# Stress Concentration Layers in Finite Deformation of Fibre-Reinforced Elastic Materials

## Abstract

We consider finite plane strain of incompressible elastic materials reinforced by inextensible fibres. Deformations of inextensible materials often give rise to stress concentration layers, which are sheets of fibres which carry infinite direct stress but finite force, and across which the shear stress may be discontinuous. For linear elastic materials reinforced by straight parallel fibres these layers are well understood, and asymptotic methods of analysis have been developed for linear elastic materials with small but finite extensibility. When finite deformations occur, a qualitatively new feature arises because, in general, the fibres become curved and then the normal stress across them may also be discontinuous. We consider two examples, namely simple shear and shear bending of a rectangular block. In both of these examples the solution for inextensible material involves surface stress concentration layers. For ‘almost inextensible’ material we obtain approximate solutions for the displacement and stress in the neighbourhood of these surfaces, and show that the solution for an ideally inextensible material can be interpreted as the limit of the solution for material with small but finite extensibility as the ratio of shear modulus to fibre extension modulus tends to zero.

### Keywords

Anisotropy Rubber Nylon Compressibility Incompressibility## Preview

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