Dynamical (time-harmonic) axisymmetric interface stress field in the finite pre-strained half-space covered with the finite pre-stretched layer

Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), the dynamical (time-harmonic) stress field in the initially finite strained half-space covered with an initially and finitely stretched layer is investigated. It is assumed that on the upper free face of the covering layer the point located force which acts is harmonic with respect to time. The corresponding boundary contact problem is solved by employing the Hankel integral transformation. Moreover, it is assumed that the material of the layer and half-space are incompressible and elastic relations for those are given through the Treloar’s potential. In the case where the initial strains are absent in the layer and half-space the considered problem formulation and solution to that coincide with the corresponding ones of the classical linear theory of elasticity for an incompressible body. The algorithm for obtaining numerical results is proposed. The numerical results regarding the stresses acting on the interface plane are presented. These results are obtained for the case where the stiffness (distortion wave velocity) of the covering layer material is less (greater) than that for the half-space material. In this case, the main attention is focused on the dependencies between the values of the stresses and frequency of the external force and also the influence of the initial strains on these dependencies. In particular, it is established that the “resonance” values of the frequency of the external force increase, but the absolute maximum values of the stresses decrease significantly with the amount of the initial tension of the covering layer.     

Effect of Rotation in a Generalized Thermoelastic Medium with Hydrostatic Initial Stress Subjected to Ramp-Type Heating and Loading

The present problem is concerned with the study of deformation of a rotating generalized thermoelastic medium with a hydrostatic initial stress. A linear temperature ramping function is used to more realistically model thermal loading of the half-space surface. The components of displacement, force stress, and temperature distribution are obtained in the Laplace and Fourier domains by applying integral transforms. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating and loading. These components are then obtained in the physical domain by applying a numerical inversion method. Some particular cases are also discussed in the context of the problem. The results are also presented graphically to show the effect of rotation and hydrostatic initial stress.     

Axially-symmetric buckling of the surface of a laminated half space with bendinh stiffness

An investigation is made of conditions that admit surface-instability in a laminated half-space that is subjected to radial compressional initial stress. In the formulation of the bifurcation problem, the laminated half-space is represented as a homogeneous half-space of Cosserat material. Constitutive relations are formulated that describe the material behavior of a laminated half-space as a Cosserat continuum. Relationships are derived between the incremental moduli defined in the Cosserat continuum and the moduli of the individual layers, the lamination consisting of adhesive layers of periodically varying stiffness. The stability condition is evaluated, and results are discussed in the particular case when one type of layer is thin, in comparison to layers of the other type.     

Spherical indentation of a transversely isotropic elastic half-space reinforced with a thin layer

The frictionless spherical indentation test is considered for a transversely isotropic elastic half-space reinforced with a thin layer whose flexural stiffness is negligible compared to its tensile stiffness. It is assumed that the deformation of the reinforcing layer can be treated as the generalized plane stress state. Closed-form analytical approximate equations for the maximum contact pressure, contact radius, and contact force are presented. The isotropic case is considered in detail.     

Dislocation tri-material solution in the analysis of bridged crack in anisotropic bimaterial half-space

The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a half-space is analyzed for a general case of elastic anisotropic bimaterials and specialized for the case of orthotropic bimaterials. The edge crack lies in the surface layer of thickness h bonded to semi-infinite substrate. It is assumed that long fibres bridge the crack. Bridging model follows from the assumption of “large” slip lengths adjacent to the crack faces and neglect of initial stresses. The crack is modelled by means of continuous distribution of dislocations, which is assumed to be singular at the crack tip. With respect to the bridged crack problems in finite dissimilar bodies, the reciprocal theorem (Ψ-integral) is demonstrated as to compute, in the present context, the generalized stress intensity factor through the remote stress and displacement field for a particular specimen geometry and boundary conditions using FEM. Also the application of the configurational force mechanics is discussed within the context of the investigated problem.     

The effects of displacement discontinuity derivatives on wave propagation—III: Body and point forces in elastic half-spaces

Based on previous work, the displacements due to arbitrary body force fields in half-spaces with, respectively, traction-free and zero-displacement surfaces are derived. The expressions allow indentification of all wave components. In particular, the contributions due to the body force at the point of observation and a contribution arising essentially from the unbounded solid case can be discerned. For the special case of a point force in the half-space with a traction-free surface, this latter contribution is compared with the exact displacements on the surface. The point force is neither normal nor tangential to the surface. Agreement seems to vary directly with the depth of the point force. When the point force is on the surface, agreement seems weakest, perhaps due to the presence of Rayleigh waves in the exact solution.     

