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1

Boundary element modeling of pyroelectric solids with shell inclusions

Sulym H., Pasternak I., Pasternak V.

Mechanics and Mechanical Engineering

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2018

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Vol. 22, nr 3

727--737

EN

The paper presents general boundary element approach for analysis of thermoelectroelastic (pyroelectric) solids containing shell-like electricity conducting permittive inclusions. The latter are modeled with opened surfaces with certain boundary conditions on their faces. Rigid displacement and rotation, along with constant electric potential of inclusions are accounted for in these boundary conditions. Formulated boundary value problem is reduced to a system of singular boundary integral equations, which is solved numerically by the boundary element method. Special attention is paid to the field singularity at the front line of a shell-like inclusion. Special shape functions are introduced, which account for this square-root singularity and allow accurate determination of field intensity factors. Numerical examples are presented.

2

Anti – plane crack emanating from the interface in a bounded smart PEMO- elastic structure

Rogowski B.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 4

1165--1199

EN

The magnetoelectroelastic analysis of two bonded dissimilar piezo-electro-magneto-elastic ceramics with a crack perpendicular to and terminating at the interface is made. By using the Fourier integral transform (in perpendicular directions in each materials), the mixed boundary conditions and continuity conditions are transformed to a singular integral equation with generalized Cauchy kernel, the solution of which has been well studied, and classical methods are directly applicable here to obtain the closed form solution. The results are presented for a permeable crack under anti-plane shear loading and in-plane electric and magnetic loadings, as prescribed electric displacement and magnetic inductions or electric and magnetic fields. The results indicate that the magnetoelectroelastic field near the crack tip in the homogeneous PEMO- elastic ceramic is dominated by a traditional inverse square-root singularity, while the coupled field near the crack tip at the interface exhibits the singularity of the power law r--α , r being the distance from the interface crack tip and α depending on the material constants of a bimaterial. In particular, electric and magnetic fields have no singularity at the crack tip in a homogeneous solid, whereas they are singular around the interface crack tip. Numerical results are given graphically to show the effects of the material properties on the singularity order, field intensity factors and energy release rates. The results presented in this paper should have potential applications to the design of multilayered magnetoelectroelastic structures.

3

Analysis of mode I conducting crack in piezo-electro-magneto-elastic layer

Rogowski B.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 1

153--176

EN

Within the theory of linear magnetoelectroelasticity, the fracture analysis of a magneto - electrically dielectric crack embedded in a magnetoelectroelastic layer is investigated. The prescribed displacement, electric potential and magnetic potential boundary conditions on the layer surfaces are adopted. Applying the Hankel transform technique, the boundary - value problem is reduced to solving three coupling Fredholm integral equations of second kind. These equations are solved exactly. The corresponding semi - permeable crack - face magnetoelectric boundary conditions are adopted and the electric displacement and magnetic induction of crack interior are obtained explicitly. This field inside the crack is dependent on the material properties, applied loadings, the dielectric permittivity and magnetic permeability of crack interior, and the ratio of the crack length and the layer thickness. Field intensity factors are obtained as explicit expressions.

4

Fracture analysis of a mode I magneto-electrically conducting crack in piezo-electro-magneto-elastic medium

Rogowski B.

International Journal of Applied Mechanics and Engineering

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2012

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Vol. 17, no. 4

1267-1295

EN

Within the theory of linear magnetoelectroelasticity, the fracture analysis of a magneto electrically conducting crack embedded in a magneto electro elastic medium is investigated. The prescribed normal stress and two cases of electromagnetic boundary conditions applied at infinity are adopted. Applying the Hankel transform technique, the boundary value problem is reduced to solving three pairs of dual coupling integral equations. These equations are solved exactly. The corresponding semi permeable crack face magneto electric boundary conditions are adopted and the electric displacement and magnetic induction of the crack interior are obtained explicitly. This field inside the crack is dependent on the material properties, applied loadings and the dielectric permittivity and magnetic permeability of the crack interior. Field intensity factors are obtained as explicit expressions.