/MAT/LAW74

Format

Definitions

Example (Aluminum)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/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/LAW74/1/1
Aluminum
#              RHO_I
               .0027
#                  E                  NU       EPSILON_P_MAX           EPSILON_T           EPSILON_M
               60400                 .33                   0                   0                   0
#   fct_ID                          EINF                  CE
         0                             0                   0
#            FSMOOTH              C_HARD                FCUT
                   1                   0                  10
#           SIGMA11Y            SIGMA22Y            SIGMA33Y
                   1                   1                   1
#           SIGMA12Y            SIGMA23Y            SIGMA31Y
                   1                   1                   1
#    TABLE                   SIGMA_SCALE         EPSPT_SCALE
        10                             0                   0
#                 TI             RHO0_CP
                   0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/TABLE/1/10
table
#DIMENSION
        3
#   fct_ID                             X                   Z
        38                             0                 293                                       
        38                            10                 293                                       
        39                            11                 293                                       
        40                            20                 293                                       
        38                             0                 400                                       
        38                            10                 400                                       
        39                            11                 400                                       
        40                            20                 400                                       
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/38
function_38
#                  X                   Y
                   0                  90                                                           
              2.5E-4                 100                                                           
                .001               104.5                                                           
                .009                 121                                                           
                 .01                 136                                                           
                 .02               143.5                                                           
                 .04                 163                                                           
                 .07               169.5                                                           
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/39
function_39
#                  X                   Y
                   0                 108                                                           
              2.5E-4                 120                                                           
                .001               125.4                                                           
                .009               145.2                                                           
                 .01               163.2                                                           
                 .02               172.2                                                           
                 .04               195.6                                                           
                 .07               203.4                                                           
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/40
function_40
#                  X                   Y
                   0                 126                                                           
              2.5E-4                 140                                                           
                .001               146.3                                                           
                .009               169.4                                                           
                 .01               190.4                                                           
                 .02               200.9                                                           
                 .04               228.2                                                           
                 .07               237.3                                                           
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

1. This material law must be used with property set /PROP/TYPE6 (SOL_ORTH), /PROP/TYPE14 (SOLID), /PROP/TYPE20 (TSHELL) or /PROP/TYPE21 (TSH_ORTH).
2. The yield stress is defined by a user function and the yield stress is compared to equivalent stress:(1)
   $${\sigma }_{\mathit{eq}}=\sqrt{F{\left({\sigma }_2-{\sigma }_3\right)}^2+G{\left({\sigma }_3-{\sigma }_1\right)}^2+H{\left({\sigma }_1-{\sigma }_2\right)}^2+2L{{\sigma }_{23}}^2+2M{{\sigma }_{31}}^2+2N{{\sigma }_{12}}^2}$$
   Where,(2)

   $$F=\frac{1}{2}\left(\frac{1}{{\sigma }_{22}^2}+\frac{1}{{\sigma }_{33}^2}-\frac{1}{{\sigma }_{11}^2}\right),\text{G}=\frac{1}{2}\left(\frac{1}{{\sigma }_{22}^2}+\frac{1}{{\sigma }_{33}^2}-\frac{1}{{\sigma }_{11}^2}\right),\text{H}=\frac{1}{2}\left(\frac{1}{{\sigma }_{22}^2}+\frac{1}{{\sigma }_{33}^2}-\frac{1}{{\sigma }_{11}^2}\right)$$

   (3)

   $$L=\frac{1}{2{\sigma }_{23}^2},\text{M}=\frac{1}{2{\sigma }_{31}^2},\text{N}=\frac{1}{2{\sigma }_{12}^2}$$

   Where, ${\sigma }_{11},{\sigma }_{22},{\sigma }_{33},{\sigma }_{12},{\sigma }_{23}$ and ${\sigma }_{31}$ represent the stress components either in the orthotropic frame if an orthotropic property is used, or in the orthogonalized isoparametric frame.

