Publication detail

Assessment of amplitude factors of asymptotic expansion at crack tip in flexoelectric solid under mode I and II loadings

PROFANT, T. SLÁDEK, J. SLÁDEK, V. KOTOUL, M.

English title

Assessment of amplitude factors of asymptotic expansion at crack tip in flexoelectric solid under mode I and II loadings

Type

journal article in Web of Science

Language

en

Original abstract

The direct flexoelectric effect is a consequence of the polarization of the material, which is proportional to the strain gradients. The strain gradients are prominent near material defects, especially at the crack tips, where the flexoelectric effect redistributes the stress field and consequently influences the crack propagation. The flexoelectricity is a size dependent effect, i.e. it depends on an internal material length parameter as the additional material characteristic. This fact makes the equilibrium, constitutive, and boundary equations complicated as well as the asymptotic solution at the crack tip contrary to the asymptotic solution in the linear elastic fracture mechanics. The matched asymptotic expansion method is applied to derive the expressions for the amplitude factors that appear in the flexoelectric asymptotic solution for the crack as functions of the stress intensity factors in the loadings of mode I or mode II. The application of the matched asymptotic expansion method is conditioned by the knowledge of the so-called boundary layer, which is evaluated from the energetic criteria at the crack tip.

English abstract

The direct flexoelectric effect is a consequence of the polarization of the material, which is proportional to the strain gradients. The strain gradients are prominent near material defects, especially at the crack tips, where the flexoelectric effect redistributes the stress field and consequently influences the crack propagation. The flexoelectricity is a size dependent effect, i.e. it depends on an internal material length parameter as the additional material characteristic. This fact makes the equilibrium, constitutive, and boundary equations complicated as well as the asymptotic solution at the crack tip contrary to the asymptotic solution in the linear elastic fracture mechanics. The matched asymptotic expansion method is applied to derive the expressions for the amplitude factors that appear in the flexoelectric asymptotic solution for the crack as functions of the stress intensity factors in the loadings of mode I or mode II. The application of the matched asymptotic expansion method is conditioned by the knowledge of the so-called boundary layer, which is evaluated from the energetic criteria at the crack tip.

Keywords in English

Direct flexoelectricity; Gradient theory; Crack; Asymptotic expansion; And amplitude factors

Released

01.05.2023

Publisher

PERGAMON-ELSEVIER SCIENCE LTD

Location

OXFORD

ISSN

1879-2146

Volume

269

Number

1.5.2023

Pages from–to

112194–112194

Pages count

22

BIBTEX


@article{BUT184016,
  author="Tomáš {Profant} and Ján {Sládek} and Vladimír {Sládek} and Michal {Kotoul},
  title="Assessment of amplitude factors of asymptotic expansion at crack tip in flexoelectric solid under mode I and II loadings",
  year="2023",
  volume="269",
  number="1.5.2023",
  month="May",
  pages="112194--112194",
  publisher="PERGAMON-ELSEVIER SCIENCE LTD",
  address="OXFORD",
  issn="1879-2146"
}