Constitutive relationship

The stresses and strain are related through a constitutive relationship.

or in tensor notation

The stress and strain are symmetric, second order tensors which can be represented in matrix form

The relationship between the stress and strain is through the constitutive relationship which is a fourth order tensor so for convenience of representing this as a matrix the stress and strain tensors are represented as vectors using modified Voigt notation:

For a general anisotropic material the stress-strain relation ship can be expressed as