Linear and non-linear possibilities
=======================================

Law of behavior
--------------------
The laws of behavior specific to these models, usable under COMPORTEMENT in STAT_NON_LINE and DYNA_NON_LINE, are documented in [:ref:`R5.03.17<r5.03.17>`] Behavioral relationships of discrete elements, except for the law ASSE_CORN [:ref:`R5.03.32<r5.03.32>`]. Possible behaviors:

* **ELAS**. In the general case, it is not necessary to assign elastic behavior to the discrete. The STAT_NON_LINE operator does this assignment by default on all the cells in the model. This assignment is then overloaded when the COMPORTEMENT keyword is processed.

    On the other hand, if a discrete is affected by a temperature and we want to take into account thermal expansion (only for a "DIS_TR_L"), it is necessary to define the expansion coefficient :math:`\alpha` and this is done by the definition of an elastic material. It is therefore necessary to define :math:`ALPHA=\alpha`, the keyword ``E`` is mandatory but its value will not be taken into account, see [:ref:`R5.03.17<r5.03.17>`].

* **ASSE_CORN**. See [:ref:`R5.03.32<r5.03.32>`]
* **ARME**
* **DIS_CHOC**
* **DIS_CONTACT**
* **ELAS**
* **DIS_VISC**
* **DIS_ECRO_CINE**
* **DIS_ECRO_TRAC**
* **DIS_BILI_ELAS**
* **DIS_GRICRA**
* **DIS_GOUJ2E**
* **CHOC_ENDO**
* **CHOC_ENDO_PENA**

In addition to the assignment of characteristics (AFFE_CARA_ELEM), the use of the "DIS_T" and "DIS_TR" models with STAT_NON_LINE, DYNA_NON_LINE, DYNA_TRAN_EXPLI involves defining material characteristics (via DEFI_MATERIAU and AFFE_MATERIAU).

With material DIS_CONTACT and behaviors DIS_CHOC and DIS_CONTACT the elastic matrix is calculated with the stiffness characteristic defined in AFFE_CARA_ELEM, while the tangent matrix is calculated via behavior DIS_CHOC or DIS_CONTACT.


Deformations
------------
The only available deformation, used in behavior relationships under the DEFORMATION keyword for the STAT_NON_LINE and DYNA_NON_LINE operators is **' PETIT '** (Cf. [:ref:`U4.51.11<u4.51.11>`]):

The deformations used for the behavioral relationship are therefore the linearized deformations calculated on the initial geometry.