Journal article
Singularities at the tip of a crack on the interface of piezoelectric bodies



Publication Details
Authors:
Specovius-Neugebauer, M.; Nazarov, S.
Publication year:
2009
Journal:
Journal of Mathematical Sciences
Pages range:
524-540
Journal acronym:
J. Math. Sci (NY)
Volume number:
159
ISSN:
1072-3374
eISSN:
1573-8795

Abstract
Singularities of elastic and electric fields are investigated at the tip of a crack on the interface of two anisotropic piezoelectric media under various boundary conditions on the crack surfaces. The singularity exponents form the spectrum of a certain polynomial pencil, and although explicit formulas are not available, this spectrum is described completely though. The mathematical results apply to problems in fracture mechanics. In this way the Griffith formulas are obtained for increments of energy functionals due to the growth of the crack, and the notion of energy release matrix is introduced. Normalization conditions for bases of singular solutions are proposed to adapt them to energy, stress, and deformation fracture criteria. Connections between these bases are determined, and additional properties of the deformation basis related to the notion of electric surface enthalpy are established


Research Areas


Last updated on 2019-25-07 at 11:26