3. Materials and behaviors

3.1. Choice of the law of behavior

The choice of the law of behavior is of course a function of the material that is being modelled, but also of the phenomena to be treated: for example, the same steel will be elasto-plastic at low temperature, and visco-plastic at high temperature. The values of the parameters of these laws (in DEFI_MATERIAU) are often identified within a very specific range of deformation, speed, and temperature.

• For elastoplastic behaviors, see

  u2.04.03

• For laws with damage (case of concrete for example), see

  u2.05.06 u2.05.06

• For metallurgy, see

  u2.03.04

• For porous media in THM, see

  u2.04.05 and r7.01.11

• For the use of CZM elements, see

  u2.05.07 u2.05.07

3.2. Tags of COMPORTEMENT

3.2.1. DEFORMATION

This keyword makes it possible to define the hypotheses used for the calculation of deformations: by default, we consider small displacements and small deformations. The type of deformation used can have a major influence on the calculation as soon as a component of the deformations exceeds a few% (typically 5%).

• PETIT: small deformations, small movements. Linearity of the deformation operator.

• GROT_GDEP: allows to treat large rotations and large displacements, but while remaining in small deformations. This is particularly useful for slender structures (modelled in beams, shells, or 3D) and the study of buckling (see for example the test

  v6.02.134 SSNL134 - Elasto-plastic ruin of Lee’s portico v6.02.134 SSNL134 - Elasto-plastic ruin of Lee’s portico).

As far as hyper-elastic laws of type ELAS_VMIS are concerned, they are not adapted to large deformations (loss of existence of the solution, see §2,1 of

r5.03.20). You have to use either a large deformation model with VMIS_ISOT, or the ELAS_HYPER behavior.

• **** GDEF_LOG **: model of large deformations, using a logarithmic deformation measure, and which allows the use of elastoplastic behavior laws with isotropic or kinematic work hardening (see the list of behaviors in

  u4.51.11 u4.51.11). Since the stress-strain relationship is hypo-elastic, this formulation is limited to low elastic deformations (but large plastic deformations).

• SIMO_MIEHE: model of large deformations of the laws of behavior based on a Von Mises criterion with isotropic work hardening, and all the isotropic work hardening behaviors associated with a material undergoing metallurgical phase changes. The elastic stress-strain relationship is hyper-elastic, which makes it possible to treat large elastic deformations (as long as it makes sense for the material used).

• other formulations exist, see

  u4.51.11 u4.51.11.

3.2.2. ALGO_INTE, ITER_INTE_MAXI, RESI_INTE_RELA, ITER_INTE_PAS

Allows you to specify the type of integration diagram to solve the equation or the system of non-linear equations formed by the equations constituting the models of behavior with internal variables. A resolution method by default is provided for each behavior. However, it is possible to change the resolution method by default for a number of behaviors (see u4.51.11).

In the case of iterative resolution (i.e. if ALGO_INTE is not ANALYTIQUE), the keywords ITER_INTE_MAXI and RESI_INTE_RELA define the maximum number of iterations and the relative residue to integrate the behavior. If this integration fails, it is possible to subdivide the time step, either locally (keyword ITER_INTE_PAS) or globally (command DEFI_LIST_INST). The default value for ITER_INTE_MAXI is 20. This may not be sufficient for some behaviors (MONOCRISTAL for example). In this case, do not hesitate to increase this parameter (100 for example). On the other hand, it is strongly recommended not to increase RESI_INTE_RELA (\({10}^{\mathrm{-}6}\) by default), otherwise you will get non-converged solutions.

The local subdivision of the time step is a means of improving the robustness of local integration, on the other hand it does not make it possible to provide a coherent tangent matrix (loss of the quadratic convergence of the global problem).

3.2.3. POST_ITER =” CRIT_RUPT “

Definition of a critical stress failure criterion by post-processing Newton iterations, at each time step. If the greatest mean principal stress in an element exceeds a given threshold \({\sigma }_{c}\), Young’s modulus is divided at the next time step by a coefficient. These two coefficients are defined under the keyword CRIT_RUPT of the DEFI_MATERIAU operator.

3.2.4. RESI_RADI_RELA

Measurement of the error due to time discretization, directly related to the rotation of the normal to the load surface. The angle between the normal to the plasticity criterion at the beginning of the time step and the normal to the plasticity criterion calculated at the end of the time step is calculated. The time step is sliced (via DEFI_LIST_INST) if the error is greater than the tolerance set by the user.

This criterion is operational for Von Mises elastoplastic behaviors with isotropic, linear and mixed kinematics work hardening and for elasto-visco-plastic behaviors of Chaboche.