# How to use the Constitutive Law class

The constitutive law behaviour is dealt with in kratos by the use of the class "ConstitutiveLaw", with a public interface defined in the file

kratos/kratos/includes/constitutive_law.h

which also provides some rather extensive inline documentation (in the form of comments in the code).

By design such file aims to provide a very flexible interface to constitutive law modelling, with the specific goal of
**maximizing the flexibility in the implementation of complex constitutive behaviours**. While such approach provide obvious advantages, it
also implies that the API is more complex than what would be strictly needed for very simple constitutive laws.

The objective of current HowTo is to provide a brief introduction to the interface

### Conventions

Through the whole section, the following convenctions will be employed:

*voigt notation:*
- 3D case:

STRAINVoigt Notation: e00 e11 e22 2*e01 2*e12 2*e02STRESSVoigt Notation: s00 s11 s22 s01 s12 s02

- 2D plane strain/axisymmetric case (4 stress components)

STRAINVoigt Notation: e00 e11 e22 2*e01STRESSVoigt Notation: s00 s11 s22 s01

- 2D plane stress

STRAINVoigt Notation: e00 e11 2*e01STRESSVoigt Notation: s00 s11 s01

The constitutive law works on the basis of the deformation gradient F, defined as

F := D(X) / D(X0)

that is, as the deformation gradient connecting the original and deformed configuration

where the initial position X0 is the one obtained by

const array_1d<double,3>& X0 = node->GetInitialPosition()

and the deformed one by

const array_1d<double,3>& X = node->Coordinates() //must coincide with X = node->GetInitialPosition() + node.FastGetSolutionStepValue(DISPLACEMENT);

The ConstitutiveLaw always returns the **total stress**