The Poynting effect

When a rectangular block of a nonlinear material is subjected to a simple shearing deformation, specific normal tractions are required to ensure that the distances between the faces of the block, i.e. its dimensions, do not change. This work investigates the time-dependent dimensional changes during shear in the absence of these normal tractions (the Poynting effect) that occur in a block composed of an incompressible nonlinearly viscoelastic fiber-reinforced solid. The material is modeled using the Pipkin–Rogers nonlinear single integral constitutive equation for viscoelasticity. This constitutive equation is used because (1) it exhibits the essential features of nonlinear viscoelasticity; (2) it is straightforward to include the material symmetry restrictions due to the reinforcing fibers. A system of nonlinear Volterra integral equations is formulated for the dimensional changes in the block. Numerical solutions are presented for the case when the standard reinforcing model for nonlinearly elastic fiber-reinforced materials is incorporated in the Pipkin–Rogers constitutive framework. The results illustrate how the time-dependent dimensional changes depend on the fiber orientation and the viscoelastic properties of the fibers relative to those of the matrix.

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

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2011.0281 ◽

2011 ◽

Vol 467 (2136) ◽

pp. 3633-3646 ◽

Cited By ~ 57

Author(s):

L. Angela Mihai ◽

Alain Goriely

Keyword(s):

Shear Deformation ◽

Simple Shear ◽

Shear Force ◽

Pure Shear ◽

Hyperelastic Materials ◽

Isotropic Materials ◽

Poynting Effect ◽

Simple Shear Deformation ◽

Biopolymer Gels

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 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.

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