Asymptotics of ‘stress intensity factors’ for solutions to wave equation at a crack tip close to external boundary

Abstract

The wave equation is considered, for all times $t\in \mathbb{R}$, in a bounded plane domain $G_{ϵ}$ with an internal crack. The distance from one of the crack tips to the external boundary of $G_{ϵ}$ is proportional to a small parameter $ϵ>0$. Dirichlet or Neumann condition is given on the whole boundary of $G_{ϵ}$. Near the crack tip, the first derivatives of solutions have square-root ($\sim r^{-1/2}$) singularities. The asymptotics of the ‘stress intensity factors’ of such singularities are deduced as $ϵ\to 0$.

Keywords:

• Wave equation
• singularly perturbed domains
• stress intensity factors

AMS CLASSIFICATIONS:

• 35B25
• 35B40
• 35LO5

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

The work was supported by the Russian Science Foundation [grant number 17-11-01126].