Engine Subroutine SIGEPSnnC for Shell Elements

This subroutine calculates the stress tensor versus the strain tensor, strain rate tensor, or user variables.

Arguments

The argument list of SIGEPSnnC and its individual arguments and descriptions are:

C-----------------------------------------------------------------------------------------
SUBROUTINE SIGEPS29C(
1     NEL    ,NUPARAM,NUVAR   ,NFUNC   ,IFUNC  ,
2     NPF    ,NPT    ,IPT     ,IFLAG   ,
2     TF     ,TIME   ,TIMESTEP,UPARAM  ,RHO0   ,
3     AREA   ,EINT   ,THKLY   ,
4     EPSPXX ,EPSPYY ,EPSPXY  ,EPSPYZ  ,EPSPZX ,
5     DEPSXX ,DEPSYY ,DEPSXY  ,DEPSYZ  ,DEPSZX ,
6     EPSXX  ,EPSYY  ,EPSXY   ,EPSYZ   ,EPSZX  ,
7     SIGOXX ,SIGOYY ,SIGOXY  ,SIGOYZ  ,SIGOZX ,
8     SIGNXX ,SIGNYY ,SIGNXY  ,SIGNYZ  ,SIGNZX ,
9     SIGVXX ,SIGVYY ,SIGVXY  ,SIGVYZ  ,SIGVZX ,
A     SOUNDSP,VISCMAX,THK     ,PLA     ,UVAR   ,
B     OFF    ,NGL    ,SHF)
C-----------------------------------------------------------------------------------------

The user’s material law can be used in isotropic mode with PID 1 or in orthotropic mode with PID 9, 10, or 11. The directions XX, YY,... are the shell local reference frame axis. Stress are computed at each integration point.

You must use the Fortran float external function FINTER to get the value Y of the function for the abscissa X.

Y=FINTER(IFUNC(I),X,NPF,TF,DYDX

Where,

Variable: Description
Y: Interpolated value
X: Abscissa value of the function
I: The i^th user’s function
DYDX: Slope
NPF, TF: Private function parameters

The SOUNDSP array should always be set by you. It is used to calculate the stability time step and the hourglass forces. The sound speed value should be equal to the plane wave speed.

For elastic or elastoplastic materials, the sound speed is given by:(1)

c = \sqrt{\frac{E}{(1 - υ^{2}) ρ_{0}}}

Use VISCMAX to calculate the time step stability when the material law formulation is viscous.

