Publication detail
The flexoelectric effect for interface cracks between two dissimilar materials
PROFANT, T. SLÁDEK, J. SLÁDEK, V.
English title
The flexoelectric effect for interface cracks between two dissimilar materials
Type
conference paper
Language
en
Original abstract
It is developed the procedure of the assessment of the amplitude factors in the asymptotic solution for the interface crack between two flexoelectric materials. The stress exponents with the appropriate eigenvectors of the regular and auxiliary solutions are evaluated from the eigenvalue problem assembled from the boundary conditions prevailing at the tip of the crack. The amplitude factors of the asymptotic solution are computed from the two-state integrals in which the regular, auxiliary, and finite element solution represent the independent equilibrium states. The obtained results show the capability of the two-state integrals to extract the dominant terms of the asymptotic solution from the weak solution of the fracture problem represented by the finite element method. The amplitude factors representing the most singular terms of the asymptotic solution at the crack tip are quantities playing an important role in the problems of crack stability criterions.
English abstract
It is developed the procedure of the assessment of the amplitude factors in the asymptotic solution for the interface crack between two flexoelectric materials. The stress exponents with the appropriate eigenvectors of the regular and auxiliary solutions are evaluated from the eigenvalue problem assembled from the boundary conditions prevailing at the tip of the crack. The amplitude factors of the asymptotic solution are computed from the two-state integrals in which the regular, auxiliary, and finite element solution represent the independent equilibrium states. The obtained results show the capability of the two-state integrals to extract the dominant terms of the asymptotic solution from the weak solution of the fracture problem represented by the finite element method. The amplitude factors representing the most singular terms of the asymptotic solution at the crack tip are quantities playing an important role in the problems of crack stability criterions.
Keywords in English
Dielectric Material, Gradient Theory, Flexoelectricity, Asymptotic Solution, Mixed FEM
Released
01.09.2023
Publisher
Materials Research Forum LLC
Location
Millersville, PA
ISBN
9781644902585
ISSN
2474-3941
Book
Advanced Topics in Mechanics of Materials, Structures and Construction AToMech1-2023
Volume
31
Edition number
31
Pages from–to
99–108
Pages count
10
BIBTEX
@inproceedings{BUT184689,
author="Tomáš {Profant} and Ján {Sládek} and Vladimír {Sládek},
title="The flexoelectric effect for interface cracks between two dissimilar materials",
booktitle="Advanced Topics in Mechanics of Materials, Structures and Construction
AToMech1-2023",
year="2023",
volume="31",
month="September",
pages="99--108",
publisher="Materials Research Forum LLC",
address="Millersville, PA",
isbn="9781644902585",
issn="2474-3941"
}