Thermal effect on gravity waves in a compressible liquid layer over a solid half-space under initial hydrostatic stress

This paper deals with the effect of temperature on gravity waves in a compressible liquid layer over a solid half-space. It has been assumed that the liquid layer is under the action of gravity, while the solid half-space is under the influence of initial compressive hydrostatic stress. When the temperature of the half-space is altered, gravity waves propagate through the liquid layer along with sub-oceanic Rayleigh waves in the system. A new frequency equation has been derived here for gravity waves and sub-oceanic Rayleigh waves. It has been shown graphically that the phase velocity of gravity waves is influenced significantly by the initial compressive hydrostatic stress present in the solid half-space, for a particular value of the phase velocity of sub-oceanic Rayleigh waves and different coupling co-efficients of the temperature.     

Reflection and transmission of plane harmonic waves at an interface between liquid and micropolar viscoelastic solid with stretch

A solution of the field equations governing small motions of a micropolar viscoelastic solid half-space with stretch is employed to study the reflection and transmission at the interface between a liquid and a micropolar viscoelastic solid with stretch. The amplitude ratios for various reflected and refracted waves are computed and depicted graphically. Effects of axial stretch and viscosity on the amplitude ratios are discussed     

On surface wave propagation in incompressible, transversely isotropic, pre-stressed elastic half-spaces

The problem of surface wave propagation for a transversely isotropic incompressible pre-stressed half-space is investigated in respect of a general in-plane fibre direction and a general angle of propagation. It is shown that the surface wave speed crucially depends on the normal static stress in the finite primary deformation. Some special cases leading to considerable simplification are pointed out. An important particular case of the fibres assumed almost inextensible is tackled both numerically and asymptotically to reveal an idealised fibre-reinforced material as a leading order approximation.     

Static deformation due to a long buried dip-slip fault in an isotropic half-space welded with an orthotropic half-space

Closed-form analytical expressions for the displacements and the stresses at any point of a two-phase medium consisting of a homogeneous, isotropic, perfectly elastic half-space in welded contact with a homogeneous, orthotropic, perfectly elastic half-space due to a dip-slip fault of finite width located at an arbitrary distance from the interface in the isotropic half-space are obtained. The Airy stress function approach is used to obtain the expressions for the stresses and the displacements. The case of a vertical dip-slip fault is considered in detail. The variations of the displacements with the distance from the fault and with depth have been shown graphically.     

Reflection of plane waves at the boundary of a pre-stressed elastic half-space subject to biaxial stretch and simple shear

This paper is concerned with the effect of finite pure homogeneous biaxial stretch together with simple shear deformation on the reflection from a plane boundary of elastic waves propagating in a half-space of incompressible isotropic elastic material. This generalizes the previous work in which, separately, pure homogeneous strain and simple shear were considered. For a special class of constitutive law, it is shown that an incident plane harmonic wave propagating in the considered plane gives rise to a surface wave in addition to a reflected wave for every angle of incidence. The amplitude of the surface wave may vanish at certain discrete angles depending on the state of stress, biaxial stretch and simple shear deformation and then specialized to recover results obtained previously. The amplitude of the reflected wave is independent of the pre-stress but does depend upon the magnitude of deformation under consideration. The dependence of the reflected and surface wave behavior on the angle of incidence, amount of shear strain, biaxial stretch and the state of stress is illustrated graphically.     

Thermo-mechanical Deformation in Magneto-micropolar Elastic Medium

The present investigation is concerned with a two-dimensional problem in electromagnetic micropolar elasticity for a half-space whose surface is subjected to distributed (concentrated or continuous) thermo-mechanical sources in the presence of a transverse magnetic field. As an application of the approach, the sources are taken as uniformly or linearly distributed. Laplace and Fourier transform techniques are used to solve the problem. The integral transforms have been inverted by using a numerical technique to obtain the components of normal strain, normal stress, tangential couple stress, and temperature distribution in the physical domain. Magnetic effects on the components of normal strain, normal stress, tangential couple stress, and temperature distribution have been depicted graphically for two different theories of generalized thermoelasticity, Lord and Shulman (L–S) theory and Green and Lindsay (G–L) theory. A particular case of interest is also deduced from the present investigation.     

