Detail publikačního výsledku

Asymptotic solution for crack in orthotropic material and strain gradient elasticity

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

Originální název

Asymptotic solution for crack in orthotropic material and strain gradient elasticity

Anglický název

Asymptotic solution for crack in orthotropic material and strain gradient elasticity

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

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

Vydáno

17.04.2026

Nakladatel

Elsevier

Periodikum

European journal of mechanics, A, Solids

Svazek

119

Číslo

April

Stát

Francouzská republika

Strany od

1

Strany do

23

Strany počet

23

URL

https://www.sciencedirect.com/science/article/pii/S0997753826001464?via%3Dihub

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"
}