Mihai, L. A. and Goriely, A. (2011) Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials. Proceedings of the Royal Society . (Submitted)

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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 socalled “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 BakerEricksen 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 obtained 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.
Item Type:  Article 

Subjects:  D  G > General 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  1396 
Deposited By:  Peter Hudston 
Deposited On:  09 Sep 2011 06:56 
Last Modified:  29 May 2015 19:05 
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