Plane problem of thermoelectromagnetoelasticity for multiply connected bodies

A problem of thermoelectroelasticity for a piezoelectric material with a plane crack of arbitrary shape in a symmetric heat flow from the crack surfaces is solved. The crack is in a plane perpendicular to the polarization axis. We establish a correspondence between the stress intensity factor (SIF) and electric displacement intensity factor (EDIF) for a piezoelectric material with a plane crack and the SIF for a thermoelastic isotropic material with a crack of the same shape under the same thermal load. This correspondence allows finding the SIF and EDIF for an electroelastic material from the solution of the thermoelastic problem. The SIF and EDIF for a penny-shape crack (for different cases of thermal loading) and a half-plane crack are found as examples Keywords: thermoelectroelasticity, transversely isotropic material, plane crack of arbitrary shape, stress intensity factor, electrical displacement intensity factorIntroduction. In studying the distribution of mechanical and electric fields in piezoceramic bodies with cavities, inclusions, and cracks under mechanical, electric, and thermal loads [10,14,15,17,24], it is necessary to take into account the properties of new piezoelectric materials.General solutions of the system of coupled equations of electroelasticity in the three-dimensional case [9, 13, 23] were used in [10,14,[18][19][20][21][22] to solve some problems of electroelasticity for a piezoceramic body with cavities, inclusions, and cracks. The stress intensity factor (SIF) and electric displacement intensity factor (EDIF) for an electroelastic body with disk-shaped and elliptic cracks were studied in [1,10,[18][19][20][21][22]. The thermostressed state of elastic isotropic and transversely isotropic bodies with a disk-shaped or elliptic crack was analyzed in [6,7,11,16], and the thermoelectrostressed state of a piezoceramic body having an elliptic crack with homogeneous and linear temperature on its surface was studied in [20,22]. General patterns of variation in the SIF in a piezoceramic body having a plane crack of arbitrary shape with known temperature on its surfaces were established in [20]. Data on the SIFs for cracks in elastic bodies under mechanical and thermal loads can be found in the monographs [7,8,12,16].Numerous results for prestressed bodies with cracks are presented in [4]. Guz [2][3][4] was the first to use the correspondence between the solution for transversely isotropic prestressed bodies under mechanical loads and the solution for elastic isotropic bodies.We extend the approach of [2-4] to the case of coupled mechanical and electric fields in piezoceramic bodies with plane cracks under thermal loading. Note that the studies [18][19][20] are also based on the ideas of [2-4] but do not give any references to [2][3][4]. We will establish a correspondence between the SIF and EDIF for a piezoceramic body having a plane crack of arbitrary shape in the isotropy plane and subject to a symmetric heat flow from the crack surfaces and the SIF for a purely elastic isotropic body with a ...

Section: Problem-solving Methodmentioning

confidence: 99%

“…In studying the distribution of mechanical and electric fields in piezoceramic bodies with cavities, inclusions, and cracks under mechanical, electric, and thermal loads [10,14,15,17,24], it is necessary to take into account the properties of new piezoelectric materials.…”

mentioning

confidence: 99%

Thermostressed state of a piezoceramic body with a plane crack in a symmetric heat flow from its surfaces

Kirilyuk

2010

“…The dependence of the EMES on the geometrical parameters of a strip with a circular hole or a crack is analyzed Introduction. In the recent decades, the electromagnetoelastic state (EMES) of piezomaterials in various electric and magnetic fields has been studied intensively [1,[9][10][11][12][13][14][15][16]. The fundamentals of electro-and magnetoelasticity and solutions of partial problems are discussed in [1, 10].…”

mentioning

confidence: 99%

Problems of electromagnetoelasticity for a half-plane and a strip with holes and cracks

