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Shot peen forming is a process widely used to shape aircraft components such as wing skins, yet its fundamental working is still crudely understood. It is understood that a light conventional peen forming treatment applied uniformly over an initially flat plate will induce isotropic in‐plane stretching of the surface layer and will thus lead to a panel curving with identical curvatures in all directions. However, [1] made the startling observation that uniformly peen formed aluminium plates of different aspect ratios all bent along their laminating direction irrespective of the peening direction. This experimental result is counterintuitive because the residual stresses due to the lamination process are 1 order to 2 orders of magnitude smaller than those induced by the shot peen forming treatment. In the present study, we apply the eigenstrain theory to estimate the effect of the different sources of anisotropy on uniformly peen formed aluminium plates. Potential sources of anisotropy included the plastic anisotropy of rolled aluminium, nonequibiaxial initial stresses that redistribute when their equilibrium is disturbed by peening, the geometry of the specimens and externally applied prestress. For the alloy and peening conditions considered, we show that plastic anisotropy had no discernible influence on the resulting shape of the peen formed specimens. Initial residual stresses, on the other hand, caused slightly larger bending loads in the rolling direction of the alloy. Although the magnitude of these loads was approximately 30 times smaller than peening‐induced loads, it was sufficient to overcome the geometric preference for rectangular sheets to bend along their long side and cause all unconstrained specimens to bend along the rolling direction instead. Our analysis highlights the importance of the history of the material that is being peened. Residual stresses already present in the part before peening must be considered to ensure good simulation predictions. [ABSTRACT FROM AUTHOR]

Present geophysical model analyzes the propagation characteristics of torsional wave in an inhomogeneous viscoelastic fiber‐reinforced layer sandwiched between superior porous layer and transversely isotropic piezoelectric subspace with imperfect interfaces. Porous layer and intermediate reinforced layer are endowed with initial stress and corrugated interfaces, whereas the lower piezoelectric half space possesses rectangular cavity at the welded contact. Earth's adjacent layers near mountainous region often endowed with initial stresses resemble the present geological setup. The material properties of intermediate layer are considered to be varying exponentially. Particular cases have been deduced for electrically open and short condition for validation with the standard Love wave expressions. Effects of the relevant parameters on resultant torsional velocity have been explored through numerical simulation and depicted for electrically short and open conditions. Findings of present model may be utilized in the field of signal testing, sensors design, seismic acoustic wave (SAW) devices, and geophysical application concerned with torsional wave based on non‐destructive evaluation. [ABSTRACT FROM AUTHOR]

Rocks in the upper mantle are extensively subjected to initial stress. The rock exhibits elastic anisotropy under the deviatoric stress, which affects the seismic response of underground structures. This paper aims to study the effect of stress‐induced anisotropy on the seismic source. The seismic moment tensor generated by a shear faulting in a homogeneous isotropic medium with initial stress is derived by using the motion description in the intermediate configuration, the constitutive relation of third‐order elasticity, and the boundary condition considering the effect of initial stress. Then the seismic moment tensor is decomposed to investigate seismic source characters quantitatively. Our results show that shear faulting in a stress‐induced anisotropic medium can produce significant non‐double‐couple (non‐DC) mechanisms, including compensated linear vector dipole (CLVD) and isotropic (ISO) components. ISO and CLVD components vary linearly with the initial shear stress on faults. In addition, stress‐induced anisotropy causes the double‐couple (DC) to deviate from the plane defined by the fault normal and slip direction. The initial stress not only affects the source intensity but also affects the propagation of seismic waves. The radiation patterns of longitudinal waves have non‐uniform lobes, which shows the characteristic of anisotropy. Stress‐induced anisotropic parameters are smaller than intrinsic anisotropy at high‐stress levels and a nearly linear function of the increased initial stress. These results underscore the importance of considering stress‐induced anisotropy in the inversion of focal mechanisms and provide a new perspective for monitoring underground stress. Plain Language Summary: Because of the Earth's gravity and crustal movement, underground rocks are subjected to three different principal stresses. The accumulation of tectonic stress is often associated with the occurrence of earthquakes. Getting a state of underground stress may help us determine whether an earthquake is likely to occur in a region. We use the third‐order elastic theory, in which the strain energy contains the cubic term of strain, and use Lagrangian boundary conditions to describe the seismic source modeled by a tangential sliding fault. The intensity of seismic sources caused by slipping faults can be characterized by seismic moment tensors. We decompose the tensors into isotropic, double‐couple, and compensated linear vector dipole components, and these components are closely related to the stress on the fault plane. Our results show that a shear faulting in stressed media may exhibit a tensile effect. The initial stress affects the source intensity and shape of radiation and affects the propagation of seismic waves. In addition, the symmetry of the stressed medium is also closely related to the initial stress. Future studies may use our work to obtain stress states in the focal region from the source information. Key Points: The incremental Piola‐Kirchhoff stress described in the intermediate state is discontinuous across the fault plane under initial stressNon‐double‐couple components generated by a shear fault in stressed media are linearly related to the initial shear stress on the fault planeThe initial stress causes the inhomogeneity of P‐wave radiation patterns and affects the travel time and amplitude of seismic waves [ABSTRACT FROM AUTHOR]

