the inclusion are presented graphically, considering different medium parameters. Results are compared with those of earlier investigations, and the effect of parameters on the DSCF is discussed.

Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves

Based on the methods of complex function, conformal mapping, and multipolar coordinate system, dynamic response of an elliptical inclusion embedded in an anisotropic half space is investigated. In order to find the solution of SH waves, the governing equation is transferred into its normalized form. Then, the scattering wave induced by the inclusion and the standing wave in the inclusion is deduced. Different incident wave angles and the corresponding anisotropy of the half space are considered to obtain the reflected waves. The elliptical inclusion is transferred into a unit circle by conformal mapping method, and then the undetermined coefficients in scattering wave and standing wave are solved by using the continuous condition at the boundary of the inclusion. Subsequently, the dynamic stress concentration factor (DSCF) around the inclusion is calculated and analyzed. Numerical results demonstrate that the distribution of the DSCF is mainly influenced by the incident wave angle and the incident wave number. It is affected by anisotropic parameters as well.

Scattering of SH Wave by a Semi-Circle Inclusion Embedded in Bi-Material Half Space Surface

ABSTRACTInvestigation of SH wave scattering by inclusions in bi-material half space is an important issue in engineering. The purpose of this work is to study the dynamic response of a semi-circle inclusion embedded in bi-material half space surface by SH wave. Graf's addition theorem, Green function method and region-matching technique are used to determine the displacement fields in the bi-material half space and the inclusion. The distributions of dynamic stress concentration factor (DSCF) around the semi-circle inclusion are depicted graphically considering different material parameters. The results show that the frequency and the incidence angle of SH wave, the rigidities of the inclusion and bi-material half space, and the distance from the inclusion to the interface have a great effect on the distribution of DSCF around the inclusion.

Dynamic response of a circular lined tunnel with an imperfect interface embedded in the unsaturated poroelastic medium under P wave

Abstract A scattering problem of a plane dilatational wave disturbed by a lined tunnel with an imperfect interface embedded in an infinite unsaturated poro-elastic solid is investigated. By means of the Helmholtz theory and the wave function expansion method, the corresponding displacements and stresses are obtained in terms of the wave functions, where the coefficients involved are determined by solving a series of linear equations. Numerical calculations are carried out to illustrate the influence of the saturation, stiffness of the interface and the frequency of the incident wave on the distribution of the radial displacement and the dynamic stress concentration factor (DSCF) in the unsaturated substrate. The present analytical solutions may serve as a starting point for future engineering practices.

A comprehensive time-domain elasto-acoustics study of a fluid-filled spherical shell embedded in an elastic medium

An exhaustive study is carried out on the mechanics of waves travelling through a coupled elasto-acoustic system of a fluid-filled, thick-walled spherical shell embedded in an elastic formation. Important but previously untouched aspects of this classical problem are addressed rigorously. An exact local theory of linear elasticity is applied to the elastic formation and the shell, whereas the linear theory of acoustics for compressible fluids is utilized. Two sets of excitation sources are considered: (i) either incident compressional or shear waves, and (ii) a general traction force acting on either one of the shell's surfaces. The origin of the incident waves can be point sources of stress waves positioned within the infinite elastic medium, shell's material or an eccentric pressure source located within the encapsulated fluid. A unified description of various incident waves in terms of a common set of spherical harmonics having their origin coinciding with the shell's center is proposed. A rigorous cross check of the current approach is performed meticulously against multiple existing limiting cases taken from the pertinent literature. The comparisons lend credence to the current approach and the associated computer code developments. More general situations that emphasize important physical features are considered next. Accordingly, case studies are chosen to represent different geometrical and material configurations when subjected to excitation sources having various origins. The effects of the relative acoustical properties are shown to be very essential in determining the physics of the interaction. Focusing of acoustical energy within an encapsulated fluid or an elastic inclusion, for instance, is determined mainly by the relative celerity of the interacting media. This has practical significance in predicting the likelihood of cavitation in the fluid field as well as the determination of the dynamic stress concentration. Several other important observations are made which have significant practical implications, for instance, in design of shock resistance structures, generation of highly focused ultrasonic pulses for the non-destructive testing or ultrasonic cleaning purposes as well as structural integrity considerations.

On the role of dynamic stress concentrations and fracture mechanics in the longitudinal tensile failure of fibre-reinforced composites

This paper investigates the role of dynamic stress concentrations, and of fracture mechanics-driven growth of critical clusters of fibres, on the longitudinal tensile failure of fibre-reinforced composites. For this purpose, we developed a semi-analytical fibre bundle model to simulate the longitudinal tensile failure of large composite bundles of continuous fibres. The model uses shear-lag to calculate the stress recovery along broken fibres, and an efficient field superposition method to calculate the stress concentration on the intact fibres, which has been validated against analytical and Finite Element (FE) results from the literature.The baseline version of the model uses static equilibrium stress states, and considers fibre failure driven by strength of materials (stress overload) as the only damage theory which can drive bundle failure. Like other models in the literature, the baseline model fails to capture the correct size effect (decreasing composite strength with bundle size) shown by experimental results.Two model variants have been developed which include dynamics stress concentrations and a fracture mechanics failure criterion respectively. To the knowledge of the authors, it is the first attempt in the literature to investigate these two effects in a fibre bundle model by direct simulation of large composite bundles. It is shown that, although the dynamic stress concentration significantly decreases the predicted bundle strength, it does not allow to predict the correct trend of the size effect. Finally, the results suggest that fracture mechanics may be the physical mechanism which is necessary to include to correctly predict the decreasing composite strength with bundle size shown by experimental results.

