### Monday, 11 October 2004 - 2:15 PM

### This presentation is part of : Horgan Symposium

### Constitutive equations for fabric-reinforced solids

**Anthony J M Spencer**, University of Nottingham, University of Nottingham, School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
In formulating constitutive equations for fibre-reinforced materials, it is usually assumed that the sense of the fibres is not relevant. A consequence is that the material has reflectional symmetry with respect to surfaces normal to the fibre directions. However it has been observed experimentally that in shearing on these surfaces of some fabric-reinforced materials, the response is dependent on the direction of the shear. The explanation is that some fabric architectures (for example, satin weaves) do not possess this reflectional symmetry.

We describe some fabric architectures and then investigate the invariance properties and formulate the constitutive equations for finite deformations of elastic fabric-reinforced materials, without assuming invariance under reversal of the fibre direction. The material is assumed to be incompressible and inextensible in two directions that are orthogonal in the reference configuration. We then specialize to the case of plane stress of these materials and apply the plane stress theory to an analysis of the ‘picture-frame’ experiment.

The emphasis of the paper is on large deformations of elastic materials, but we also refer briefly to viscous, plastic and viscoplastic material behaviours.

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