3. If ${\epsilon }_p$ (plastic strain) reaches ${\epsilon }_p^{max}$ , in one integration point, the solid element is deleted.
4. If largest principal strain ${\epsilon }_1>{\epsilon }_t$ , stress is reduced using the following relation:(4)
   $$\sigma =\sigma \left(\frac{{\epsilon }_m-{\epsilon }_1}{{\epsilon }_m-{\epsilon }_t}\right)$$
5. If ${\epsilon }_1>{\epsilon }_m$ , the stress is reduced to 0 (but the element is not deleted).
6. The table for yield stress definition can be 2-dimensional or 3-dimensional.
   • If the table is 2-dimensional, its parameters are assumed to represent respectively plastic strain and strain rate $\left({\epsilon }^p,\dot{\epsilon }\right)$ .

     Then if ${\epsilon }_{m-1}^p\le {\epsilon }^p\le {\epsilon }_m^p$ and ${\dot{\epsilon }}_{n-1}\le \dot{\epsilon }\le {\dot{\epsilon }}_n$ yield is linearly interpolated between the four values of the table corresponding to $\left({\epsilon }_i^p,{\dot{\epsilon }}_j\right),i=m-1,m;j=n-1,n$ .

   • If the table is 3-dimensional, its parameters are assumed to represent respectively plastic strain, strain rate, and temperature $\left({\epsilon }^p,\dot{\epsilon },T\right)$ .

     Then if ${\epsilon }_{m-1}^p\le {\epsilon }^p\le {\epsilon }_m^p$ and ${\dot{\epsilon }}_{n-1}\le \dot{\epsilon }\le {\dot{\epsilon }}_n$ and $T_{q-1}\le T\le T_q$ yield is linearly interpolated between the eight values of the table corresponding to $\left({\epsilon }_i^p,{\dot{\epsilon }}_j,T_k\right),i=m-1,m;j=n-1,n;k=q-1,q$ .

     If $\left({\epsilon }^p,\dot{\epsilon }\right)$ or $\left({\epsilon }^p,\dot{\epsilon },T\right)$ falls out of the range of the table, yield stress is obtained by linear extrapolation. Thus, it is necessary to input into the table the static curves corresponding to zero strain rate (entry $\dot{\epsilon }=0$ should belong to the table definition).

     Values of the table are yield stress values.

7. If yield stress also depends on temperature, the table is 3-dimensional:
   If the /HEAT/MAT option is not associated to the material identifier, adiabatic conditions are assumed and temperature is computed as:(5)

   $${\rm T}=T_i+\frac{E_{\mathit{int}}}{\rho C_p\left(\mathit{Volume}\right)}$$
   Where,

   E_int

   Internal energy computed by $\rho$ ,

   Volume

   Current density and volume

   C_p

   Heat capacity per mass unit

   Otherwise, the finite element formulation for heat transfer must be asked for (I_form =1 in option /HEAT/MAT); initial temperature and specific heat input in the option /HEAT/MAT will then be used.

8. The evolution of Young's modulus:
   • If fct_ID_E > 0, the curve defines a scale factor for Young's modulus evolution with equivalent plastic strain, which means the Young's modulus is scaled by the function $\mathrm{f}\left({\overline{\epsilon }}_p\right)$ :(6)
     $$E\left(t\right)=E\cdot \text{f}\left({\overline{\epsilon }}_p\right)$$

     The initial value of the scale factor should be equal to 1 and it decreases.

   • If fct_ID_E = 0, the Young's modulus is calculated as:(7)
     $$E\left(t\right)=E-\left(E-E_{\mathit{inf}}\right)\left[1-\exp \left(-C_E{\overline{\epsilon }}_p\right)\right]$$

     Where, E and E_inf are respectively, the initial and asymptotic value of Young's modulus, ${\overline{\epsilon }}_p$ accumulated equivalent plastic strain.

     Note: If fct_ID_E = 0 and C_E = 0, Young's modulus E is kept constant.