Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials
KAUST Grant NumberKUK-C1-013-04
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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.
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.
SponsorsThis 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).
PublisherThe Royal Society