Asymptotic solution of the elasticity equations in the vicinity of an elliptical crack front

Yaron Schapira; Zohar Yosibash

doi:10.1016/j.engfracmech.2019.106774

Asymptotic solution of the elasticity equations in the vicinity of an elliptical crack front

Yaron Schapira, Zohar Yosibash^*

^*Corresponding author for this work

School of Mechanical Engineering

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

The asymptotic solution of the elasticity equations in the vicinity of an elliptical singular edge is derived and presented explicitly for an elliptical crack with traction free BCs. It is composed of edge stress intensity functions (ESIFs), which are functions along the singular edge, eigenfunctions and their shadows. The recursive equations to derive the eigenfunctions and their shadows are provided. The explicit presentation of the series is required to identify the different quantities of interest as the ESIFs and the T-stresses and allows the extension of the quasi dual function method for the extraction of the ESIFs along elliptical singular edge. We also present the dual eigenfunctions needed to extract K_I in the case of an elliptical crack with traction free BCs.

Original language	English
Article number	106774
Journal	Engineering Fracture Mechanics
Volume	223
DOIs	https://doi.org/10.1016/j.engfracmech.2019.106774
State	Published - Jan 2020

Keywords

3-D singularities
Elliptical crack
Stress intensity functions

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10.1016/j.engfracmech.2019.106774

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title = "Asymptotic solution of the elasticity equations in the vicinity of an elliptical crack front",

abstract = "The asymptotic solution of the elasticity equations in the vicinity of an elliptical singular edge is derived and presented explicitly for an elliptical crack with traction free BCs. It is composed of edge stress intensity functions (ESIFs), which are functions along the singular edge, eigenfunctions and their shadows. The recursive equations to derive the eigenfunctions and their shadows are provided. The explicit presentation of the series is required to identify the different quantities of interest as the ESIFs and the T-stresses and allows the extension of the quasi dual function method for the extraction of the ESIFs along elliptical singular edge. We also present the dual eigenfunctions needed to extract KI in the case of an elliptical crack with traction free BCs.",

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doi = "10.1016/j.engfracmech.2019.106774",

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AU - Schapira, Yaron

AU - Yosibash, Zohar

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N2 - The asymptotic solution of the elasticity equations in the vicinity of an elliptical singular edge is derived and presented explicitly for an elliptical crack with traction free BCs. It is composed of edge stress intensity functions (ESIFs), which are functions along the singular edge, eigenfunctions and their shadows. The recursive equations to derive the eigenfunctions and their shadows are provided. The explicit presentation of the series is required to identify the different quantities of interest as the ESIFs and the T-stresses and allows the extension of the quasi dual function method for the extraction of the ESIFs along elliptical singular edge. We also present the dual eigenfunctions needed to extract KI in the case of an elliptical crack with traction free BCs.

AB - The asymptotic solution of the elasticity equations in the vicinity of an elliptical singular edge is derived and presented explicitly for an elliptical crack with traction free BCs. It is composed of edge stress intensity functions (ESIFs), which are functions along the singular edge, eigenfunctions and their shadows. The recursive equations to derive the eigenfunctions and their shadows are provided. The explicit presentation of the series is required to identify the different quantities of interest as the ESIFs and the T-stresses and allows the extension of the quasi dual function method for the extraction of the ESIFs along elliptical singular edge. We also present the dual eigenfunctions needed to extract KI in the case of an elliptical crack with traction free BCs.

KW - 3-D singularities

KW - Elliptical crack

KW - Stress intensity functions

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Asymptotic solution of the elasticity equations in the vicinity of an elliptical crack front

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Keywords

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