Kaloerov

Петренко

2011

Self Cite

The methods of complex potentials, conformal mappings, Cauchy integrals, and least-squares are used to develop a method for determining the electromagentoelastic state (EMES) of a multiply connected half-plane, with the boundary conditions on the straight-line boundary satisfied exactly. The method underlies an approximate method for determining the EMES of a strip with arbitrarily arranged holes and cracks. The dependence of the EMES on the geometrical parameters of a strip with a circular hole or a crack is analyzed Introduction. In the recent decades, the electromagnetoelastic state (EMES) of piezomaterials in various electric and magnetic fields has been studied intensively [1,[9][10][11][12][13][14][15][16]. The fundamentals of electro-and magnetoelasticity and solutions of partial problems are discussed in [1, 10]. In [3], methods for solving two-dimensional and plane problems of electro-and magnetoelasticity for piezoelectric bodies with holes, cracks, and inclusions are presented and problems of electroelasticity (magnetoelasticity) for multiply connected half-planes and strips are solved.In the present paper, these methods are extended to multiply connected electromagnetoelastic half-planes and strips [7,8].1. Problem for Half-Plane. Consider a multiply connected anisotropic lower half-plane S bounded by a straight-line boundary L + and the boundaries of elliptic holes L l ( , ) l = 1 L (Fig. 1). The boundaries of the holes can go over into cracks,

“…Methods for solving three-dimensional contact problems for elastic bodies were developed in [2, 3, 10, etc.]. The wide use of piezoceramic materials, which are very fragile, necessitates detailed study of the distribution of mechanical and electric fields in electroelastic bodies near cavities, inclusions, cracks, punches [5,[8][9][10][12][13][14][15][16][17][18][19][20]. However, the solution of three-dimensional problems of electroelasticity involves certain mathematical difficulties because the original system of equations for determining the electric and strain states is a complex coupled system of differential equations [5] (see [9,11] for its general solutions).…”

mentioning

confidence: 99%

Contact interaction of two compressed electroelastic half-spaces

Kirilyuk

Levchuk

2010

The contact interaction of two compressed electroelastic transversely isotropic half-spaces with different properties is studied. One of the half-spaces has an axisymmetric notch of special shape. The contact plane coincides with the plane of isotropy of the half-spaces. Explicit formulas for the contact pressure, displacements, and the size of the gap between piezoelectric half-spaces are derived. These contact characteristics for transversely isotropic and isotropic elastic half-spaces are obtained as special cases Keywords: transversely isotropic electroelastic half-space, piezoceramic body, axisymmetric notch, elastic and electric fields Introduction. Methods for solving three-dimensional contact problems for elastic bodies were developed in [2, 3, 10, etc.]. The wide use of piezoceramic materials, which are very fragile, necessitates detailed study of the distribution of mechanical and electric fields in electroelastic bodies near cavities, inclusions, cracks, punches [5,[8][9][10][12][13][14][15][16][17][18][19][20]. However, the solution of three-dimensional problems of electroelasticity involves certain mathematical difficulties because the original system of equations for determining the electric and strain states is a complex coupled system of differential equations [5] (see [9,11] for its general solutions). Specific contact problems for electroelastic bodies were solved in [8, 9, 14, etc.]. Two-dimensional contact problems for bodies with notches were addressed in [6].The paper [4] was the first to propose to solve contact problems by using the correspondence between the solution for prestressed transversely isotropic bodies and the solution for elastic isotropic bodies. The review [1] presents results on numerous contact problems for prestressed bodies.The present paper applies the approach of [4] to the case of electroelastic half-spaces. Note that the studies [16][17][18][19] are also based on the ideas of [4] but do not give any reference to [4]. We will study the contact interaction (without friction) of two electroelastic transversely isotropic half-spaces with different properties. One of them has an axisymmetric notch of special shape, and the interface between the half-spaces coincides with the plane of isotropy. We will derive explicit expressions for the contact pressure, displacements, and the size of the gap between the electroelastic half-spaces. The contact characteristics for transversely isotropic and isotropic elastic half-spaces follow from these expressions as special cases [7].1. Problem Formulation. Let us consider two transversely isotropic electroelastic half-spaces, one (body 1) being bounded by the plane z = 0, and the other (body 2) containing a shallow axisymmetric notch of shape described by the expression