Thermoelectroelastic state of a piezoceramic body with a spheroidal cavity in a uniform heat flow

A general approach based on complex variable theory is proposed to determine the magnetoelastic state of a body with an infinite row of elliptic inclusions under the action of magnetic and elastic fields. Numerical solutions to a two-dimensional problem for a body made of Terfenol-D magnetostrictive material and piezomagnetic ceramic material and having circular, elliptic, and rectilinear inclusions made of a different material are presented depending on the geometry of the inclusions, their material characteristics, the spacing between them, and the type of applied load Introduction. The interaction of mechanical, thermal, and electromagnetic fields is of much interest for solid mechanics [2,3,16]. This is first because of the prospective use of magnetic materials in modern electronics, engineering, and instrumentation [10] and ample opportunities for predicting and modeling the effective properties of available materials and creating new materials with prescribed magnetoelastic properties for specific structures [9,11,12,[14][15][16][17][18][19]. In studying issues of magnetoelasticity, special attention is given to the magnetoelastic state of multiply connected piezomagnetic materials. The papers [6, 13] offer a method to solve two-dimensional problems of magnetoelasticity for piezomagnetic bodies with holes and cracks and for a body with an elliptic piezomagnetic inclusion made of a different material [1], which can go over into a plane inclusion in a specific case (a rectilinear inclusion in a plate). This method is used here to solve a two-dimensional periodic problem of magnetoelasticity for a body (plate) with inclusions made of a different piezomagnetic (magnetostrictive) material.Problem Formulation. Consider a piezomagnetic matrix body with a periodic row of identical elliptic cavities with parallel generating surfaces. Inclusions of a different piezomagnetic material are soldered-in without interference into the cavities to provide perfect contact conditions. The body is subjected at infinity to constant external forces and magnetic field of constant intensity such that the matrix and inclusions are in a two-dimensional magnetoelastic state that does not vary along the generatrices of the cylindrical cavities (inclusions). Body forces, initial magnetization, and rigid-body rotations of the body as a whole and of each inclusion as a whole are absent.We choose a rectangular coordinate system Oxyz with the Oz-axis directed along the generatrices of the cylindrical cavities (inclusions). The cross-section of the piecewise-homogeneous body by the plane Oxy is a multiply connected plane S bounded by the identical and equally spaced boundaries L l ( , , , ) l = ± ± 0 1 2 K of the elliptic holes with semiaxes a and b and centers aligned along the Ox-axis (Fig. 1) and finite domains S l bounded by the boundaries L l . Denote the center-to-center

Magnetoelastic problem for a bodywith periodic elastic inclusions

Kaloerov

Boronenko

2006

Electroelastic stress state of a piezoceramic body with a paraboloidal cavity

Kirilyuk

Levchuk

2006

The static equilibrium of an electroelastic transversely isotropic space with a paraboloidal cavity under axisymmetric mechanical and electric loads is analyzed. Paraboloidal coordinates and special harmonic functions are used to obtain an exact solution. The distribution of stresses and electric-flux density over the surface of the cavity subject to internal pressure is analyzed as an example Keywords: piezoelectricity, three-dimensional problem, paraboloidal cavity, force and electric fields Introduction. Various transducers and sensors are often made of piezoceramic materials (where the mechanical and electric fields are coupled) that are highly brittle. This necessitates a detailed study of the concentration of mechanical and electric fields in electroelastic bodies with defects such as cavities, inclusions, and cracks. However, solving three-dimensional problems of electroelasticity involves significant mathematical difficulties, because the original equations of electrostressed state constitute a complicated system of partial differential equations [2,5]. This is why plane problems of electroelasticity were studied more adequately (see, e.g., [3,12,18]). These studies address both the two-dimensional electroelastic state near single cavities, inclusions, and cracks and the interaction of concentrators of electric and mechanical fields. Three-dimensional problems of electroelasticity for an infinite medium with cavities, inclusions, and cracks were solved in [1,2,7,[9][10][11][12][13][15][16][17][18][19][20][21]. The papers [7,17,20] propose approaches to find general solutions to coupled equations of electroelasticity for a transversely isotropic body. The electrostressed state and intensity factors for stress and electric-flux density in an infinite medium with penny-shaped and elliptic cracks were analyzed in [9, 10] and [14,15,17], respectively. Purely elastic problems for isotropic and transversely isotropic media with a paraboloidal inclusion were solved in [6,8].

Elastic state of a transversely isotropic piezoelectric body with an arbitrarily oriented elliptic crack

Kirilyuk

2008

The elastic stress state in a piezoelectric body with an arbitrarily oriented elliptic crack under mechanical and electric loads is analyzed. The solution is obtained using triple Fourier transform and the Fourier-transformed Green's function for an unbounded piezoelastic body. Solving the problem for the case of a crack lying in the isotropy plane, for which there is an exact solution, demonstrates that the approach is highly efficient. The distribution of the stress intensity factors along the front of a crack in a piezoelectric body under uniform mechanical loading is analyzed numerically for different orientations of the crack Keywords: piezoelasticity, flat elliptical crack, arbitrary orientation, stress intensity factor, electric-field intensity factorIntroduction. Use of piezoceramic materials, which are quite brittle, in creating various transducers necessitates a detailed study into the concentration of mechanical and electric fields in electroelastic bodies with defects such as cavities, inclusions, and cracks. However, solving three-dimensional problems of electroelasticity involves certain mathematical difficulties because the original equations of electrostressed state constitute a complicated coupled system of differential equations [1,4]. Plane problems of electroelasticity are addressed in [11,13,14,22,26], which analyze the two-dimensional electroelastic state near single cavities, inclusions, cracks and the interaction of stress concentrators in electric and mechanical fields. Similar approaches are proposed in [5,23] to construct general solutions to the coupled equations of electroelasticity for transversely isotropic bodies and to find the exact solutions to some problems of electroelasticity for a special orientation of the polarization axis of the ceramic body. It was usually assumed that the polarization axis is aligned with the axis of revolution of the stress concentrator or is perpendicular to the crack plane [6, 8-12, 16-24, 26]. With other orientations of the polarization axis, these approaches appeared inefficient in solving three-dimensional problems. The results on stress intensity factors (SIFs) for circular and elliptic cracks in elastic media are detailed in [3,7,15,25]. Similar studies for electroelastic bodies (with the same assumption as to the polarization axis) are conducted in [6, 8-10, 16-18, 21]. The SIFs for a circular crack arbitrarily oriented relative to the polarization axis of the piezoceramic material are analyzed in [2].The present paper extends the studies [2, 25] to an electroelastic material. To solve the problem, we will use the triple Fourier transform, Fourier-transformed Green's function for an electroelastic anisotropic medium, and Cauchy's residue theorem. The special contour integrals arising during the solution will be evaluated using Gaussian quadratures. In special cases, the results obtained will be compared with data obtained by other methods. The intensity factors for stresses and electric-flux density at the front of an elliptic crack will be cal...