Aluminium skins on the lower wings of most commercial aircraft are shaped using shot peen forming. This process, which involves bombarding the skins with hard shot, uses nonuniform plastic flow to induce curvatures—in the same way that differential expansion makes metal bilayers bend when heated. Here, we investigate experimentally how constraining conditions affect the final shape of peen formed parts. We report peen forming experiments for 4.9‐mm‐thick rectangular 2024–T3 aluminium sheets of different aspect ratios uniformly shot peened on one face with a low intensity saturation treatment. Some specimens were free to deform during peening while others were elastically prestressed in a four‐point bending jig. For each aspect ratio and prestress condition, residual stresses were measured near the peened surface with the hole drilling method. Additional residual stress profiles were also obtained with the slitting method. The residual stress measurements show that the progressive deformation of unconstrained specimens had the same effect as an externally applied prestress. For the peening conditions investigated, this progressive deformation caused unconstrained strips to exhibit curvatures 33% larger than identical strips held flat during peening. Furthermore, we found that the relative importance of material anisotropy and geometric effects did determine the bending direction of unconstrained specimens. [ABSTRACT FROM AUTHOR]

Using a thermal shock of the ramp type, the authors constructed a unique mathematical three‐phase‐lag scheme in a compressed rotating isotropic homogeneous micropolar thermo‐viscoelastic medium. The model is applied to solve an issue of an exactly performing half‐space exposed to defined boundary circumstances with an electromagnetic field. Normal mode analysis and Lame's potentials methods were used to obtain the analytical answers. The authors were interested in studying the effect of the initial stress, ramp time, magnetic field, and rotation on distributing, displacement, temperature, and stress, as well as induced electric and magnetic distribution. The findings showed that the impact of the viscous, ramp parameter, rotation, phase lag, magnetic field, and initial stress on the micropolar thermo‐viscoelastic medium is distinct. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a volume fraction, electromagnetic field, photothermal, and initial stress impact on a homogeneous isotropic semiconducting generalized thermoelasticity solid. Three generalized thermoelasticity theories are considered: classical dynamical (CD), Lord and Shulman (LS), and dual‐phase‐lags (DPL). The equations governing the problem are presented considering the voids, photothermal, semiconducting, initial stress, and parameters concerning the theory of thermoelasticity in a generalized form. We applied the normal mode technique analysis to solve the algebraic system of equations in this phenomenon under suitable boundary conditions. The results showed that the photothermal, voids as a volume fraction, process of semiconductor, electromagnetic field, thermal relaxation times, and initial stress have a significant impact on the phenomenon. The physical quantities with some analytical comparisons are introduced analytically and displayed in graphs. A comparison was made between the obtained results and the works presented by others. If the volume fraction, electromagnetic field, and initial stress are neglected, the results obtained are deduced to Abo‐Dahab and Lotfy as a special case from the present study. The results obtained with neglecting the external parameters, viz, electromagnetic field, initial stress, voids, and phase lags, and considering the Laplace transform technique agree with the results of other works. [ABSTRACT FROM AUTHOR]

