A Magnetoelastic Field in a Ferromagnetic with an Elliptic Inclusion

A stress–strain problem is solved for an infinite isotropic magnetically soft body containing an elliptic inclusion. It is assumed that the body is in an external magnetic field. The basic characteristics of the stress–strain state and the induced magnetic field are determined and their features at the inclusion are analyzed. Graphs are drawn for the total magnetoelastic and Maxwell stresses versus the ratio of the ellipse axes and the angle of dip, and tabular maximum stresses versus the magnetic induction and the magnetic properties of the material.     

A Magnetoelastic Field in a Ferromagnetic Medium with a Spherical Cavity

The problem on the stress–strain state of an infinite isotropic body made of a magnetically soft material and containing a spherical cavity is considered. It is assumed that the body is under an external magnetic field. The basic characteristics of the stress–strain state and the magnetic field induced are determined and their singularities near the cavity are studied. Graphs are presented for the total magnitoelastic and Maxwell stresses as functions of the magnetic induction, the angle of dip, and the mechanical and magnetic properties of the material     

The Stress State of a Transversely Isotropic Ferromagnetic with a Parabolic Crack in a Homogeneous Magnetic Field

The magnetoelastic problem for a transversely isotropic ferromagnetic body with a parabolic crack in the plane of isotropy is solved explicitly. The body is in an external magnetic field, which is perpendicular to the plane of isotropy. The field induces elastic strains and a magnetic field in the body. The characteristics of the stress–strain distribution and induced magnetic field are determined; and their singularities 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     

The Stress State of a Ferromagnetic with a Spheroidal Inclusion in a Homogeneous Magnetic Field

The stress–strain state of an infinite isotropic magnetically soft ferromagnetic body with a spheroidal inclusion is analyzed. It is assumed that the body is in an external magnetic field. The basic stress–strain characteristics and the induced magnetic field near and inside the inclusion are analyzed. The plots and the table presented show how the total magnetoelastic and Maxwell stresses near and inside the inclusion depend on the ratio of the spheroid axes, the latitude angle, and the magnetic induction when the medium and the inclusion are dissimilar materials.     

Stress–Strain State of a Ferromagnetic with a Paraboloidal Inclusion in a Homogeneous Magnetic Field

The stress–strain state of an infinite elastic soft ferromagnetic medium with an elliptic paraboloidal inclusion is analyzed. The material of the inclusion is a soft ferromagnetic too. The medium is in a magnetic field directed along the minor axis of the elliptic section of the paraboloid by a plane perpendicular to its axis. The main characteristics of the stress–strain state and induced magnetic fields in the medium and inclusion are determined. The features of the stress distribution over the inclusion boundary are studied     

Stress Concentration in a Soft Ferromagnetic with an Elliptic Inclusion in a Homogeneous Magnetic Field

The paper addresses a stress–strain problem for an infinite soft ferromagnetic body with an elliptic inclusion. The body is in a homogeneous magnetic field B ₀₁. The basic stress–strain characteristics and induced magnetic field in the body and inclusion are determined and their features in the neighborhood of the inclusion are studied. The magnetoelastic and Maxwell stresses are plotted against the ratio of ellipse axes and the latitude angle. Maximum stresses versus magnetic induction and mechanical and magnetic properties of the material are tabulated     

The Stress–Strain State of an Elastic Ferromagnetic Medium with an Ellipsoidal Inclusion in a Homogeneous Magnetic Field

A stress–strain problem is solved for an infinite elastic magnetically soft medium with an ellipsoidal inclusion in an external magnetic field. The main characteristics of the stress–strain state and induced magnetic fields in the medium and the inclusion are determined and their distribution over the surface of the inclusion is analyzed     

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.     

Stability of Plates with an Oblique Edge Crack under Tension

The stress–strain state and local buckling of thin plates with an oblique edge crack are studied. An expression for critical stresses is derived     

Influence of Variable Thickness on Displacements and Stresses in Nonthin Cylindrical Orthotropic Shells with Elliptic Cross-Section

The influence of varying thickness at constant mass on the stress–strain state of orthotropic cylindrical shells with elliptic cross-section is analyzed by solving two-dimensional boundary-value problems     

Elastoplastic state of flexible spherical shells with a reinforced elliptic hole

The elastoplastic state of a thin spherical shell weakened by an elliptic hole is analyzed. Finite deflections are considered. The hole is reinforced with a thin ring. The shell is made of an isotropic homogeneous material. The load is internal pressure. A relevant problem is formulated and solved numerically with allowance for physical and geometrical nonlinearities. The distribution of stresses, strains, and displacements along the elliptic boundary and in the zone of their concentration is studied. The stress–strain state of the shell near the hole is analyzed Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 93–101, December 2008.     

A Note on the Iterative Solution of Stress Problems for Plates and Shallow Shells

A technique based on a refined iterative theory and the numerical method of local variations is developed and used to determine the stress–strain state of transversely isotropic shallow shells and plates. All the components of the stress–strain state and boundary-layer effects are taken into account. The solutions are analyzed for accuracy and convergence.     

