Antiplane shear crack in a prestressed elastic medium based on the couple stress theory

A prestressed elastic medium containing a mode-Ⅲcrack is studied by means of the couple stress theory(CST).Based on the CST under initial stresses,a governing differential equation along with a mixed boundary value problem is established.The singularities of the couple stress and force stress near the crack tips are analyzed through the asymptotic crack-tip fields resulting from the characteristic expansion method.To determine their intensity,a hypersingular integral equation is derived and numerically solved with the help of the Chebyshev polynomial.The obtained results show a strong size-dependence of the out-of-plane displacement on the crack and the couple stress intensity factor(CSIF)and the force stress intensity factor(FSIF)around the crack tips.The symmetric part of the shear stress has no singularity,and the skew-symmetric part related to the couple stress exhibits an r^(-3/2)singularity,in which r is the distance from the crack tip.The initial stresses also affect the crack tearing displacement and the CSIF and FSIF.

PROPAGATION OF LOVE WAVES IN PRESTRESSED PIEZOELECTRIC LAYERED STRUCTURES LOADED WITH VISCOUS LIQUID

We investigate analytically the effect of initial stress in piezoelectric layered structures loaded with viscous liquid on the dispersive and attenuated characteristics of Love waves, which involves a thin piezoelectric layer bonded perfectly to an unbounded elastic substrate. The effects of initial stress in the piezoelectric layer and the viscous coefficient of the liquid on the phase velocity of Love waves are analyzed. Numerical results are presented and discussed. The analytical method and the results can be useful for the design of chemical and biosensing liquid sensors.

WAVE LOCALIZATION IN RANDOMLY DISORDERED PERIODIC PIEZOELECTRIC RODS WITH INITIAL STRESS

The elastic wave localization in disordered periodic piezoelectric rods with initial stress is studied using the transfer matrix and Lyapunov exponent method. The electric field is approximated as quasi-static. The effects of the initial stress on the band gap characteristics are investigated. The numerical calculations of localization factors and localization lengths are performed. It can be observed from the results that the band structures can be tuned by exerting the suitable initial stress. For different values of the piezoelectric rod length and the elastic constant, the band structures and the localization phenomena are very different. Larger disorder degree can lead to more obvious localization phenomenon.

Strain-rate effect on initial crush stress of irregular honeycomb under dynamic loading and its deformation mechanism

The seemingly contradictory understandings of the initial crush stress of cellular materials under dynamic loadings exist in the literature, and a comprehensive analysis of this issue is carried out with using direct information of local stress and strain. Local stress/strain calculation methods are applied to determine the initial crush stresses and the strain rates at initial crush from a cell-based finite element model of irregular honeycomb under dynamic loadings. The initial crush stress under constant-velocity compression is identical to the quasi-static one, but less than the one under direct impact, i.e. the initial crush stresses under different dynamic loadings could be very different even though there is no strain-rate effect of matrix material. A power-law relation between the initial crush stress and the strain rate is explored to describe the strain-rate effect on the initial crush stress of irregular honeycomb when the local strain rate exceeds a critical value, below which there is no strain-rate effect of irregular honeycomb. Deformation mechanisms of the initial crush behavior under dynamic loadings are also explored.The deformation modes of the initial crush region in the front of plastic compaction wave are different under different dynamic loadings.

Mathematical Modelling and 3D FEM Analysis of the Influence of Initial Stresses on the ERR in a Band Crack’s Front in the Rectangular Orthotropic Thick Plate

This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initially before the loading of the crack's edge planes.The initial stretching or compressing of the plate causes uniformly distributed normal stress to appear acting in the direction which is parallel to the plane on which the band crack is located.After the appearance of the initial stress in the plate it is assumed that the crack's edge planes are loaded with additional uniformly distributed normal forces and the ERR caused with this additional loading is studied.The corresponding boundary value problem is formulated within the scope of the so-called 3D linearized theory of elasticity which allows the initial stress on the values of the ERR to be taken into consideration.Numerical results on the influence of the initial stress,anisotropy properties of the plate material,the crack’s length and its distance from the face planes of the plate on the values of the ERR,are presented and discussed.In particular,it is established that for the relatively greater length of the crack’s band,the initial stretching of the plate causes a decrease,but the initial compression causes an increase in the values of the ERR.