Surface wave propagation in a fluid-saturated incompressible porous medium

A study of surface wave propagation in a fluid-saturated incompressible porous half-space lying under a uniform layer of liquid is presented. The dispersion relation connecting the phase velocity with wave number is derived. The variation of phase velocity and attenuation coefficients with wave number is presented graphically and discussed. As a particular case, the propagation of Rayleigh type surface waves at the free surface of an incompressible porous half-space is also deduced and discussed.     

Behavior of Rayleigh surface waves in an anisotropic media lying over a prestressed orthotropic half-space

The present paper discusses the propagation of Rayleigh waves in an anisotropic layer with finite thickness lying over a prestressed orthotropic half-space. An anisotropic media and orthotropic media are supposed for the upper layer and lower half-space, respectively. Dispersion equation and displacement components are computed in a compact form considering the case that the displacement and stress are continuous at the interface and stress vanishes on a free surface. Graphs are sketched to represent the effect of density, initial stress and height of the layer on wave velocity. The graphs are also configured to exhibit the mode of propagation of Rayleigh waves. This paper is an attempt to explain the nature of Rayleigh waves mathematically.     

The Effect of Gravity on Plane Waves in a Rotating Thermo-Microstretch Elastic Solid for a Mode-I Crack with Energy Dissipation

The present article is aimed at studying the effect of gravity on the general model of the equations of generalized thermo-microstretch for a homogeneous isotropic elastic half-space solid rotating about the fixed axis of rotation and whose surface is subjected to a Mode-I crack problem considered. The problem is in the context of the Green and Naghdi theory (GN). The normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses, and microstress distribution. The variations of the considered variables perpendicular to the axis of rotation are illustrated graphically. Comparisons are made with the results in the presence and absence of gravity and rotational frequency of a particular case for the generalized micropolar thermoelasticity elastic medium (without microstretch constants) between the two types (II, III).     

Effects of uncertainty on background permittivity in one-dimensional linear inverse scattering

We discuss the role of uncertainties in the knowledge of the background in inverse scattering for a buried object under the distorted Born approximation. In particular, we focus on the role played by inaccuracy in the knowledge of the dielectric permittivity of the host medium, with reference to both a lossless half-space and a lossless three-layered medium. This investigation allows us to show how reconstruction of an inhomogeneity in a three-layered medium is more critical than in the case of a half-space (two-layered) geometry.     

基于指数强化模型的预拉力影响角型材拉弯的回弹分析

为从理论上研究预拉力对角型材拉弯回弹的影响,采用指数强化材料模型,在分析角型材截面应力应变分布的基础上,建立了型材转台式拉弯解析模型.分析讨论了预拉力对角型材截面应力分布和加载弯矩的影响规律,并计算得到了回弹角随预拉力变化的规律曲线.与采用双线性强化材料模型的解析计算结果比较表明:采用指数强化材料模型计算的回弹结果与实...     

Mixed‐Mode Stress Intensity Factors for Partially Opened Cracks

Failure considerations under mixed-mode loading require knowledge about the influence of friction between partially closed crack faces in the case of a negative mode-I stress intensity factor. A simple relation is derived, which allowes to compute friction contributions to the mode-II stress intensity factor K_II for the case of negative mode-I stress intensity factors K_I. The relation is exact for the limit case of an edge crack in a half-space. It can be shown that small cracks in finite bodies can also be described with sufficient accuracy.     

Punch and crack problems in transversely isotropic bodies

An exact solution is proposed for the mixed boundary-value problem in a transversely isotropic half-space. Here, certain arbitrary shear tractions are prescribed inside a circular region, outside of which certain arbitrary tangential displacements are given. The normal stresses are supposed to be known all over the boundary. A particular case is considered, in detail, where normal stresses vanish all over the boundary with the shear tractions vanishing inside the circular region. A closed form expression is obtained for the tangential displacements inside the circular region directly through the displacements outside. As an example, a penny-shaped crack in an infinite transversely isotropic body is considered with arbitrary shear tractions acting on both sides of the crack. The formulae for the tangential displacements inside the circle and the shear stresses outside are obtained. Special cases where uniform shear and a concentrated tangential force arise are also discussed.