/MAT/LAW109

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/UNIT/2275
unit_Mg_mm_s
                  Mg                  mm                   s
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#-  2. MATERIALS:
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/MAT/LAW109/18/2275
Aluminium
#        Init. dens.         
              7.8E-9
#                  E                  Nu
             70000.0                  .3         
#                 CP                 Eta                Tref                Tini
              0.45E9                0.95               293.0               293.0        
#  Tab_Yld  Tab_Temp              Xscale              Yscale                                 Ismooth
        25        26                 1.0                 1.0                                       1
#  tab_eta          xcsale_eta
        34                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/TABLE/1/25
Yld Functions : plastic strain + strain rate dependency
#DIMENSION
         2
#   FCT_ID                             X                                                     Scale_y
         2                           0.0                                                        1.0
         2                      100000.0                                                        1.35
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/TABLE/1/26
 Yld Functions (quasistatic): plastic strain + temperature dependency
#DIMENSION
         2
#   FCT_ID                             X                                                     Scale_y
         2                         293.0                                                        1.00
         2                        1000.0                                                        0.70
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/TABLE/1/34
taylor-quinney coef = f(strain rate, temp)
#DIMENSION
         2
#   FCT_ID                             X                                                     Scale_y
        35                           239                                                         1.0
        35                          1000                                                         0.9
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/FUNCT/35
taylor-quinney factor = f(strain.rate)
#                  X                   Y
               0.000                   0                                                            
               0.002                   0                                                            
                0.04                   1                                                            
           1000000.0                   1                                                            
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/FUNCT/2
ALU Stress-strain
          0.00000            310.0
          9.3E-04            330.8
          1.1E-03            334.5
          2.1E-03            339.9
          2.6E-03            340.9
          3.3E-03            342.3
          6.1E-03            344.7
          7.8E-03            346.0
          9.1E-03            347.1
          1.0E-02            348.7
          1.2E-02            350.7 
          1.4E-02            352.6 
          1.6E-02            354.0 
          1.8E-02            356.5 
          2.0E-02            358.7 
          3.0E-02            369.0 
          3.5E-02            373.5 
          1.0                410.0
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#enddata
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1. Yield criterion using isotropic von Mises equivalent stress:(1)
   $$\varphi ={\sigma }_{VM}-{\sigma }_y$$
2. Yield stress hardening defined by tabulated input as:(2)
   $${\sigma }_y={\mathrm{f}}_h\left({\epsilon }_p,{\dot{\epsilon }}_p\right)\frac{{\mathrm{f}}_t\left({\epsilon }_p,T\right)}{{\mathrm{f}}_t\left({\epsilon }_p,T_{ref}\right)}$$
   Where,

   ${\mathrm{f}}_h\left({\epsilon }_p,{\dot{\epsilon }}_p\right)$

   Function table of yield stresses depending on plastic strain and plastic strain rate.

   ${\mathrm{f}}_t\left({\epsilon }_p,T\right)$

   Table ID of quasi-static yield function depending on plastic strain and temperature.

   $T_{ref}$

   Reference temperature. Corresponds to conditions during experimental tests.

3. In adiabatic conditions, the temperature is updated using:(3)
   $$T=T_0+\frac{\eta \cdot {\mathrm{f}}_{\eta }\left({\epsilon }_p,{\dot{\epsilon }}_p,T\right)}{\rho Cp}$$

   Where, $\eta$ is the constant Taylor-Quinney coefficient which may be modified by introducing scalar factor defined by function ${\mathrm{f}}_{\eta }\left({\epsilon }_p,{\dot{\epsilon }}_p,T\right)$ .

   Otherwise, if /HEAT/MAT is present in the model, the temperature is imposed on all elements and cannot be updated using Equation 3.

   Function ${\mathrm{f}}_{\eta }\left({\epsilon }_p,{\dot{\epsilon }}_p,T\right)$ may be one dimensional, two-dimensional, or three-dimensional, but the first abscissa is always strain rate and the second one may be only the temperature.