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

L. A. Mihai, A. Goriely

Research output: Contribution to journalArticlepeer-review

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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.
Original languageEnglish (US)
Pages (from-to)3633-3646
Number of pages14
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume467
Issue number2136
DOIs
StatePublished - Aug 10 2011
Externally publishedYes

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