In [19] it is explained that substituting the infinitesimal strains in the classical Hooke law by the Lagrangian strain and the stress by the Piola-Kirchoff stress of the second kind does not lead to a physically sensible material law. In particular, such a model (also called St-Venant-Kirchoff material) does not exhibit large stresses when compressing the volume of the material to nearly zero. An alternative for isotropic materials is the following stored-energy function developed by Ciarlet [17] ( and are Lamé's constants):

(295) |

The stress-strain relation amounts to ( is the Piola-Kirchoff stress of the second kind) :

det | (296) |

and the derivative of with respect to the Green tensor reads (component notation):

detdet | (297) |

This model was implemented into CalculiX by Sven Kaßbohm. The definition consists of a *MATERIAL card defining the name of the material. This name HAS TO START WITH ”CIARLET_EL” but can be up to 80 characters long. Thus, the last 70 characters can be freely chosen by the user. Within the material definition a *USER MATERIAL card has to be used satisfying:

First line:

- *USER MATERIAL
- Enter the CONSTANTS parameter and its value, i.e. 2.

Following line:

- (Young's modulus).
- (Poisson's coefficient).
- Temperature.

Repeat this line if needed to define complete temperature dependence.

For this model, there are no internal state variables.

Example: *MATERIAL,NAME=CIARLET_EL *USER MATERIAL,CONSTANTS=2 210000.,.3,400.

defines an isotropic material with elastic constants =210000. and =0.3 for a temperature of 400 (units appropriately chosen by the user). Recall that

(298) |

and

(299) |