The Discrete-Analytical Solution Method for Investigation Dynamics of the Sphere with Inhomogeneous Initial Stresses

The paper deals with a development of the discrete-analytical method for the solution of the dynamical problems of a hollow sphere with inhomogeneous initial stresses.The examinations are made with respect to the problem on the natural vibration of the hollow sphere the initial stresses in which is caused by internal and external uniformly distributed pressure.The initial stresses in the sphere are determined within the scope of the exact equations of elastostatics.It is assumed that after appearing this static initial stresses the sphere gets a dynamical excitation and mechanical behavior of the sphere caused by this excitation is described with the so-called three-dimensional linearized equations of elastic wave propagation in initially stressed bodies.For the solution of these equations,which have variable coefficients,the discrete analytical solution method is developed and applied.In particular,it is established that the convergence of the numerical results with respect to the number of discretization is very acceptable and applicable for the considered type dynamical problems.Numerical results on the influence of the initial stresses on the values of the natural frequencies of the hollow sphere are also presented and these results are discussed.

Lateral resonances in initial stressed 1-3 piezocomposites

A theoretical analysis of the lateral resonances in 1-3 piezocomposites with poling initial stress is conducted using the Bloch wave theory. Based on the linear piezoelectricity theory, theoretical formulations that include initial stress for the propagation of acoustic plane waves are made. Numerical calculations are performed to study the effects of the initial stress on the lateral mode frequencies and the stop band. It is found that lateral mode frequencies increase with the piezoelectricity of the piezocomposites, but decrease with the poling initial stress. The influence of the initial shear stress on the lateral mode frequencies is minimal, and can thus be neglected.

Constitutive relation of weakly anisotropic polycrystal with microstructure and initial stress

Man （Nondestr Test Eval 15：191-214, 1999） derived the constitutive relation of a weakly-textured orthorhombic aggregate of cubic crystallites with effects of microstructure and initial stress. In this paper, a computational expression on the integration ∫SO（3） Q^× D^1m0dg is given. Then, by means of the computational expression, the general constitutive relation of a weakly-textured anisotropic polycrystal with the consideration of microstructure and initial stress is derived. As special cases of our general constitutive relation, two constitutive relations are given for an isotropic polycrystal and a weakly-textured anisotropic aggregate of cubic crystallites. The acoustoelastic tensor of the reference cubic crystal is derived to determine the material constants of the polycrystal. Two examples are given for understanding the physical meaning of the texture coefficients and the constitutive relations.

Crack initiation of granite under uniaxial compression tests:A comparison study

In this study,a combination of acoustic emission(AE)method(AEM)and wave transmission method(WTM)is used to investigate the behaviors of AE and ultrasonic properties corresponding to initial fracturing in granitic rocks.The relationships of AE characteristics,frequency spectra,and spatial locations with crack initiation(CI)are studied.The anisotropic ultrasonic characteristics,velocity distributions in different ray paths,wave amplitudes,and spectral characters of transmitted waves are investigated.To identify CI stress,damage initiations characterized by strain-based method(SBM),AEM and WTM are compared.For granite samples,it shows that the ratio of CI stress to peak strength estimated by SBM ranges from 0.4 to 0.55,and 0.49-0.6 by WTM,which are higher than that of AEM(0.38-0.46).The CI stress identified by AEM indicates the onset of microcracking,and the combination of AEM and WTM provides an insight into the detection of rock damage initiation and anisotropy.

Bi-stable states of initially stressed elastic cylindrical shell structures with two piezoelectric surface layers

A theoretical model is proposed in this paper to predict the bi-stable states of initially stressed cylindrical shell structures attached by surface anisotropic piezoelectric layers.The condition for existence of bi-stability of the shell structural system is presented and analytical expressions for corresponding rolled-up radii of the stable shell are given based on the principle of minimum strain energy.The resulting solution indicates that the shell system may have two stable configurations besides its initial state under a combined action of the actuating electric field and initial stresses characterized by the bending moment.If the piezoelectric layer materials act as only sensor materials without the actuating electric field,initial stresses may produce the bi-stable states,but one corresponding to its initial state.For the shell without initial stresses,the magnitude in the actuating electric field determines the number of the stable states,one or two stable configurations besides the initial state.The theoretical prediction for the bi-stable states is verified by finite element method（FEM） simulation by using the ABAQUS code.