In this paper, the propagation of harmonic plane waves is considered in a generalized thermoelastic medium with diffusion and voids in the presence of initial stress, magnetic field, rotation, and gravity in the context of thermoelastic models; classical, Lord Shulman, Green Lindsay as well as dual‐phase‐lag models. We applied the boundary conditions in the physical domain using the normal mode method technique on the surface to obtain the displacements, stresses, temperature, diffusion concentration, and the volume fraction field. Influence of initial stress, magnetic field, rotation, and gravity on temperature, stresses, concentration of diffusion, and the volume fraction is observed through a numerical example. The results obtained will be compared in the presence and absence of the new considered variables, also with the previous results obtained by the others and displayed graphically. [ABSTRACT FROM AUTHOR]

An analytical solution has been attained to establish the closed form expression of stress intensity factor at the tip of a semi-infinite crack, dynamically propagating in an initially stressed transversely isotropic poroelastic strip due to Love-type wave for the case of concentrated force of constant intensity as well as for the case of constant load. The study presents the sound effect of various affecting parameters viz. speed of the crack, length of the crack, horizontal compressive/tensile initial stress, vertical compressive/tensile initial stress, porosity parameter and anisotropy parameter on the stress intensity factor. In order to delineate the effects of these aforementioned parameters on the stress intensity factor graphically, numerical simulations have been accomplished. One of the major highlight of the paper is the comparative study carried out for horizontal compressive/tensile initial stress, vertical compressive/tensile initial stress, porosity parameter and anisotropy parameter with the case when the strip is isotropic, non-porous and free from initial stresses. Wiener-Hopf technique and the Fourier integral transform has been effectuated for the procurement of the closed form expression (exact solution) of stress intensity factor. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the influence of initial stress on the frequency equation of flexural waves in a transversely isotropic circular cylinder permeated by a magnetic field. The problem is represented by the equations of elasticity taking into account the effect of the magnetic field as given by Maxwell's equations in the quasi-static approximation. The free stress conditions on the inner and outer surfaces of the hollow circular cylinder were used to form a frequency equation in terms of the wavelength, the cylinder radii, the initial stress and the material constants. The frequency equations have been derived in the form of a determinant involving Bessel functions and its roots given the values of the characteristic circular frequency parameters of the first three modes for various geometries. These roots, which correspond to various modes, have been verified numerically and represented graphically in different values for the initial stress. It is recognized that the flexural elastic waves in a solid body propagated under the influence of initial stress can be differentiated in a clear manner from those propagated in the absence of an initial stress. We also observed the initial stress has a great effect on the propagation of magnetoelastic flexural waves. Therefore this research is theoretically useful to convey information on electromagnetic properties of the material: for example through a precise measurement of the surface current induced by the presence of the magnetic field. [ABSTRACT FROM AUTHOR]

The well-known Hencky solution is only applicable to the problem of deformation of the elastic circular membrane without initial stress under transverse uniformly-distributed loads. The problem considered here is a more general case: an initial tensile or compressive stress has been present in the initially flat circular membrane before the membrane is subjected to the transverse loads. The closed-form solution of the considered problem was presented and all the expressions obtained here for displacements, strains and stresses have the same form as those in the well-known Hencky solution. The initial stress plays an important role in the determination of numerical value of the integral constant controlling membrane equation. The solution obtained here can be regressed into the well-known Hencky solution when the initial stress is equal to zero, and it is therefore called extended Hencky solution. [ABSTRACT FROM AUTHOR]