Magnetoelastic fracture of soft ferromagnetic materials

Effects of magnetic field on fracture toughness of soft ferromagnetic materials were studied using experimental techniques and theoretical models. The manganese–zinc ferrite with a single-edge-notch-beam (SENB) were chosen to be the specimen and the Vickers’ indentation specimen subjected to a magnetic field were chosen to be the specimens. Results indicate that there is no significant variations of the measured fracture toughness of the manganese–zinc ferrite ceramic in the presence of the magnetic field. The theoretical model involves an anti-plane shear crack with finite length in an infinite magnetostrictive body where an in-plane magnetic field prevails at infinity. Magnetoelasticity is used. The crack-tip elastic field is different from that of the classical mode III fracture problem. Furthermore, the magnetoelastic fracture of the soft ferromagnetic material was studied by solving the stress field for a soft ferromagnetic plane with a center-through elliptical crack. The stress field at the tip of a slender elliptical crack is obtained for which only external magnetic field normal to the major axis of the ellipse is applied at infinity. The results indicate that the near field stresses are governed by the magnetostriction and permeability of the soft ferromagnetic material. The induction magnetostrictive modulus is a key parameter for finding whether magnetostriction or magnetic-force-induced deformation is dominant near the front an elliptically-shaped crack. The influence of the magnetic field on the apparent toughness of a soft ferromagnetic material with a crack-like flaw can be regarded approximately in two ways: one possesses a large induction magnetostrictive modulus and the other has a small modulus. Finally, a small-scale magnetic-yielding model was developed on the basis of linear magnetization to interpret the experimental results related to the fracture of the manganese–zinc ferrite ceramics under magnetic field. Studied also is the fracture test of the soft ferromagnetic steel with compact tension specimens published in the existing literature.     

Magneto-electro-elastic antiplane analysis of a bimaterial BaTiO3–CoFe2O4 composite wedge with an interface crack

The antiplane analysis is made for a bimaterial BaTiO₃–CoFe₂O₄ composite wedge containing an interface crack. The coupled magneto-electro-elastic field is induced by the piezoelectric/piezomagnetic BaTiO₃–CoFe₂O₄ composite materials. For the crack problems, the intensity factors of stress, strain, electric displacement, electric field, magnetic induction and magnetic field at crack tips are derived analytically. Also, the energy density criterion is applied to predict the fracture behavior of the interface crack. The numerical results also show that the energy release rate for a crack in a single wedge is negative.     

Axisymmetric Dynamic Problem of Coupled Thermoviscoplasticity

An axisymmetric dynamic thermoviscoelastic problem is formulated with allowance for the coupling of mechanical and thermal fields. The behavior of the material is described by the Bodner–Partom model. A technique for numerical solution of the problem is developed. The laws governing the stress–strain state and the temperature field of a circular disk under forced flexural vibrations are studied     

Triaxial compressive behavior of rock with mesoscopic heterogenous behavior: Strain energy density factor approach

The strain energy density factor approach is used in conjunction with a micromechanics model to investigate the condition and direction of shear failure for brittle rock subjected to triaxial compression. Moderate confinement in addition to localized deformation and damage are considered. Quantified are the effects of the various geometric and load parameters that involve the interaction of microcrack, friction and the confining pressure such that the path of the wing crack is taken into account. The influence of all microcracks with different orientations are introduced into the constitutive relation. The closed-form solution for the complete stress–strain relation of rock containing microcracks is obtained. It is shown that the complete stress–strain relationship includes linear, nonlinear hardening, rapid stress drop and strain softening effects. The theoretical results show that deviation of the direction of wing cracks from the line of the pre-existing crack decreases with increasing confinement pressure and friction coefficient. Theoretical predictions and experimental results show good agreement.     

Rolling of a Rigid Cylinder over a Half-Plane with Initial Stresses (Harmonic and Bartenev–Khazanovich Potentials)

An asymmetric quasistationary problem for a prestressed half-plane with harmonic and Bartenev–Khazanovich potentials is solved based of the linearized theory of elasticity. The Mehler–Fock integral transform is used to solve the differential equations that describe the stress–strain state of the half-plane. The dependences of the normal and tangential stresses and stress intensity factors on the elongation are plotted     

Contact Stress Distribution Under a Rigid Cylinder Rolling Over a Prestressed Strip

A nonsymmetric quasistationary problem for a strip with initial stresses is solved under the linearized theory of elasticity for harmonic and Bartenev–Khazanovich potentials. The Hankel integral transform is used to solve the differential equations that describe the stress–strain state of the strip. The dependences of the normal and tangential stresses and stress intensity factors on the elongation are plotted     

Thermoelastoplastic Nonaxisymmetric Stress-Strain Analysis of Laminated Shells of Revolution

A technique for nonaxisymmetric thermoelastoplastic stress–strain analysis of laminated shells of revolution is developed. It is assumed that there is no slippage and the layers are not separated. The problem is solved using the geometrically linear theory of shells based on the Kirchhoff–Love hypotheses. The thermoplastic relations are written down in the form of the method of elastic solutions. The order of the system of partial differential equations obtained is reduced by means of trigonometric series in the circumferential coordinate. The systems of ordinary differential equations thus obtained are solved by Godunov's discrete-orthogonalization method. The nonaxisymmetric thermoelastoplastic stress–strain state of a two-layered shell is analyzed as an example     

Elastic–plastic near field solution of an eccentric crack under shear in a finite width plate

The near crack line analysis method is used to investigate an eccentric crack loaded by shear forces in a finite width plate, and the analytical solution is obtained in this paper. The solution includes: the unit normal vector of the elastic–plastic boundary near the crack line, the elastic–plastic stress fields near crack line, variations of the length of the plastic zone along the crack line with an external loads, and the bearing capacity of a finite plate with a centric crack loaded by shear stress in the far field. The results obtained in this paper are sufficiently precise near the crack line because the assumptions of small scale yielding theory have not been made and no other assumptions have been taken. Subsequently, the present results are compared with the traditional line elastic fracture mechanical solutions and elastoplastic near field solutions under small scale yielding condition. On the basis of the minimum strain energy density (SED) theory, the minimum values of SED in the vicinity of the crack tip are determined, the initial growth orientation of crack are determined. It is found that the normalized load under large scale yielding condition is higher than those under small scale yielding condition when the length of the plastic zone is the same.