Modeling and analysis of the transient response of viscoelastic solids

ABSTRACT In this paper, an incremental finite element model (IFEM) for the transient analysis of viscoelastic solids is developed. The viscoelastic constitutive response is modeled based on the hereditary integral. Two new incremental constitutive forms suitable for finite element implementation are derived; creep-based (CB) and relaxation-based (RB) and, as a consequent, the difficulties associated with the interconversion from the relaxation modulus to the creep compliance and vice versa are avoided. Creep compliance and relaxation modulus are, respectively, modeled using generalized Kelvin–Voigt model and generalized Wiechert’s model. To check the validity, the computational procedure, semi-analytical solution is derived for simple viscoelastic cases using Laplace and inverse Laplace transform techniques. The obtained results from the computational procedure are compared with that obtained from the derived semi-analytical solution. To show the validity and applicability of the developed model, two different applications under different excitation patterns are presented. In each application, the time response for displacements and stresses, especially for the dynamic stress concentration factor for both elastic and viscoelastic analyses are investigated. Moreover, the dissipative recoverable nature of the viscoelastic solids under different loading-unloading excitation patterns is illustrated.

Analytical study of SH wave scattering by a cylindrical cavity in the two-dimensional and approximately linear inhomogeneous medium

Based on the complex function method, shear horizontal wave scattering in the two-dimensional and approximately linear inhomogeneous medium is investigated analytically in this work. A new pair of transformation is proposed to normalize the governing equation of the two-dimensional inhomogeneous medium. Then wave fields and the corresponding stresses are expressed by complex variables. With the help of the boundary condition at the cavity, the undetermined coefficients are determined. By controlling the ratio of two inhomogeneous parameters, the medium can be modeled as two-dimensional inhomogeneous and approximately linear inhomogeneous. Finally, the parametric study presents that wave number and inhomogeneous parameters have significant influences on dynamic stress concentration factor around the cavity in different kinds of inhomogeneous media.

Dynamic stress concentration and failure characteristics around elliptical cavity subjected to impact loading

Wave function expansion method is used to solve the scattering and dynamic stress concentration around the elliptic cavity in the full plane under steady state linear elastic stationary incident SH wave with arbitrary angle. Under the elliptical coordinate system, Mathieu equation is obtained by separating variables from Helmholtz equation. Considering the simplicity of Mathieu function in solving elliptic boundary problem, the incident plane wave is expanded into the series of Mathieu function, and the full wave function is obtained from the stress boundary condition of the elliptic cavity, then the response of the elliptic cavity subjected to the steady state linear elastic stationary incident SH wave is obtained. Through the Fourier integral transformation of transient impact, the dynamic stress concentration of transient incident SH wave around an elliptical cavity can be obtained. In addition, the finite element method (FEM) numerical simulation software LS-DYNA is used to calculate the dynamic stress concentration and plastic deformation around the elliptical cavity with transient impact. Furthermore, the influence of the initial stress on plastic deformation is obtained. The results show that the incident angel, wave number and the ellipse axis ratio have great influence on the distribution of dynamic stress concentration and the failure of the elliptical cavity.

The dynamic stress analysis of an infinite piezoelectric material strip with a circular cavity

The scattering of SH guided wave by a circular cavity in an infinite piezoelectric material strip is analyzed by using “mirror image method” and guided wave theory, and the analytical expressions of guided wave function satisfying stress free and electric insulation conditions on the upper and lower horizontal boundaries of the strip domain are obtained. The analytical expression of the scattered wave around a circular cavity is constructed by using the method of multiple mirror superposition and wave function expansion. The integral equations are established and solved by the boundary conditions of the circular cavity, and the analytical expressions of the dynamic stress concentration factor and the electric field intensity factor are obtained. The effects of incident wave frequency, dielectric parameters and circular cavity position on electric field intensity concentration factor (EFICF) and dynamic stress concentration factor (DSCF) are analyzed by numerical examples. Besides, the analytical solutions obtained in this article are compared with the finite element solutions and the analytical solutions in previous literature to verify the correctness and accuracy of the conclusions in this article. And the conclusions in this article are of great reference value to the selection and ultrasonic nondestructive testing of anti-seismic materials.

