Orthotropic Material

For an orthotropic material the constitutive matrix simplifies to

however it is easier to define the inverse of the constitutive relationship

where is the compliance matrix. Elastic orthotropic behaviour is governed by nine independent elastic constants: three elastic moduli, three Poisson's ratios and three shear moduli. Three further (dependent) Poisson's ratios are 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

Note: if , and then the orthotropic material reduces to an isotropic material.