Publication detail

Asymptotic solutions for interface cracks between two dissimilar flexoelectric materials

PROFANT, T. SLÁDEK, J. SLÁDEK, V.

English title

Asymptotic solutions for interface cracks between two dissimilar flexoelectric materials

Type

journal article in Web of Science

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 represents 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 represents 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

01.05.2023

Publisher

TAYLOR & FRANCIS INC

Location

PHILADELPHIA

ISSN

1537-6494

Number

22.6.2023

Pages from–to

112194–112194

Pages count

15

BIBTEX


@article{BUT184018,
  author="Tomáš {Profant} and Ján {Sládek} and Vladimír {Sládek} and Michal {Kotoul},
  title="Asymptotic solutions for interface cracks between two dissimilar flexoelectric materials",
  year="2023",
  number="22.6.2023",
  month="May",
  pages="112194--112194",
  publisher="TAYLOR & FRANCIS INC",
  address="PHILADELPHIA",
  issn="1537-6494"
}