Dynamic Stress around a Cylindrical Nano-Inclusion with an Interface in a Right-Angle Plane under SH-Wave

Based on the surface elasticity theory, the scattering of shear wave (SH-wave) by a cylindrical nano-inclusion with an interface in a right-angle plane is studied using the method of complex variable function. The dynamic stress concentration factor along the interface of inclusion by the SH-wave and scattering cross section are derived and numerically evaluated. The surface effect, the incident wave’s frequency, the shear modulus, and the distances from the center of nano-inclusion to the right-angle boundaries show the different degrees effects on the DSCF. Our results can aid in analyzing the mechanical properties of nonuniform nanocomposites. The proposed method can better solve the scattering problem of the holes/inclusions on noninfinite elastic substrates.

Scattering of a shear horizontal wave by a circular cavity in a piezoelectric bi-material strip based on guided wave theory

The scattering problem of a shear horizontal guided wave in a piezoelectric bi-material strip is analysed by means of the "mirror method," the Green’s function method and guided wave theory. A harmonic out-of-plane line-source force is applied at the junction of two-phase materials. Then, the bi-material strip is divided into two parts, and a pair of in-plane electric fields and a pair of counter-planar forces are applied to the vertical boundary. According to the boundary conditions, the Fredholm integral equation of the first kind is established by using the conjunction method. By effectively truncating the integral equation, the integral equation is simplified to an algebraic equation. The electric field intensity concentration factor and dynamic stress concentration factor around the circular cavity are obtained. The research content of this article is of great reference value in non-destructive testing, providing a reference for the judgement of the reliability of a piezoelectric bi-material strip.

Using Refined Theory to Studied Elastic Wave Scattering and Dynamic Stress Concentrations in Plates with Two Cutouts

In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.

Elastic Wave Scattering and Dynamic Stress Concentrations around Double Holes in Piezoelectric Media

In this paper, on the basis of Liu’s complex function and conformal mapping methods, supplemented by local coordinate system method, e-type piezoelectric material and elastic wave scattering and dynamic stress concentrations problems with double holes question are studied, and an analytical solution is given to the problems. On the basis of multiple scattering of elastic wave theory, put forward the study about microscopic dynamics model to dynamic stress in the structure of piezoelectric composites as well as dynamic playing field. As an example, the numerical results of the dynamic stress distribution around the hole in case double equal diameter holes are given in the paper, and the influence of incident wave number and hole-spacing parameters on the dynamic stress concentration factor is analyzed.

Dynamic Stress Concentration in a Piezoelectric Material with a Non-Circular Hole Subjected to an SH-Wave

Dynamic Stress Concentration in a Piezoelectric Material with a Non-Circular Hole Subjected to an SH-Wave

Dynamic Stress Analysis of a Circular‐Lined Tunnel in Composite Strata‐SH Wave Incidence

It is necessary to study the problem of seismic wave scattering in composite stratum for tunnel engineering because the existence of composite strata will make the stress of tunnels more complicated during earthquakes. In this thesis, a series solution of the scattering wave field of the composite strata and lining is obtained using the complex function method. According to the stress and displacement boundary conditions between the composite stratum and the lining, a series of equations are established and are solved by means of Fourier transformation and finite term truncation, and the calculation errors are also discussed. Through programming calculations, the dynamic stress concentration factor (DSCF) of circular tunnels in the two types of composite strata, “hard‐over‐soft” and “soft‐over‐hard,” is analyzed when SH waves propagate, and certain conclusions on the scattering of SH waves that are distinguished from the case of single homogeneous layers are reached. The research in this article reveals some phenomena. For the Q345 steel lining in the calculation examples, it is found in this paper that increasing the thickness of the lining is effective to reduce the influence of the DSCF. But, for C30 concrete, increasing the thickness of the lining reduces the DSCF of the outer surface while increasing the DSCF of the inner surface.

Concentration of dynamic stresses in an elastic space with twoperiodic array of elliptical cracks

Normal incidence of the plane time-harmonic longitudinal wave on double-periodic array of coplanar elliptical cracks, which are located in 3D infinite elastic space is considered. Corresponding symmetric wave scattering problem is reduced to a boundary integral equation for the displacement jump across the crack surfaces in a unit cell by means of periodic Green’s function, which is presented in the form of Fourier integrals. A regularization technique for this Green’s function involving special lattice sums in closed forms is adopted, which allows its effective calculation in a wide range of wave numbers. The boundary integral equation is correctly solved by using the mapping method. The frequency dependencies of mode-I stress intensity factor in the vicinity of the crack front points for periodic distances in the system of elliptical cracks are revealed.

Dynamic stress state around shallow-buried cavity under transient P wave loads in different conditions

The failure of underground structure is always caused by local stress redistribution resulted from transient impact loads. An analytical model is established and solved by using the complex variable function method to illustrate the dynamic stress concentration around a shallow-buried cavity under transient P wave loads. The transient wave response is attained as an integration of steady-state wave response in circular frequency domain. By adopting a Butterworth filter, the jump points in the dynamic stress concentration factor (DSCF) curve which is not in line with the overall trend is filtered out to obtain more reasonable results. The convergence and accuracy of the solutions are verified and discussed in detail. DSCF distributions of high wavenumber incidences differ from that of low wavenumber incidences significantly in amplitudes and distribution patterns. The effects of the cavity depth, incidence angle and position of wave peak on DSCF distributions are illustrated.