Neuroprotective effects of atorvastatin against cerebral ischemia/reperfusion injury through the inhibition of endoplasmic reticulum stress

Cerebral ischemia triggers secondary ischemia/reperfusion injury and endoplasmic reticulum stress initiates cell apoptosis. However, the regulatory mechanism of the signaling pathway remains unclear. We hypothesize that the regulatory mechanisms are mediated by the protein kinase-like endoplasmic reticulum kinase/eukaryotic initiation factor 2α in the endoplasmic reticulum stress signaling pathway. To verify this hypothesis, we occluded the middle cerebral artery in rats to establish focal cerebral ischemia/reperfusion model. Results showed that the expression levels of protein kinase-like endoplasmic reticulum kinase and caspase-3, as well as the phosphorylation of eukaryotic initiation factor 2α, were increased after ischemia/reperfusion. Administration of atorvastatin decreased the expression of protein kinase-like endoplasmic reticulum kinase, caspase-3 and phosphorylated eukaryotic initiation factor 2α, reduced the infarct volume and improved ultrastructure in the rat brain. After salubrinal, the specific inhibitor of phosphorylated eukaryotic initiation factor 2α was given into the rats intragastrically, the expression levels of caspase-3 and phosphorylated eukaryotic initiation factor 2α in the were decreased, a reduction of the infarct volume and less ultrastructural damage were observed than the untreated, ischemic brain. However, salubrinal had no impact on the expression of protein kinase-like endoplasmic reticulum kinase. Experimental findings indicate that atorvastatin inhibits endoplasmic reticulum stress and exerts neuroprotective effects. The underlying mechanisms of attenuating ischemia/reperfusion injury are associated with the protein kinase-like endoplasmic reticulum kinase/eukaryotic initiation factor 2α/caspase-3 pathway.

Rayleigh-type wave propagation in incompressible visco-elastic media under initial stress

Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation is determined to study the effect of differ- ent types of parameters such as inhomogeneity, initial stress, wave number, phase velocity, damping factor, visco-elasticity, and incompressibility on the Rayleigh-type wave prop- agation. It is found that the affecting parameters have a significant effect on the wave propagation. Cardano＇s and Ferrari＇s methods are deployed to estimate the roots of dif- ferential equations associated with layer and semi-infinite media. The MATHEMATICA software is applied to explicate the effect of these parameters graphically.

Propagation of P-and S-waves in initially stressed gravitating half space

The present paper contributes in studying the phase velocities of P- and S-waves in a half space subjected to a compressive initial stress and gravity field. The density and acceleration due to gravity vary quadratically along the depth. The dispersion equation is derived in a closed form. It is shown that the phase velocities depend not only on the initial stress, gravity, and direction of propagation but also on the inhomogeneity parameter associated with the density and acceleration due to gravity. Various particular cases are obtained, and the results match with the classical results. Numerical investigations on the phase velocities of P- and S-waves against the wave number are made for various sets of values of the material parameters, and the results are illustrated graphically. The graphical user interface model is developed to generalize the effect.

Effect of irregularity on the propagation of torsional surface waves in an initially stressed anisotropic poro-elastic layer

The paper studies the propagation of torsional surface waves in an initially stressed anisotropic poro-elastic layer over a semi-infinite heterogeneous half space with linearly varying rigidity and density due to irregularity at the interface. The irregularity is taken in the half space in the form of a rectangle. It is observed that torsional surface waves propagate in this assumed medium. In the absence of the irregularity, the velocity equation of the torsional surface wave is also obtained. For a layer over a homogeneous half space, the velocity of torsional surface waves coincides with that of the Love waves.

Size-dependent thermoelastic initially stressed micro-beam due to a varying temperature in the light of the modified couple stress theory

The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress(MCS)theory.Although many models have been incorporated into the literature,there is still room for introducing an improved model in this context.In this work,we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity.The MCS theory is used to investigate the material length scale effects.Using the Laplace transform,the temperature,deflection,displacement,flexure moment,and stress field variables of the micro-beam are derived.The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced.The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.

Forced and Natural Vibrations of an Orthotropic Pre-Stressed Rectangular Plate with Neighboring Two Cylindrical Cavities

Forced and natural vibrations of a rectangular pre-stressed orthotropic compositeplate containing two neighboring cylindrical cavities whose cross sections are rectangularwith rounded-off corners are investigated numerically. It is assumed that all the end surfacesof the rectangular pre-stressed composite plate are simply supported and subjected to auniformly distributed normal time-harmonic force on the upper face plane. The consideredproblem is formulated within the Three-Dimensional Linearized Theory of Elastic Waves inInitially Stressed Bodies (TDLTEWISB). The influence of mechanical and geometricalparameters as well as the initial stresses and the effect of cylindrical cavities on the dynamicalcharacteristics of the rectangular orthotropic composite plate are analyzed and discussed.