The paper presents a study of propagation of shear wave (SH-wave) in an orthotropic elastic medium under initial stress sandwiched by a homogeneous semi-infinite medium and an inhomogeneous half-space. The technique of separation of variables has been adopted to get the analytical solutions for the dispersion relation in a closed form. The propagation of SH-waves is influenced by inhomogeneity parameters and initial stress parameter. Velocities of SH-waves are calculated numerically for different cases. As a special case when the intermediate layer and half-space are homogeneous, computed frequency equation coincides with general equation of Love wave. To study the effect of inhomogeneity parameters and initial stress parameter, we have plotted the velocity of SH-wave in several figures and observed that the velocity of wave decreases with the increases of non-dimensional wave number. It can be found that the phase velocity decreases with the increase of inhomogeneity parameters. We observed that the velocity of SH-wave decreases with the increases of initial stress parameter in both homogeneous and inhomogeneous media. GUI has been developed by using MATLAB to generalize the effect of the parameters discussed. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Experimental investigation of repeated impacts on aluminium plates is performed using drop weights impacting from either constant or variable heights. In repeated impacts of constant and variable heights, the effect of plasticity is noticeable on the specimens in the very first impact. The effect of strain hardening is observed at higher impact numbers. Stiffness of plates is decreased by initiation and propagation of cracks in the specimens. Finally, perforation and penetration occur at the ultimate consecutive impacts. Numerical simulations of repeated impacts are also conducted using continuum damage mechanics by Abaqus software. Lemaitre's model is used as the damage model, and the code is written in Vumat subroutine. The effect of initial uniaxial and biaxial tensile stress on the plates is considered in repeated impacts, and it is concluded that plates with initial tensile uniaxial stress at transverse edges have maximum values of contact force and absorbed energy. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, the propagation of Love waves in a fiber-reinforced layered medium lying over an elastic orthotropic half-space under initial stress has been investigated. We have obtained the velocity equations for Love wave in this media. It is observed that propagation of Love wave is influenced by reinforced parameters and initial stressed parameter. The velocity of Love wave has been computed for three different cases. Our computed equation of Love wave coincides with the standard equation of Love wave for the case of homogeneous layer and homogeneous half-space (AEH Love, 1911). To study the effect of reinforced and initial stressed parameters, we have computed the numerical values for phase velocity and plotted in several figures. It is observed that the phase velocity decreases with the increases of reinforced parameters and initial stressed parameter. Using MATLAB software, GUI has been developed to generalize the effect of various parameters. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Within the framework of the piecewise homogeneous body model and through the application of the three-dimensional linearized theory of elastic waves in an initially stressed body, the torsional wave dispersion in pre-stretched bi-material compounded cylinders is investigated. It is assumed that the elasticity relations of the materials of the components of the cylinders are given through the Murnaghan potential. The numerical investigations are made for steel (St) (as a material for the solid cylinder) and bronze (Br) (as a material for a hollow covering cylinder). According to the numerical results obtained, the influence of the problem parameters such as the initial stresses in the components of the bi-material compounded cylinder, the values of the mechanical and physical constants of the components, and the geometrical parameters (such as the relation of the thickness of the covering cylinder with the radius of the inner solid cylinder on the dispersion curves) are analyzed. [ABSTRACT FROM AUTHOR]

A new method for the in vivo characterization of the physical properties of skin is presented. This comprises an ultrasound device to measure the vertical displacement of the surface of the skin, as well as its thickness and that of the hypodermis under suction. In combination with this, a mathematical model is used to calculate the following skin parameters: Young’s modulus, the initial stress and an index of non-elasticity. These parameters were evaluated from the volar forearm and the forehead of 30 male and 30 females, of similar ages (28 ± 6-years-old). The sensitivity of the testing procedure, allowing the characterization of the mechanical parameters of the skin, easily differentiated these two sites, and in some cases, differences between women and men were demonstrated. The main results showed for both sexes that the thickness (P = 0.0001), Young’s modulus (P = 0.0001), and the index of non-elasticity (P = 0.0001) were greater for the forehead than for the ventral forearm, but that the initial stress was lower (P = 0.0001). The results show that the skin is thicker, stiffer and less tense and elastic on the forehead than on the ventral forearm, suggesting structural differences between these two sites (collagen fibre network, elastic fibres, epidermis, stratum corneum, microvascularization, actinic damage, presence of sebaceous glands, etc.). It is hoped that this device will be useful for the evaluation of certain skin disorders (scleroderma, Ehlers–Danlos syndrome, cutis laxa, oedema, etc.) and their therapy, as well as being a useful tool in skin ageing and cosmetic product assessment. [ABSTRACT FROM AUTHOR]