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:
STRAIN Voigt Notation: e00 e11 e22 2*e01 2*e12 2*e02 STRESS Voigt Notation: s00 s11 s22 s01 s12 s02
- 2D plane strain/axisymmetric case (4 stress components)
STRAIN Voigt Notation: e00 e11 e22 2*e01 STRESS Voigt Notation: s00 s11 s22 s01
- 2D plane stress
STRAIN Voigt Notation: e00 e11 2*e01 STRESS Voigt 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