Modeling fracture in the context of a strain-limiting theory of elasticity: a single anti-plane shear crack

Handle URI:
http://hdl.handle.net/10754/598854
Title:
Modeling fracture in the context of a strain-limiting theory of elasticity: a single anti-plane shear crack
Authors:
Rajagopal, K. R.; Walton, J. R.
Abstract:
This paper is the first part of an extended program to develop a theory of fracture in the context of strain-limiting theories of elasticity. This program exploits a novel approach to modeling the mechanical response of elastic, that is non-dissipative, materials through implicit constitutive relations. The particular class of models studied here can also be viewed as arising from an explicit theory in which the displacement gradient is specified to be a nonlinear function of stress. This modeling construct generalizes the classical Cauchy and Green theories of elasticity which are included as special cases. It was conjectured that special forms of these implicit theories that limit strains to physically realistic maximum levels even for arbitrarily large stresses would be ideal for modeling fracture by offering a modeling paradigm that avoids the crack-tip strain singularities characteristic of classical fracture theories. The simplest fracture setting in which to explore this conjecture is anti-plane shear. It is demonstrated herein that for a specific choice of strain-limiting elasticity theory, crack-tip strains do indeed remain bounded. Moreover, the theory predicts a bounded stress field in the neighborhood of a crack-tip and a cusp-shaped opening displacement. The results confirm the conjecture that use of a strain limiting explicit theory in which the displacement gradient is given as a function of stress for modeling the bulk constitutive behavior obviates the necessity of introducing ad hoc modeling constructs such as crack-tip cohesive or process zones in order to correct the unphysical stress and strain singularities predicted by classical linear elastic fracture mechanics. © 2011 Springer Science+Business Media B.V.
Citation:
Rajagopal KR, Walton JR (2011) Modeling fracture in the context of a strain-limiting theory of elasticity: a single anti-plane shear crack. International Journal of Fracture 169: 39–48. Available: http://dx.doi.org/10.1007/s10704-010-9581-7.
Publisher:
Springer Nature
Journal:
International Journal of Fracture
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
6-Jan-2011
DOI:
10.1007/s10704-010-9581-7
Type:
Article
ISSN:
0376-9429; 1573-2673
Sponsors:
The work of KRR on this publication was partially supported by the Office of Naval Research, while the work of JRW was supported in part by the Air Force Office of Scientific Research and by Award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorRajagopal, K. R.en
dc.contributor.authorWalton, J. R.en
dc.date.accessioned2016-02-25T13:42:30Zen
dc.date.available2016-02-25T13:42:30Zen
dc.date.issued2011-01-06en
dc.identifier.citationRajagopal KR, Walton JR (2011) Modeling fracture in the context of a strain-limiting theory of elasticity: a single anti-plane shear crack. International Journal of Fracture 169: 39–48. Available: http://dx.doi.org/10.1007/s10704-010-9581-7.en
dc.identifier.issn0376-9429en
dc.identifier.issn1573-2673en
dc.identifier.doi10.1007/s10704-010-9581-7en
dc.identifier.urihttp://hdl.handle.net/10754/598854en
dc.description.abstractThis paper is the first part of an extended program to develop a theory of fracture in the context of strain-limiting theories of elasticity. This program exploits a novel approach to modeling the mechanical response of elastic, that is non-dissipative, materials through implicit constitutive relations. The particular class of models studied here can also be viewed as arising from an explicit theory in which the displacement gradient is specified to be a nonlinear function of stress. This modeling construct generalizes the classical Cauchy and Green theories of elasticity which are included as special cases. It was conjectured that special forms of these implicit theories that limit strains to physically realistic maximum levels even for arbitrarily large stresses would be ideal for modeling fracture by offering a modeling paradigm that avoids the crack-tip strain singularities characteristic of classical fracture theories. The simplest fracture setting in which to explore this conjecture is anti-plane shear. It is demonstrated herein that for a specific choice of strain-limiting elasticity theory, crack-tip strains do indeed remain bounded. Moreover, the theory predicts a bounded stress field in the neighborhood of a crack-tip and a cusp-shaped opening displacement. The results confirm the conjecture that use of a strain limiting explicit theory in which the displacement gradient is given as a function of stress for modeling the bulk constitutive behavior obviates the necessity of introducing ad hoc modeling constructs such as crack-tip cohesive or process zones in order to correct the unphysical stress and strain singularities predicted by classical linear elastic fracture mechanics. © 2011 Springer Science+Business Media B.V.en
dc.description.sponsorshipThe work of KRR on this publication was partially supported by the Office of Naval Research, while the work of JRW was supported in part by the Air Force Office of Scientific Research and by Award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSpringer Natureen
dc.subjectElasticityen
dc.subjectImplicit theoriesen
dc.subjectMode III fractureen
dc.titleModeling fracture in the context of a strain-limiting theory of elasticity: a single anti-plane shear cracken
dc.typeArticleen
dc.identifier.journalInternational Journal of Fractureen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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