3. Operands#
3.1. Keywords COMPORTEMENT/NEWTON#
The syntax for these keywords is described in document [U4.51.03] and [U4.51.11].
3.2. Keyword CONVERGENCE#
◊ CONVERGENCE =_F ()
If neither of the following two operands is present, then everything is as follows: RESI_GLOB_RELA = 1.E-6.
3.2.1. Operand RESI_GLOB_RELA/RESI_GLOB_MAXI#
◊ |RESI_GLOB_REAL = resrel, [R]
The algorithm continues global iterations as long as:
\(\underset{i=\mathrm{1,}\dots ,\mathrm{nbddl}}{\mathrm{max}}\mid {F}_{i}^{n}\mid >\text{resrel}\mathrm{.}\mathrm{max}\mid L\mid\)
where \({F}^{n}\) is the residue of iteration \(n\) and \(L\) is the vector of the imposed load and the support reactions (Cf. [R5.03.01] for more details).
When the loading and the support reactions become zero, i.e. when \(L\) is zero (for example in the case of a total discharge), we try to pass from the relative convergence criterion RESI_GLOB_RELA to the absolute convergence criterion RESI_GLOB_MAXI. This operation is transparent for the user (alarm message sent in the.mess file). When the vector \(L\) becomes different from zero again, we automatically go back to the relative convergence criterion RESI_GLOB_RELA.
However, this failover mechanism cannot work at the first step of time. Indeed, to find a reasonable value of RESI_GLOB_MAXI automatically (since the user did not enter it), we need to have had at least one step converged on a RESI_GLOB_RELA mode. Therefore, if the load is zero from the first moment, the calculation stops. The user must then already check that the zero load is normal from the point of view of the modeling he is doing, and if this is the case, find another convergence criterion (RESI_GLOB_MAXI for example).
If this operand is not present, the test is performed with the value by default, unless RESI_GLOB_MAXI is present.
◊ |RESI_GLOB_MAXI = resmax, [R]
The algorithm continues global iterations as long as:
\(\underset{i=\mathrm{1,}\dots ,\mathrm{nbddl}}{\mathrm{max}}\mid {F}_{i}^{n}\mid >\text{resmax}\)
where \({F}^{n}\) is the residue of iteration \(n\) (Cf. [R5.03.01] for more details). If this operand is absent, the test is not performed.
If both RESI_GLOB_RELA and RESI_GLOB_MAXI are present, both tests are performed.
3.2.2. Operand ITER_GLOB_MAXI#
◊ ITER_GLOB_MAXI = /10 [DEFAUT]
/maglob
Maximum number of iterations performed to solve the global problem at each point in time (10 by default).
3.3. OPTION =” THER “#
Thermo-mechanical test to validate the consideration of temperature variation in the laws of behavior (see V6.07.108). These tests make it possible to verify the following two points:
Thermal expansion is well calculated (taking into account the variation of thermal expansion with temperature)
The variation of the material coefficients with temperature is correct, especially in the incremental resolution of the behavior.
It is a double simulation, the first in thermomechanics, the second in pure mechanics. The first will be validated in comparison with the second, assuming of course that the tested behavior provides a correct solution in pure mechanics.
The first simulation (solution that we are trying to validate) consists in applying a temperature variation to a material point, for example by blocking the following deformations \(x\): \({\varepsilon }_{\mathrm{xx}}=0\). The imposed temperature increases linearly as a function of time.
The second simulation (which must be equivalent to the first) consists in applying to the same material point an imposed deformation following \(x\): \({\varepsilon }_{\mathrm{xx}}=-{\varepsilon }^{\mathrm{th}}=-\alpha (T)(T-{T}_{\mathrm{ref}})\), in pure mechanics. Indeed, for any behavior (assuming the additive decomposition of deformations):
\({\sigma }_{\mathrm{xx}}=E(T)({\varepsilon }_{\mathrm{xx}}-{\varepsilon }^{\mathrm{th}}-{\varepsilon }_{\mathrm{xx}}^{p})\)
in the first case, \({\sigma }_{\mathrm{xx}}=E(T)(0-{\varepsilon }^{\mathrm{th}}-{\varepsilon }_{\mathrm{xx}}^{p})\), and in the second: \({\sigma }_{\mathrm{xx}}=E(T)(\varepsilon -{\varepsilon }_{\mathrm{xx}}^{p})\).
