In this paper, an analytical method for seeking the solution of a static crack problem in a piezoelectric medium biaxially loaded at infinity is illustrated. A transformation of similarity is induced by the 6x6 fundamental matrix in order to express the equations governing the problem in terms of complex potentials. The application of the boundary conditions leads then to the formulation of a Hilbert problem whose solution allows to obtain the generalized stress and displacement components. Incipient branching angle, through the maximum hoop stress criterion, and Energy Release Rates are also investigated. Permeable, impermeable and semipermeable crack cases are all taken into account. Numerical results and graphs are presented and discussed for different materials and loading conditions, with particular highlight given to the influence of different ratios between remote loads on fracture quantities.

Analytical Formulation by Means of Complex Potentials of Crack Models in a Piezoelectric Material

TORNABENE, FRANCESCO;VIOLA, ERASMO
2007

Abstract

In this paper, an analytical method for seeking the solution of a static crack problem in a piezoelectric medium biaxially loaded at infinity is illustrated. A transformation of similarity is induced by the 6x6 fundamental matrix in order to express the equations governing the problem in terms of complex potentials. The application of the boundary conditions leads then to the formulation of a Hilbert problem whose solution allows to obtain the generalized stress and displacement components. Incipient branching angle, through the maximum hoop stress criterion, and Energy Release Rates are also investigated. Permeable, impermeable and semipermeable crack cases are all taken into account. Numerical results and graphs are presented and discussed for different materials and loading conditions, with particular highlight given to the influence of different ratios between remote loads on fracture quantities.
Materiali e Metodi Innovativi nell’Ingegneria Strutturale
1
16
C. Boldrini; F. Tornabene; E. Viola
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/48618
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