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 language | English |
|---|---|
| Pages (from-to) | 21-38 |
| Number of pages | 18 |
| Journal | Journal of the Mechanics and Physics of Solids |
| Volume | 84 |
| Early online date | 15 Jul 2015 |
| DOIs | |
| Publication status | Published - Nov 2015 |
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Keywords
- Elastostatic plane strain
- neo - Hookean elastomer
ASJC Scopus subject areas
- Mechanical Engineering
- Mechanics of Materials
- Condensed Matter Physics
Cite this
The elastostatic plane strain mode I crack tip stress and displacement fields in a generalized linear neo-Hookean elastomer. / Begley, Matthew R.; Creton, Costantino; McMeeking, Robert M.
In: Journal of the Mechanics and Physics of Solids, Vol. 84, 11.2015, p. 21-38.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - The elastostatic plane strain mode I crack tip stress and displacement fields in a generalized linear neo-Hookean elastomer
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
Y1 - 2015/11
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
UR - http://www.scopus.com/inward/record.url?scp=84938067434&partnerID=8YFLogxK
U2 - 10.1016/j.jmps.2015.07.005
DO - 10.1016/j.jmps.2015.07.005
M3 - Article
AN - SCOPUS:84938067434
VL - 84
SP - 21
EP - 38
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
SN - 0022-5096
ER -