Definitions

Argument	Format	Description
`NEL`	Integer read only scalar	Number of elements per group. In Radioss Engine subroutines, the element data are treated by groups for vectorization. This argument is machine-dependent and set by Radioss.
`NUPARAM`	Integer read only scalar	Size of the user parameter array.
`NUVAR`	Integer read only scalar	Number of user element variables.
`NFUNC`	Integer read only scalar	Number of functions used for material law.
`IFUNC`	Integer array read only	Array of size `NFUNC` with function indexes.
`NPF`	Integer array private data	Array used by `FINTER` (float external function).
`NPT`	Integer read only scalar	Number of layers or integration points.
`IPT`	Integer read only scalar	Current layer or interrogation point.
`IFLAG`	Integer array read only scalar	Array of size `NEL` with geometrical flags.
`TF`	Integer array private data	Array used by `FINTER` (float external function).
`TIME`	Float read only	Current time.
`TIMESTEP`	Float read only	Current time step.
`UPARAM`	Float array read only	User material parameter array of size `NUPARAM`.
`RHO0`	Float array read only	Array of size `NEL` with initial densities.
`AREA`	Float array read only	Array of size `NEL` with current element surfaces.
`EINT`	Float array read only	Array of size 2*`NEL` with internal membrane and bending energy.
`THKLY`	Float array write only	Array of size `NEL` with the layer thickness at each integration point.
`EPSPXX`, `EPSPYY`, `EPSPXY`, `EPSPYZ`, `EPSPZX`	Float array read only	Arrays of size `NEL` containing $ε$ strain rates in directions XX and YY and $γ$ strains in directions XY, YZ, and ZX.
`DEPSXX`, `DEPSYY`, `DEPSXY`, `DEPSYZ`, `DEPSZX`	Float array read only	Arrays of size `NEL` containing $ε$ strain increments in directions XX and YY and $γ$ strain increments in directions XY, YZ, and ZX.
`EPSXX`, `EPSYY`, `EPSXY`, `EPSYZ`, `EPSZX`	Float array read only	Array of size `NEL` containing $ε$ strains in directions XX and YY and $γ$ strains in directions XY, YZ, and ZX.
`SIGOXX`, `SIGOYY`, `SIGOZZ`, `SIGOXY`, `SIGOYZ`, `SIGOZX`	Float array read only	Array of size `NEL` containing old (previous time step) elastoplastic stresses in directions XX, YY, ZZ, XY, YZ, and ZX.
`SIGNXX`, `SIGNYY`, `SIGNXY`, `SIGNYZ`, `SIGNZX`	Float array write only	Array of size `NEL` containing new computed elastoplastic stresses in directions XX, YY, XY, YZ, and ZX.
`SIGVXX`, `SIGVYY`, `SIGVZZ`, `SIGVXY`, `SIGVYZ`, `SIGVZX`	Float array write only	Array of size `NEL` containing viscous stresses in directions XX, YY, XY, YZ, and ZX.
`SOUNDSP`	Float array write only	Array of size `NEL` containing sound speed.
`VISCMAX`	Float array write only	Array of size `NEL` containing the maximum damping modulus.
`THK`	Float array read write	Array of size `NEL` containing total thickness.
`PLA`	Float array read write	Array of size `NEL` containing plastic strain.
`UVAR`	Float array read write	Array of size `NEL`*`NUVAR` containing user element variables.
`OFF`	Float array read write	Array of size `NEL` containing deleted element flags. 0 If the element is OFF 1 If the element is ON
`NGL`	Integer array read only	Array of size `NEL` containing the external element number.

Shell Element Law Output

Unlike solid elements, shell elements do not have any variables specific to user’s law that are saved in time-history and animation.

Data Necessary for QEPH Compatibility

With QEPH, you must provide Radioss information relative to plasticity so that physical stabilization can be accurately calculated. Yield value and value Et/E (tangent modulus divided by Young’s modulus) must be given back to Radioss in the user law (SIGEPS29C.F, SIGEPS30C.F, or SIGEPS31C.F) to be compatible with the QEPH element.

This can be done through a call to routine SET_U_SHLPLAS.

The prototype of this routine and the necessary data to provide are:

C-------------------------------------------------------------------------
C     New routine : SET_U_SHLPLAS allows to return to Altair Radioss,
C                                Yield and Et/E for all elements.
C
C      Description of the arguments to be given to 
C      SET_U_SHLPLAS(NEL,YLD,ETSE) :
C---------+-----------+---+----------------------------------------------
C VAR     | SIZE      |TYP| DEFINITION
C---------+-----------+---+----------------------------------------------
C NEL     |  1          | I  |   NUMBER OF ELEMENTS
C YLD     |  NEL     | F |  YIELD VALUE FOR EACH ELEMENT,
C                              (FOR THE CURRENT INTEGRATION POINT)
C ETSE    |  NEL     | F |  VALUE FOR EACH ELEMENT,
C                              AND THE CURRENT INTEGRATION POINT OF :
C                            ETSE = 1             in case of an elastic increment
C                                     = H/(H+E)   in case of a plastic increment
C          where H : plastic tangent modulus, 
C                 E : Young modulus
C---------+---------+---+---+--------------------------------------------

The arrays YLD and ETSE, defined in the routine SET_U_SHLPLAS, have to be declared as local variables in the user material routines SIGEPS29C.F, SIGEPS30C.F, and SIGEPS30C.F with a sufficiently-long NEL.

Use the following statement in case these routines are compiled with a compiler that supports Fortran 90.

DOUBLE PRECISION YLD(NEL), ETSE(NEL)

This statement is not possible if the compiler only supports Fortran 77, since NEL is set by Radioss and given as an argument to the user routine. Therefore, the dynamic allocation is intended in this statement. In this case, use the following statement.

DOUBLE PRECISION YLD(4096), ETSE(4096)

The statement must be sufficient in all cases, meaning the value of NEL given from Radioss to the user routine should be less than 4096.