# Fabric Material

A fabric material is a variant on an orthotropic material but only exists for the 2D case.

As wth an orthotropic material it is easier to define the inverse of the constitutive relationship

where is the compliance matrix. Fabric orthotropic behaviour is governed by four independent elastic constants: two elastic moduli, a Poisson's ratios and a shear modulus. These are

– the elastic modulus in the warp direction per unit width
– the elastic modulus in the fill (weft) direction per unit width
– the Poissons ratio in the warp-fill direction
– the shear modulus in the warp-fill direction per unit width

The further (dependent) Poisson's ratio is defined through the relationship

These material properties are defined relative to a material principal directions giving a compliance matrix .

A stable material must satisfy the following conditions

Using these relationships leads to the following conditions which apply to the Poisson's ratios