/MAT/LAW66

Block Format Keyword This law models an isotropic tension-compression elasto-plastic material law using user-defined functions for the work-hardening portion of the stress-strain (plastic strain versus stress). This law can be defined for compression and tension.

Format

(1)	(3)	(5)	(7)	(9)	(10)
/MAT/LAW66/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$
`E`	$υ$	`C`_hard	`F`_cut	`F`_smooth	`I`_{yld_rate}
`P`_c	`P`_t	`Ec`	`RPCT`

Read only if I_{yld_rate} = 0, 1 or 2

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`fct_ID`_c	`fct_ID`_t	`Fscale`_c		`Fscale`_t
${\dot{ε}}_{0}$		`c`		$σ_{y 0}$		`VP`

Read only if I_{yld_rate} = 3

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`fct_ID`_c	`fct_ID`_t	`Fscale`_c		`Fscale`_t
`Frate_ID`_c	`Frate_ID`_t	`Fscale_rate`_c		`Fscale_rate`_t

Read only if I_{yld_rate} = 4

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`NFUNCC`	`NFUNCT`

For each NFUNCC

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`fct_ID`_c		${\dot{ε}}_{i}^{c}$		`Fscale`_c

For each NFUNCT

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`fct_ID`_t		${\dot{ε}}_{i}^{t}$		`Fscale`_t

Definition

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier. (Integer, maximum 10 digits)
`mat_title`	Material title. (Character, maximum 100 characters)
$ρ_{i}$	Initial density. (Real)	$[\frac{kg}{m^{3}}]$
`E`	Young's modulus. (Real)	$[Pa]$
$υ$	Poisson's ratio. (Real)
`C`_hard	Hardening coefficient. = 0 Hardening is full isotropic model. = 1 Hardening uses the kinematic Prager-Ziegler model. = between 0 and 1 Hardening is interpolated between the two models. (Real)
`F`_smooth	Smooth strain rate option flag. = 0 (Default) No strain rate smoothing. = 1 Strain rate smoothing active. (Integer)
`F`_cut	Cutoff frequency for strain rate filtering, Appendix: Filtering. Default = 10³⁰ (Real)	$[Hz]$
`I`_{yld_rate}	Rate effect on the yield stress flag. = 1 (Default) Using Cowper-Symonds: $1 + {(\frac{\dot{ε}}{{\dot{ε}}_{0}})}^{\frac{1}{c}}$ = 2 By using: $1 + cLn (\frac{\dot{ε}}{{\dot{ε}}_{0}})$ = 3 By using two load curves to scale the yield stress (`fct_ID`_c) in compression and tension (`fct_ID`_t). = 4 By using different functions for compression and tension for different strain rate values. (Integer)
`P`_c	Limit pressure in compression. Default = 0 (Real)	$[Pa]$
`P`_t	Limit pressure in tensile. Default = 0 (Real)	$[Pa]$
`Ec`	(Optional) Compression Young’s modulus. 2 (Real)	$[Pa]$
`RPCT`	Scale factor used on `P`_c and `P`_t. 2 (Real)
`fct_ID`_c	Compression yield stress. (Integer)
`fct_ID`_t	Tension yield stress. (Integer)
`Fscale`_c	Scale factor for ordinate (stress) in `fct_ID`_c. Default = 1.0 (Real)	$[Pa]$
`Fscale`_t	Scale factor for ordinate (stress) in `fct_ID`_t. Default = 1.0 (Real)	$[Pa]$
`c`	Strain rate parameter. (Real)
${\dot{ε}}_{0}$	Reference strain rate. Default = 1.0 (Real)	$[\frac{1}{s}]$
$σ_{y 0}$	Initial yield stress. Default = 0 (Real)	$[Pa]$
`VP`	Strain rate choice flag. = 0 Strain rate effect on the yield stress is depending on the total strain rate. = 1 Strain rate effect on the yield stress is depending on plastic strain rate. In this case, there is no strain rate filtering, so `F`_smooth and `F`_cut are not used. Only available if `I`_{yld_rate} = 1 (Cowper Symonds). 3 (Integer)
`Frate_ID`_c	Compression strain rate effect function identifier. (Integer)
`Frate_ID`_t	Tension strain rate effect function identifier. (Integer)
`Fscale_rate`_c	Scale factor for ordinate (stress) in `Frate_ID`_c. Default = 1.0 (Real)	$[Pa]$
`Fscale_rate`_t	Scale factor for ordinate (stress) in `Frate_ID`_t. Default = 1.0 (Real)	$[Pa]$
`NFUNCC`	Number of compression function. (Integer)
`NFUNCT`	Number of tension function. (Integer)
${\dot{ε}}_{i}^{c}$	`i`^th compression strain rate `i` =1,`NFUNCC`. (Real)	$[\frac{1}{s}]$
${\dot{ε}}_{i}^{t}$	`i`^th tension strain rate `i`=1,`NFUNCT`. (Real)	$[\frac{1}{s}]$

