Publication detail

Asymptotic solution for crack in orthotropic material and strain gradient elasticity

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

English title

Asymptotic solution for crack in orthotropic material and strain gradient elasticity

Type

WoS Article

Language

en

Original abstract

The asymptotic solution for the displacement and stress fields at the tip of the crack in homogeneous orthotropic material governed by the strain gradient elasticity based on the simplified Mindlin's Form II gradient theory is derived. The Lekhnitskii-Eshelby-Stroh (LES) formalism is applied and generalized to the fracture problem in the strain gradient elasticity for an orthotropic material. The expressions for the displacements and stress functions are derived. According to the LES formalism, the Cauchy type stresses and double stresses are expressed as the partial derivatives of the stress functions. The stress singularity exponent is evaluated from the condition of the stress-free crack faces at its tip and consequently it is derived the expression for the J-integral. The particular components of the asymptotic solutions for the displacements and the Cauchy type stresses are discussed as well as the strong singular auxiliary force tractions in front of the crack. The influence of the material symmetry orientation with respect to the crack plane orientation is shown.

Keywords in English

gradient elasticity; crack; asymptotic solution; Leknitskii-Eshelby-Stroh formalism;

Released

2026-04-17

Publisher

Elsevier

Journal

European journal of mechanics, A, Solids

Volume

119

Number

April

Pages from–to

1–23

Pages count

23

BIBTEX


@article{BUT211670,
  author="Tomáš {Profant} and Miroslav {Hrstka} and  {} and  {} and Michal {Kotoul}",
  title="Asymptotic solution for crack in orthotropic material and strain gradient elasticity",
  journal="European journal of mechanics, A, Solids",
  year="2026",
  volume="119",
  number="April",
  pages="1--23",
  doi="10.1016/j.euromechsol.2026.106160",
  issn="0997-7538",
  url="https://www.sciencedirect.com/science/article/pii/S0997753826001464?via%3Dihub"
}