Journal of Engineering Mathematics

, Volume 95, Issue 1, pp 347–357

# Azimuthal shear of doubly fibre-reinforced, non-linearly elastic cylindrical tubes

Article

## Abstract

A doubly fibre-reinforced, non-linearly elastic tube subject to azimuthal shear is analysed. The materials involved are neo-Hookean models augmented with a function that accounts for the existence of two unidirectional reinforcements. This function endows the material with its anisotropic character and quantifies the effect associated with the two preferred material directions. The nature of the anisotropy considered has a particular influence on the shear response of the material, in contrast to previous analyses in which the effect of the anisotropy was taken to depend only on the stretch in the fibre directions. The inner boundary of the tube is fixed while the outer boundary is subject to a given shear traction. Non-smooth solutions arise inside the tube at a critical value of the shear stress, which can be obtained with the well-known Maxwell line analysis.

## Keywords

Discontinuous solutions Fibre-reinforced materials Finite deformations Maxwell line

## Notes

### Acknowledgments

The authors acknowledge support from the Ministerio de Ciencia, Spain, under Project DPI2011-26167. Mustapha El Hamdaoui also thanks the Ministerio de Economía y Competitividad, Spain, for funding under Project DPI2008-03769 and Grant BES-2009-027812.

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