It is therefore sufficient, at any moment, to apply \({\varepsilon }_{\mathrm{xx}}=-{\varepsilon }^{\mathrm{th}}=-\alpha (T)(T-{T}_{\mathrm{ref}})\) for mechanical calculation.
Moreover, in order to obtain the same results in both cases, it is necessary, at each time step of the second simulation, to perform the pure mechanical calculation with coefficients whose values are interpolated as a function of the temperature at the current instant (operand list_mater).
3.3.1. Operand MATER#
♦ MATER = subdue,
This keyword allows you to enter the name of the material (subdue) defined by DEFI_MATERIAU [U4.43.01], where the parameters necessary for the chosen behavior, functions of temperature, are provided.
3.3.2. Operand LIST_MATER#
♦ LIST_MATER = list_master,
This keyword makes it possible to fill in a list of materials (list_mater), defined by DEFI_MATERIAU [U4.43.01], whose constant parameters correspond to those of mater, interpolated as a function of temperature.
3.3.3. Operands ALPHA/YOUNG#
ALPHA = alpha, [function]
YOUNG = young, [function]
These keywords make it possible to fill in the Young’s modulus and the coefficient of thermal expansion as a function of temperature, in order to calculate the thermal deformations and the corresponding stresses.
3.3.4. Operands TEMP_INIT/TEMP_FIN/INST_FIN#
TEMP_INIT = temp_init, [R]
TEMP_FIN = temp_end, [R]
◊ INST_FIN = temp_end, [R]
These keywords are used to fill in the initial and final temperatures, as well as the final moment of the transient (corresponding to temp_fin), which is \(1.\) by default.
3.3.5. Operands NB_VARI/VARI_TEST#
NB_VARI = nb_vari, [I]
◊ VARI_TEST = vari_test, [Kn]
These keywords allow you to specify the number of internal variables for the chosen behavior, as well as the internal variables to be tested (by default, all internal variables are tested).
3.3.6. OperandsD_ SIGM_EPSI/C_ PRAG#
◊ D_ SIGM_EPSI = d_sigm_epsi, [function]
◊ C_ PRAG = c_prag, [function]
In the particular case of linear kinematic work hardening behaviors, these keywords make it possible to define the kinematic work hardening slope as a function of temperature. This slope is equal to:
d_sigm_epsi for behavior VMIS_CINE_LINE,
c_prag for behaviors VMIS_ECMI_LINE, VMIS_ECMI_TRAC.
3.3.7. Operand SUPPORT#
◊ SUPPORT = /' POINT '[DEFAUT]
/” ELEMENT “
See [U4.51.12]
3.4. OPTION = “MECA”#
Pure mechanical test, which involves a simulation of a load path in deformations at a material point, i.e. on a model such that the stress and deformation states are homogeneous at all times. It thus makes it possible to test a certain number of behavior models, in order to verify the robustness of their numerical integration, their insensitivity to a change of units, the invariance with respect to a global rotation applied to the problem, and the accuracy of the tangent matrix. For each modeling, this test involves an inter-comparison between the reference solution (obtained with a very fine time step), the solution with a moderately coarse discretization, the solution with the effect of temperature (or another control variable), the solution by changing the system of units (\(\mathrm{Pa}\) in \(\mathrm{MPa}\)), and the solution obtained after rotation or symmetry (see document [v6.07.101]).
3.4.1. Operand LIST_MATER#
♦ LIST_MATER = list_master,
This keyword allows you to enter a list of 2 materials (list_mater), defined by DEFI_MATERIAU [U4.43.01], whose constant parameters are evaluated either in \(\mathit{Pa}\) or in \(\mathit{Mpa}\).
