The Stress State of a Transversally Isotropic Piezoceramic Body with a Parabolic Crack in a Uniform Heat Flow

The explicit solution is constructed for a static thermoelastic problem for an infinite transversally isotropic piezoceramic body containing a heat-insulated parabolic crack in the isotropy plane. The crack surface is assumed free of forces. The body is under a uniform heat flow, which is perpendicular to the crack surface and is far from the crack itself. The problem is solved for two cases of electric conditions on the crack surface. In the first case, an electric potential is absent on the crack surface and, in the second case, the normal component of the electric-displacement vector is equal to zero. The intensity factors, which depend on the heat flow, crack geometry, and the thermoelectroelastic properties of the piezoceramic body, are determined for the force field and electric displacement near the crack tip     

Static Equilibrium of an Elastic Orthotropic Medium with an Elliptic Crack under Bending

The static-equilibrium problem for an elastic orthotropic space with an elliptic crack is solved. The stress state of the space is represented as a superposition of the principal and perturbed states. To solve the problem, Willis' approach is used. It is based on the Fourier transform in spatial variables, the Fourier-transformed Green function for anisotropic material, and Cauchy's residue theorem. The contour integrals appearing during solution are evaluated using Gaussian quadratures. The results for particular cases are compared with those obtained by other authors. The influence of anisotropy on the stress intensity factors is studied __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 72–81, August 2005.     

Stress State of a Transversely Isotropic Ferromagnetic with an Elliptic Crack in a Homogeneous Magnetic Field

The magnetoelastic stress-strain problem for a transversely isotropic ferromagnetic body with an elliptical crack in the isotropy plane is solved explicitly. The body is in an external magnetic field perpendicular to the isotropy plane. The magnetic field induces elastic strains and an internal magnetic field in the body. The main characteristics of stress-strain state and induced magnetic field are determined and their features in the neighborhood of the crack are analyzed. Formulas for the stress intensity factors of the mechanical and magnetic fields near the crack tip are presented__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 48–59, January 2005.     

The Thermoelectroelastic State of a Transversally Isotropic Piezoceramic Body with a Spheroidal Cavity in a Uniform Heat Flow

A static thermoelectroelastic problem for an infinite transversally isotropic body containing a spheroidal cavity is explicitly solved. The symmetry axis of the spheroid coincides with the anisotropy axis of the body. It is assumed that at a rather large distance from the cavity the body is in a uniform heat flow directed along the anisotropy axis. Formulas are derived for the stress components and the projections of the electric displacement vector near the cavity, which depend on the heat-flow value, cavity geometry, and the thermoelectroelastic properties of the material. The solution of the problem for a body with a disk-like crack is obtained as a partial case from the solution of the problem for a piezoceramic body with a spheroidal cavity. The stress intensity factors for the force and electric fields are determined near the crack     

横观各向同性体中的埋藏裂纹

本文采用奇异积分方程法分析了横观各向同性体中的埋藏裂纹。建立了张开型埋藏裂纹的Cauchy型奇异积分方程。当裂纹面和弹性对称轴垂直时,得到的裂纹张开位移方程的求解与各向同性情况类似。当裂纹面和弹性对称轴平行时,根据加权余量法,建立了弱解方程。给出两个算例,计算了圆形裂纹和椭圆形裂纹上的张开位移分布。数值结果表明：本文的方法是有效的。横观各向同性体中,埋藏裂纹方位任意时的裂纹张开位移方程,根据本文的方法易于得到。     

The Edge Effect in a Laminated Composite with a Transversally Isotropic Filler

The edge effects in a laminated composite with a regular structure are considered. The equations of the linear theory of elasticity of piecewise-homogeneous media are used as a mathematical and mechanical model. An approximate solution is obtained on the basis of the mesh approach. An example of solving a specific problem is given and the results are analyzed     

Bending of Nonthin Transversally Isotropic Plates with Curvilinear Openings

The problem on the spatial stress–strain state of a nonthin transversally isotropic plate with a curvilinear nearly circular opening is considered. The plate is assumed to be subject to bending moments on the opening contour and at infinity. To solve the problem, it is proposed to make mutual use of two well-know methods — expansion of the displacement and stress components into Fourier series in Legendre polynomials of the thickness coordinate and boundary-shape perturbation. The equations and recurrent relations necessary for solution of the problem in an arbitrary approximation are presented     

Exact Analytical Solutions of Three-Dimensional Static Thermoelastic Problems for a Transversally Isotropic Body in Curvilinear Coordinate Systems

An approach to the solution of three-dimensional static thermoelastic problems for a transversally isotropic (the case of rectangular anisotropy) body is proposed. The results of construction of the general analytic solutions to thermoelastic problems for canonical bodies are systematized. The exact analytic solutions of three-dimensional problems are obtained. It is assumed that the bodies under consideration are thermoelastic and their boundary surface corresponds to the coordinate surfaces in coordinate systems that allow separating the variables in the three-dimensional Laplace equation. The stress concentration near cavities and inclusions is studied. The stress intensity factors near elliptic and hyperbolic cracks are determined. Formulas are presented for the stress intensity factors on the surface of a rigid elliptic inclusion and inside the body near a homogeneity under various thermal effects     

Short-Term Microdamageability of Fibrous Composites with Transversally Isotropic Fibers and a Microdamaged Binder