Propagation of Love waves in non-homogeneous substratum over initially stressed heterogeneous half-space

The paper studies the propagation of Love waves in a non-homogeneous substratum over an initially stressed heterogeneous half-space. The dispersion equation of phase velocity is derived. The velocities of Love waves are calculated numerically as a function of kH and presented in a number of graphs, where k is the wave number, and H is the thickness of the layer. The case of Gibson＇s half-space is also considered. It is observed that the speed of Love waves is finite in the vicinity of the surface of the half-space and vanishes as the depth increases for a particular wave number. It is also observed that an increase in compressive initial stresses causes decreases of Love waves velocity for the same frequency, and the tensile initial stress of small magnitude in the half-space causes increase of the velocity.

Torsional Wave in a Dissipative Cylindrical Shell Under Initial Stresses

The dispersion relation of torsional wave in a dissipative,incompressible cylindrical shell of infinite length incorporating initial stresses effects is investigated.The governing equation and closed form solutions are derived with the aid of Biot’s principle.Phase velocity and damping of torsional wave are obtained analytically and the influences of dissipation and initial stresses are studied in details.We proposed a new method for obtaining the phase and damping velocities of torsional wave in a complex form.Numerical results analyzing the torsional wave propagation incorporating initial stress effects are analyzed and presented in graphs.The analytical and numerical solutions reveal that,the dissipation as well as the initial stresses have notable impacts on the phase velocity of torsional wave in a pre-stressed dissipative cylindrical shell.The numerical results reveal that,the initial stresses and dissipation,considerably,effect the phase velocity of the torsional wave.It has been observed that,any change in dissipation parameter(δ)produces a substantial change in damping velocity of torsional wave.In addition,it can be seen that,the phase velocity increases as the initial stress parameter increases.Finally,the result of numerical simulation illustrated the influence of dissipation and initial stresses on damping and phase velocities of torsional wave propagation.The conclusion made shown the consistency with the Biot’s incremental deformation theory,and the effective on model such as engineering mechanics and displacement of particles.

Propagation of a Thermoelastic Wave in a Half-Space of a Homogeneous Isotropic Material Subjected to the Effect of Rotation and Initial Stress

The propagation of thermoelastic waves in a homogeneous,isotropic elastic semi-infinite space is subjected to rotation and initial stress,which is at temperature T_(0)-initially,and whose boundary surface is subjected to heat source and load moving with finite velocity.Temperature and stress distribution occurring due to heating or cooling and have been determined using certain boundary conditions.Numerical results have been given and illustrated graphically in each case considered.Comparison is made with the results predicted by the theory of thermoelasticity in the absence of rotation and initial stress.The results indicate that the effect of the rotation and initial stress is very pronounced.

Dynamics of the Moving Ring Load Acting in the System“Hollow Cylinder+Surrounding Medium”with Inhomogeneous Initial Stresses

This paper studies the influence of the inhomogeneous initial stress state in the system consisting of a hollow cylinder and surrounding elastic medium on the dynamics of the moving ring load acting in the interior of the cylinder.It is assumed that in the initial state the system is compressed by uniformly distributed normal forces acting at infinity in the radial inward direction and as a result of this compression the inhomogeneous initial stresses appear in the system.After appearance of the initial stresses,the interior of the hollow cylinder is loaded by the moving ring load and so it is required to study the influence of the indicated inhomogeneous initial stresses on the dynamics of this moving load.This influence is studied with utilizing the so-called threedimensional linearized theory of elastic waves in elastic bodies with initial stresses.For solution of the corresponding mathematical problems,the discrete-analytical solution method is employed and the approximate analytical solution of these equations is achieved.Numerical results obtained within this method and related to the influence of the inhomogeneous initial stresses on the critical velocity of the moving load and on the response of the interface stresses to this load are presented and discussed.In particular,it is established that the initial inhomogeneous initial stresses appearing as a result of the action of the aforementioned compressional forces cause to increase the values of the critical velocity of the moving load.