3.4.2. Operands POISSON/YOUNG#
POISSON = fish, [R]
YOUNG = young, [R]
These keywords are used to fill in the Young’s modulus and the Poisson’s ratio.
3.4.3. Operands LIST_NPAS/LIST_TOLE#
◊ LIST_NPAS = list_npas, [L_i]
◊ LIST_TOLE = list_tole, [L_r]
These keywords make it possible to specify the discretization in time and the corresponding tolerances.
By default, \(\text{list\_npas}\mathrm{=}\mathrm{[}\mathrm{1,1}\mathrm{,1}\mathrm{,1},\mathrm{1,}\mathrm{5,}25\mathrm{]}\) (4 « equivalent » problems with the coarsest discretization, i.e. 1 increment per load segment, then discretization variation: 1 then 5 then 25 increments per segment).
By default, \(\text{list\_tole}\mathrm{=}4\mathrm{\times }\mathrm{[}1.E\mathrm{-}10\mathrm{]}+\mathrm{[}1.E\mathrm{-}1\mathrm{]}+2\mathrm{\ast }\mathrm{[}1.E\mathrm{-}2\mathrm{]}+\mathrm{[}1.E\mathrm{-}8\mathrm{]}\). The precision required for equivalent problems is deliberately very low (otherwise there is a risk of a bug). The following clarifications are looser, since behaviors are generally sensitive to time discretization. The last value is the tolerance on the tangent matrix.
3.4.4. Operand PREC_ZERO#
◊ PREC_ZERO = prec_zero, [L_r]
This keyword makes it possible to provide a « numerical » zero for each variable tested, in order to calculate a significant relative error. prec_zero therefore has the same length as vari_test. By default this list is set to: \(3\mathrm{\times }1.E\mathrm{-}10\).
3.4.5. Operand VARI_TEST#
◊ VARI_TEST = vari_test, [Kn]
List of components tested, assumed to be invariant in equivalent problems (rotation, unit change). By default vari_test = (“V1”, VMIS “,” TRACE “).
3.4.6. Operand SUPPORT#
◊ SUPPORT = /' POINT '[DEFAUT]
/” ELEMENT “
See [U4.51.12]
3.4.7. Keyword MODELISATION#
The keyword MODELISATION allows, in the case SUPPORT =” ELEMENT “, to perform the calculation on a 3D element or on a 2D element, under plane constraints. It is not available in the case SUPPORT =” POINT “, because it suffices to impose a zero value on the components corresponding to the plane stresses or to the plane deformations to obtain the same result.
3.4.8. Keyword ANGLE#
This keyword allows you to specify an angle (in degrees) to perform an overall rotation around \(Z\) applied to both loading, meshing, and stripping. Above all, this makes it possible to verify the reliability of the integration of behavior, as in tests COMP001, COMP002.
By default, the rotation is identically zero.
In the case of materials with an intrinsic orientation (orthotropy, crystalline behaviors), the keyword MASSIF should also be used, with a first angle value identical to that provided under ANGLE.
3.4.9. Keywords MASSIF/ANGL_EULER/ANGL_REP#
These keywords make it possible to define an orientation intrinsic to the material (orthotropy, crystalline behaviors), and make it possible to use the keyword MASSIF from AFFE_CARA_ELEM [U4.42.01] in the macro-command.
By default, the orientation is zero, and AFFE_CARA_ELEM is not used as a step.
3.4.11. Operand VALE_PERT_RELA#
Allows you to define the value of the numerical relative disturbance that is involved in the calculation of the disturbed matrix. For more details refer to [U4.51.11].
3.4.12. Operand PRECISION#
Operand PRECISIONpermet defines the value above which the analytic matrix and the disturbed matrix are considered to be different.
3.4.13. Operand PREC_ZERO#
◊ PREC_ZERO = [R]
Below PREC_ZERO, we don’t compare the values of the terms in the tangent matrix. This makes it possible to manage situations where the terms of the disturbed tangent matrix are very close to zero.
3.5. Operand INFO#
Specify the details of the information printed in the message file.
In INFO =2 mode, we print all the tables produced by SIMU_POINT_MAT.