Example (Aluminum)

#RADIOSS STARTER
/UNIT/1
unit for mat
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW66/1/1
Aluminum
#              RHO_I
               .0027
#                  E                  Nu              C_hard               F_cut  F_smooth Iyld_rate
               60400                 .33                   0                   0         0         4
#                P_c                 P_t
                 500                 600
#   NFUNCC    NFUNCT
         2         2
#funct_IDc                     Epsilon_c             Fscalec
        38                            10                   1                                                  
        40                            40                 1.6                                                  
#funct_IDt                     Epsilon_t             Fscalet
        38                            10                   1                                                  
        40                            40                 1.6                                                  
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/38
function_38
#                  X                   Y
                   0                  90                                                            
                 .08                 170                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/40
function_40
#                  X                   Y
                   0                  90                                                            
                 .08                 170                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Example (Optional Compression Young’s Modulus)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
## Material Law 
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW66/1
20MAT124_20degree                                                                                   
#              RHO_I
1.25000000000000E-09
#                  E                  Nu              C_hard               F_cut  F_smooth Iyld_rate
            210000.0               0.33                 0.0                 0.0         0         1
#                P_c                 P_t                  EC                RPCT
                 0.0                 0.0              70000.
#funct_IDc funct_IDt             Fscalec             Fscalet
        34        34              100.0              200.0
#          Epsilon_0                   c            Sigma_Y0        VP
                 0.0                 0.0                 0.0         0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
##HWCOLOR curves 24 9
/FUNCT/24
20deg_TENSION                                                                                       
#                  X                   Y
                 0.0         0.200535124
1.11148000000000E-04          0.23893938
2.47763000000000E-04         0.274602617
3.84248000000000E-04         0.308164207
5.81974000000000E-04         0.354639794
7.98180000000000E-04         0.395218545
1.03131900000000E-03          0.43242102
         0.001382833         0.473801266
         0.001747862         0.508073173
         0.002139804         0.539268776
         0.002704889         0.577068218
         0.003299031         0.610692299
         0.004078009         0.646563755
         0.005715537         0.702190108
                 1.0                0.75
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/34
20deg_COMPRESSION                                                                                   
#                  X                   Y
                 0.0         0.709520996
         0.002556758         0.768542475
         0.005112572         0.814793042
         0.007700089         0.850991269
         0.010231756         0.877769462
         0.012846771         0.896395146
         0.015380438         0.909432849
         0.020500175         0.924867455
         0.030979299         0.948100519
         0.073545677         1.001804424
         0.126630132         1.075808748
         0.245056814          1.17707424
                 1.0                 1.2
#enddata

Comments

This is an isotropic elastic-plastic law. The yield stress is defined by using the compression and tension yield stress versus effective plastic strain for the both (compression and tension). When exceeded, the two pressures P_t and P_c, determine if the tension yield stress or compression yield stress is used respectively.
If the pressure is between these two values, the yield stress is given by:

If $- P_{t} \leq P \leq P_{c}$ (1)
$\begin{array}{l} σ_{y} = α σ_{y}^{t} (ε_{p}) + (1 - α) σ_{y}^{c} (ε_{p}) \\ α = \frac{P_{c} - P}{P_{e} + P_{t}} \end{array}$

If $P_{t} = P_{c} = 0$ , or the pressure is out of the two values range, the yield stress is given by:

$σ_{y} = σ_{y}^{t} (ε_{p})$ if $P \leq 0$

$σ_{y} = σ_{y}^{c} (ε_{p})$ if $P > 0$
If Ec is defined, the Young's modulus is defined as:
- Young’s modulus is E, if P > -RPCT * P_t
- Young’s modulus is Ec, if P < RPCT * P_c
- Linear interpolation is done between E and Ec, if -RPCT * P_t < P < RPCT * P_c
Yield stress is computed as:
If VP= 1:

$σ_{y} (ε_{p}, {\dot{ε}}_{p}) = σ_{y}^{s} (ε_{p}) + σ_{y 0} {(\frac{{\dot{ε}}_{p}}{{\dot{ε}}_{0}})}^{\frac{1}{c}}$ if $σ_{y 0} > 0$

$σ_{y} (ε_{p}, {\dot{ε}}_{p}) = σ_{y}^{s} (ε_{p}) [1 + {(\frac{{\dot{ε}}_{p}}{{\dot{ε}}_{0}})}^{\frac{1}{c}}]$ if $σ_{y 0} = 0$

If VP= 0:

$σ_{y} (ε_{p}, {\dot{ε}}_{p}) = σ_{y}^{s} (ε_{p})$ if $σ_{y 0} > 0$

$σ_{y} (ε_{p}, {\dot{ε}}_{p}) = σ_{y}^{s} (ε_{p})$ if $σ_{y 0} = 0$

with $σ_{y}^{t} (ε_{p})$ being static yield stress and $σ_{y 0}$ being initial yield stress.
/VISC/PRONY can be used with this material law to include viscous effects.