3. Implementation in code_aster

The number of kinematic work hardening surfaces in the model is fixed at twelve. The first eleven surfaces cover the range of shear deformations between \({10}^{-5}\) and \(\mathrm{2,0}\times {10}^{-2}\). An elastic linear behavior is considered for deformations smaller than \({10}^{-5}\) and a maximum shear deformation of \(\mathrm{2,0}\times {10}^{-2}\). The interpolation values used are as follows:

γ1=1.00000000e-05

γ2=2.15443469e-05

γ3=4.64158883e-05

γ4=1.00000000e-04

γ5=2.15443469e-04

γ6=4.64158883e-04

γ7=1.00000000e-03

γ8=2.15443469e-03

γ9=4.64158883e-03

γ10=1.00000000e-02

γ11=2.00000000e-02

Beyond a shear deformation of \(\mathrm{2,0}\times {10}^{-2}\), the results of the model will be approximate because the last surface, positioned at a shear deformation of \(\mathrm{1,0}\times {10}^{-1}\), simply allows the model to provide a response between \(\mathrm{2,0}\times {10}^{-2}\) and \(\mathrm{1,0}\times {10}^{-1}\).

3.1. Internal variables

The following internal variables (StateVariable and AuxiliaryStateVariable in language MFront) are available when calculating with Iwan’s law of behavior:

Eel (1-6)	Elastic deformation tensor
pp (7-18)	Vector of scalar plastic multipliers \(>\)
X (19-91)	Kinematic work hardening tensor vector \({\text{X}}_{\text{n}}\)
fn (92-103)	Load surface value vector

3.2. Model description under MFront

The behavior is defined in the iwan.mfront file.

Parser/ DSL	Implicit
Algorithm	NewtonRaphson
	@Theta 1. @IterMax 50 @Epsilon 1.E-12
Internal variables (@StateVariable)	real pp [1:12]
Auxiliary internal variables (@AuxiliaryStateVariable)	Stensor X [1:12] realfn [1:12]
Command variables (@ExternalStateVariable)	none
Modelizations	“3D” “AXIS” “D_ PLAN “
Deformations	“PETIT” “PETIT_REAC” “GDEF_LOG”