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Some theorems of incremental thermoelectroelasticity

100%

Montanaro A.

Archives of Mechanics

2010

tom Vol. 62, nr 1

49-72

We extend to incremental thermoelectroelasticity with biasing fields certain classical theorems, which have been stated and proved in linear thermopiezoelectricity referred to a natural configuration. A uniqueness theorem for the solutions to the initial boundary value problem, the generalized Hamilton principle and the theorem of reciprocity of work are deduced for incremental fields, superposed on finite biasing fields in a thermoelectroelastic body.

On 3D anticrack problem of thermoelectroelasticity

100%

Kaczyński A.

Acta Mechanica et Automatica

2018

tom Vol. 12, no. 2

109--114

A solution is presented for the static problem of thermoelectroelasticity involving a transversely isotropic space with a heat-insulated rigid sheet-like inclusion (anticrack) located in the isotropy plane. It is assumed that far from this defect the body is in a uniform heat flow perpendicular to the inclusion plane. Besides, considered is the case where the electric potential on the anticrack faces is equal to zero. Accurate results are obtained by constructing suitable potential solutions and reducing the thermoelectromechanical problem to its thermomechanical counterpart. The governing boundary integral equation for a planar anticrack of arbitrary shape is obtained in terms of a normal stress discontinuity. As an illustration, a closed-form solution is given and discussed for a circular rigid inclusion.

An interface anticrack in a periodic two-layer piezoelectric space under vertically uniform heat flow

58%

Kaczyński A. , Kaczyński B.

2018

tom Vol. 22, nr 3

667--681

This paper aims to investigate 3D static thermoelectroelastic problem of a uniform heat flow in a bi-material periodically layered space disturbed by a thermally and electrically-insulated rigid sheet-like inclusion (so-called anticrack) situated at one of the interfaces. An approximate analysis of the considered laminated composite is given in the framework of the homogenized model with microlocal parameters. Accurate results are obtained by constructing suitable potential solutions and reducing to the corresponding homogeneous thermoelectromechanical (or thermomechanical) anticrack problems. The governing boundary integral equation for a planar interface anticrack of arbitrary shape is derived in terms of a normal stress discontinuity. As an illustration, a complete solution for a rigid circular inclusion is obtained in terms of elementary functions and interpreter from the failure perspective. Unlike existing solutions for defects at the interface of materials, the solution obtained displays no oscillatory behavior.