Stress state of a piezoceramic body with a plane crack opened by a rigid inclusion

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We determine the electrostressed state of a piezoceramic medium with an arbitrarily oriented triaxial ellipsoidal inclusion under homogeneous mechanical and electric loads. Use is made of Eshelby's equivalent inclusion method generalized to the case of a piezoelectric medium. Solving the problem for a spheroidal cavity with the axis of revolution aligned with the polarization axis demonstrates the high efficiency of the approach. A numerical analysis is carried out. The stress distribution along the surface of the arbitrarily oriented triaxial ellipsoidal inclusion is studied Keywords: piezoelectric body, triaxial ellipsoidal inclusion, arbitrary orientation, generalized equivalent inclusion method, stress distribution, electric displacementIntroduction. The great many recent publications on coupled mechanical and electric fields in piezoelectric bodies are indicative of the high interest in this field of electroelasticity. The electric and stress states of piezoceramic bodies with cavities, inclusions, and cracks as stress concentrators are studied in [1-21, etc.]. The exact solution for a transversely isotropic electroelastic medium with a spheroidal cavity or inclusion can only be found if the axis of revolution of the stress concentrator is aligned with the polarization axis of the material [4,8,[16][17][18]. This solution is obtained either using the general-form solutions of the homogeneous equations of coupled electroelasticity or finding an electroelastic analog of the Eshelby tensor [5,10] for an ellipsoid of revolution, which is much easier to determine with such an orientation.The problem to be solved here is more difficult due to both geometry and orientation of the inhomogeneity. We will consider a transversely isotropic piezoelectric medium with an arbitrarily oriented triaxial ellipsoidal inhomogeneity. To solve the problem, we will use Eshelby's equivalent inclusion method generalized to the case of an electroelastic medium. The path integrals will be evaluated using Gaussian quadratures. In the particular case where the axis of revolution of the cavity is aligned with the polarization axis of the material, the numerical results agree with those obtained by other authors. We will also study the stress distribution over the surface of the triaxial ellipsoidal inhomogeneity (inclusion) with different orientations.

Section: Analysis Of Numerical Resultssupporting

confidence: 88%

Stress state of a piezoelectric elastic medium with an arbitrarily oriented triaxial ellipsoidal inclusion

Babich

Kirilyuk

2009

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“…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].…”

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confidence: 99%

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

Kaloerov

Петренко

2011

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%

“…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.…”

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confidence: 99%

Contact interaction of two compressed electroelastic half-spaces

Kirilyuk

Levchuk

2010

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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