The elastostatic plane strain mode I crack tip stress and displacement fields in a generalized linear neo-Hookean elastomer

Matthew R. Begley, Costantino Creton, Robert M. McMeeking*

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A general asymptotic plane strain crack tip stress field is constructed for linear versions of neo-Hookean materials, which spans a wide variety of special cases including incompressible Mooney elastomers, the compressible Blatz-Ko elastomer, several cases of the Ogden constitutive law and a new result for a compressible linear neo-Hookean material. The nominal stress field has dominant terms that have a square root singularity with respect to the distance of material points from the crack tip in the undeformed reference configuration. At second order, there is a uniform tension parallel to the crack. The associated displacement field in plane strain at leading order has dependence proportional to the square root of the same coordinate. The relationship between the amplitude of the crack tip singularity (a stress intensity factor) and the plane strain energy release rate is outlined for the general linear material, with simplified relationships presented for notable special cases.

Original languageEnglish
Pages (from-to)21-38
Number of pages18
JournalJournal of the Mechanics and Physics of Solids
Volume84
Early online date15 Jul 2015
DOIs
Publication statusPublished - Nov 2015

Fingerprint

elastostatics
plane strain
crack tips
elastomers
Elastomers
Crack tips
stress distribution
Elasticity
strain energy release rate
stress intensity factors
Energy release rate
cracks
Strain energy
Stress intensity factors
configurations
Cracks

Keywords

  • Elastostatic plane strain
  • neo - Hookean elastomer

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

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title = "The elastostatic plane strain mode I crack tip stress and displacement fields in a generalized linear neo-Hookean elastomer",
abstract = "A general asymptotic plane strain crack tip stress field is constructed for linear versions of neo-Hookean materials, which spans a wide variety of special cases including incompressible Mooney elastomers, the compressible Blatz-Ko elastomer, several cases of the Ogden constitutive law and a new result for a compressible linear neo-Hookean material. The nominal stress field has dominant terms that have a square root singularity with respect to the distance of material points from the crack tip in the undeformed reference configuration. At second order, there is a uniform tension parallel to the crack. The associated displacement field in plane strain at leading order has dependence proportional to the square root of the same coordinate. The relationship between the amplitude of the crack tip singularity (a stress intensity factor) and the plane strain energy release rate is outlined for the general linear material, with simplified relationships presented for notable special cases.",
keywords = "Elastostatic plane strain, neo - Hookean elastomer",
author = "Begley, {Matthew R.} and Costantino Creton and McMeeking, {Robert M.}",
note = "Date of Acceptance: 06/07/2015 Acknowledgment This work was commenced while RMM was supported by Laboratoire PPMD at ESPCI Paris Tech for a research visit, which is gratefully acknowledged. MRB gratefully acknowledges the support of the National Science Foundation, through Award CMII 1063714.",
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AU - Begley, Matthew R.

AU - Creton, Costantino

AU - McMeeking, Robert M.

N1 - Date of Acceptance: 06/07/2015 Acknowledgment This work was commenced while RMM was supported by Laboratoire PPMD at ESPCI Paris Tech for a research visit, which is gratefully acknowledged. MRB gratefully acknowledges the support of the National Science Foundation, through Award CMII 1063714.

PY - 2015/11

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N2 - A general asymptotic plane strain crack tip stress field is constructed for linear versions of neo-Hookean materials, which spans a wide variety of special cases including incompressible Mooney elastomers, the compressible Blatz-Ko elastomer, several cases of the Ogden constitutive law and a new result for a compressible linear neo-Hookean material. The nominal stress field has dominant terms that have a square root singularity with respect to the distance of material points from the crack tip in the undeformed reference configuration. At second order, there is a uniform tension parallel to the crack. The associated displacement field in plane strain at leading order has dependence proportional to the square root of the same coordinate. The relationship between the amplitude of the crack tip singularity (a stress intensity factor) and the plane strain energy release rate is outlined for the general linear material, with simplified relationships presented for notable special cases.

AB - A general asymptotic plane strain crack tip stress field is constructed for linear versions of neo-Hookean materials, which spans a wide variety of special cases including incompressible Mooney elastomers, the compressible Blatz-Ko elastomer, several cases of the Ogden constitutive law and a new result for a compressible linear neo-Hookean material. The nominal stress field has dominant terms that have a square root singularity with respect to the distance of material points from the crack tip in the undeformed reference configuration. At second order, there is a uniform tension parallel to the crack. The associated displacement field in plane strain at leading order has dependence proportional to the square root of the same coordinate. The relationship between the amplitude of the crack tip singularity (a stress intensity factor) and the plane strain energy release rate is outlined for the general linear material, with simplified relationships presented for notable special cases.

KW - Elastostatic plane strain

KW - neo - Hookean elastomer

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