The theory of microdamageability of fibrous composites with transversally isotropic fibers and a microdamaged isotropic porous matrix is proposed. Microdamages in the matrix are simulated by pores filled with particles of the destroyed material that resist compression. The criterion of damage in the matrix microvolume is taken in the Schleicher–Nadai form. It accounts for the difference between the ultimate tensile and compressive loads. The ultimate strength is a random function of coordinates with Weibull distribution. The stress–strain state and effective properties of the material are determined from the stochastic equations of the elastic theory for a fibrous composite with porous components. The equations of deformation and microdamage are closed by the equations of porosity balance in the matrix. Nonlinear diagrams of the concurrent processes of deformation of fibrous materials and microdamage of the matrix are plotted. The effect of the physical and geometrical parameters on them is studied     

A Model of the Short-Term Damageability of a Transversally Isotropic Material

The effective deformation properties and the stress–strain state of a material are determined on the basis of the stochastic equations of elastic theory, which allow for the random nature of microdamages. The problem on the stress-strain state of a porous transversally isotropic material under uniform loading with specified strains is solved using the model proposed. To this end, a numerical–analytical algorithm is proposed. This algorithm is based on the stochastic method of conditional moment functions and the combined iteration method, which is used to solve a transcendental equation. Using this approach, as an example, a nonlinear macrodeformation diagram is plotted and the behavior of a transversally isotropic porous material under biaxial tension is studied     

General Spatial Dynamic Problem for an Elliptic Crack under the Action of a Normal Shear Wave,with Consideration for the Contact Interaction of the Crack Faces

Consideration is given to the contact interaction of the faces of a stationary plane elliptical crack under the action of a harmonic shear wave normally incident on the crack surface. The dependence of the mode II and III stress intensity factors on the wave number is studied for different values of the friction coefficient     

Stress Concentration in a Transversally Isotropic Piezoceramic Cylinder Near a Hyperboloidal Neck

The coupled electric and elastic fields near a hyperboloidal neck in a piezoceramic cylinder under static loading are studied. Uniform tensile forces and potential difference are applied to its ends. The dependences of the stress components and the projections of the electric-displacement vector near the neck on the load and the neck curvature are plotted     

Interaction of an Ellipsoidal Inclusion with an Elliptic Crack in an Elastic Material under Triaxial Tension

The interaction of an elastic ellipsoidal inclusion with an elliptic crack in an infinite elastic medium under triaxial loading is analyzed. The stress state in the elastic space is represented as a superposition of the principal state and perturbed states, which are due to the presence and interaction of the inclusion and the crack. The analytical solution of the problem is found using the method of equivalent inclusion, the potential of an inhomogeneous ellipsoid, and a system of harmonic functions for an elliptic crack. The effect of triaxial loading on the stress intensity factors is analyzed     

Volterra's Theory of Elastic Dislocations for a Transversally Isotropic Homogeneous Hollow Cylinder

This work will consider Volterra's theory of elastic dislocations in the case of a transversally isotropic homogeneous hyperelastic hollow cylinder. We obtain explicit equations for the vector field of displacements, for tensor fields of strain and stress, and for forces upon the boundary.     

Two-Phase Filtration in a Transversally Isotropic Porous Medium: Experiment and Theory

The results of an experimental determination of the relative phase permeabilities during flow of two immiscible fluids in stratified sandstone with transversally isotropic characteristics are presented. The measurements were performed on samples oriented in three directions: along, perpendicular to and at an angle of 45° to the stratification plane. An approximate solution of the problem of steady two-phase flow toward a finite gallery in an anisotropic porous medium for arbitrary relative orientation of the gallery and the principal axes of the absolute permeability tensor is given. This solution was tested against the experimental results. The good agreement between the theoretical and experimental results makes it possible to recommend for engineering calculations both the relations between the absolute and phase permeabilities for transversally isotropic and orthotropic porous media and the approximate solution obtained.     

Constitutive Equations of an Isotropic Hyperelastic Body

Stress—strain equations for an isotropic hyperelastic body are formulated. It is shown that the strain energy density whose gradient determines stresses can be defined as a function of two rather than three arguments, namely, strain–tensor invariants. In the case of small strains, the equations become relations of Hooke's law with two material constants, namely, shear modulus and bulk modulus.     

A Ring-Shaped Plastic Zone at an Elliptic Crack under Triaxial Axisymmetric Loading

The paper addresses a three-dimensional problem for an elliptic crack with a ring plastic zone under uni- and triaxial loading at infinity. The normal stresses in the plastic zone are found from the conditions that the stresses are constrained and the plane strain is local and from the yield criterion for the given material. The size of the elliptic ring is calculated by Rice's variational formula. It is shown that the constraint ratio for plastic strains under triaxial loading may be greater than that under loads close to hydrostatic tension. The contour of the plastic zone is confocal to the initial crack     

含币形裂纹的压电体在点力和点电荷作用下的裂纹张开位移

本文利用Chen和Shioya给出的在横观各向同性压电无限体内币形裂纹上下表面作用对称法向点力和点电荷情形下的解,结合压电材料之功的互等定,用初等函数的形式给出了在压电无限体中任意一点作用任意点力和点电荷情形下币形裂纹的张开位移,并对PZT－4压电陶瓷和非压电材料作了计算分析。     

Interaction of an Ellipsoidal Inclusion with an Elliptic Crack in an Elastic Medium

An approach is considered to how to allow for the interaction between an ellipsoidal heterogeneity (inclusion) and an elliptic crack in an elastic medium. Using the superposition of perturbed stress states, the boundary conditions are satisfied on the ellipsoidal surface by the method of equivalent inclusion and on the crack surface by the least-squares method. A numerical analysis is carried out. Typical mechanical effects are revealed. In the calculations, the stress state near the ellipsoidal heterogeneity is approximated by a polynomial of the second degree in Cartesian coordinates, whereas the load on the crack surface is simulated by a polynomial of the fourth degree in Cartesian coordinates. In particular cases, the results are in good agreement with the data obtained by other authors