3. Nonlinear possibilities

3.1. Laws of behavior

All the laws of behavior that can be used on continuous meshes make physical sense for these models and are assignable as long as they are accessible from COMPORTEMENT in STAT_NON_LINE (Cf. [U4.51.11]). Or in MECA_STATIQUE (elastic linear in small deformations)

Note that a law of behavior is specific to this modeling (dedicated to the calculation of limit load, cf. [R7.07.01]):

/'NORTON_HOFF'

3.2. Deformations

The available deformations, used in behavioral relationships under the keyword DEFORMATION for the operators STAT_NON_LINE, DYNA_NON_LINE, and CALCUL are (Cf. [U4.51.11]):

/'PETIT'

The deformations used for the behavioral relationship are the linearized deformations.

/'SIMO_MIEHE'
       'GDEF_LOG'

Allows calculations in large plastic deformations to be carried out.

In MECA_STATIQUE, we are elastic with small deformations.

3.3. Newton’s method

For solving the problem using the Newton-Raphson method in non-linear operators, the elastic matrix is not available. It is therefore necessary to use under the keyword NEWTON for the operators STAT_NON_LINE and DYNA_NON_LINE (Cf. [U4.51.11]):

/PREDICTION = 'TANGENTE'

The prediction phase is carried out with the tangent matrix.

/MATRICE = 'TANGENTE'

The matrix used for global iterations is the tangent matrix

Note:

The formulation used leads to non-positive matrices and current solvers do not always know how to solve the linear systems associated with them well. In case of convergence difficulties, it may therefore be useful to test the other solvers available in the code or the other renumbering methods (cf. [U4.50.01]).