Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials

Handle URI:
http://hdl.handle.net/10754/599343
Title:
Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials
Authors:
Mihai, L. A.; Goriely, A.
Abstract:
Motivated by recent experiments on biopolymer gels whereby the reverse of the usual (positive) Poynting effect was observed, we investigate the effect of the so-called 'adscititious inequalities' on the behaviour of hyperelastic materials subject to shear. We first demonstrate that for homogeneous isotropic materials subject to pure shear, the resulting deformation consists of a triaxial stretch combined with a simple shear in the direction of the shear force if and only if the Baker-Ericksen inequalities hold. Then for a cube deformed under pure shear, the positive Poynting effect occurs if the 'sheared faces spread apart', whereas the negative Poynting effect is obtained if the 'sheared faces draw together'. Similarly, under simple shear deformation, the positive Poynting effect is obtained if the 'sheared faces tend to spread apart', whereas the negative Poynting effect occurs if the 'sheared faces tend to draw together'. When the Poynting effect occurs under simple shear, it is reasonable to assume that the same sign Poynting effect is btained also under pure shear. Since the observation of the negative Poynting effect in semiflexible biopolymers implies that the (stronger) empirical inequalities may not hold, we conclude that these inequalities must not be imposed when such materials are described. © 2011 The Royal Society.
Citation:
Mihai LA, Goriely A (2011) Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467: 3633–3646. Available: http://dx.doi.org/10.1098/rspa.2011.0281.
Publisher:
The Royal Society
Journal:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
10-Aug-2011
DOI:
10.1098/rspa.2011.0281
Type:
Article
ISSN:
1364-5021; 1471-2946
Sponsors:
This paper is based on the work supported by award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (A. G.), and also by the National Science Foundation under grant DMS-0907773 (A. G.). A. G. is a Wolfson/Royal Society Merit Award holder. The support by the Engineering and Physical Sciences Research Council of Great Britain under research programme EP/D048400/1 for LAM is gratefully acknowledged. The authors would also like to thank Michel Destrade for stimulating discussions and for kindly showing them the preprint to Destrade et al. (in press).
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Full metadata record

DC FieldValue Language
dc.contributor.authorMihai, L. A.en
dc.contributor.authorGoriely, A.en
dc.date.accessioned2016-02-28T05:49:37Zen
dc.date.available2016-02-28T05:49:37Zen
dc.date.issued2011-08-10en
dc.identifier.citationMihai LA, Goriely A (2011) Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467: 3633–3646. Available: http://dx.doi.org/10.1098/rspa.2011.0281.en
dc.identifier.issn1364-5021en
dc.identifier.issn1471-2946en
dc.identifier.doi10.1098/rspa.2011.0281en
dc.identifier.urihttp://hdl.handle.net/10754/599343en
dc.description.abstractMotivated by recent experiments on biopolymer gels whereby the reverse of the usual (positive) Poynting effect was observed, we investigate the effect of the so-called 'adscititious inequalities' on the behaviour of hyperelastic materials subject to shear. We first demonstrate that for homogeneous isotropic materials subject to pure shear, the resulting deformation consists of a triaxial stretch combined with a simple shear in the direction of the shear force if and only if the Baker-Ericksen inequalities hold. Then for a cube deformed under pure shear, the positive Poynting effect occurs if the 'sheared faces spread apart', whereas the negative Poynting effect is obtained if the 'sheared faces draw together'. Similarly, under simple shear deformation, the positive Poynting effect is obtained if the 'sheared faces tend to spread apart', whereas the negative Poynting effect occurs if the 'sheared faces tend to draw together'. When the Poynting effect occurs under simple shear, it is reasonable to assume that the same sign Poynting effect is btained also under pure shear. Since the observation of the negative Poynting effect in semiflexible biopolymers implies that the (stronger) empirical inequalities may not hold, we conclude that these inequalities must not be imposed when such materials are described. © 2011 The Royal Society.en
dc.description.sponsorshipThis paper is based on the work supported by award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (A. G.), and also by the National Science Foundation under grant DMS-0907773 (A. G.). A. G. is a Wolfson/Royal Society Merit Award holder. The support by the Engineering and Physical Sciences Research Council of Great Britain under research programme EP/D048400/1 for LAM is gratefully acknowledged. The authors would also like to thank Michel Destrade for stimulating discussions and for kindly showing them the preprint to Destrade et al. (in press).en
dc.publisherThe Royal Societyen
dc.subjectAdscititious inequalitiesen
dc.subjectBiopolymersen
dc.subjectNonlinear elasticityen
dc.subjectPoynting effecten
dc.subjectPure shear stressen
dc.subjectSimple shear deformationen
dc.titlePositive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materialsen
dc.typeArticleen
dc.identifier.journalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciencesen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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