/MAT/LAW93 (ORTH_HILL) or (CONVERSE)

Format

Definitions

Example (Curve Input)

#RADIOSS STARTER
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/UNIT/1
unit for mat
                  kg                  mm                  ms
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#-  2. MATERIALS:
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/MAT/LAW93/1/1
plastic
#              RHO_I
            1.111E-6
#                E11                 E22                 E33                 G12                Nu12
               1.111               1.111               1.111               1.111                0.11
#                G13                 G23                Nu13                Nu23
               1.111               1.111                0.11                0.11
#    Nrate
         2
#   Ifunct                        Yscale              Epsdot
       141                         0.001                 0.1
       141                         0.002                 0.2	   
#               SigY                 QR1                 CR1                 QR2                 CR2
                 0.0                 0.0                 0.0                 0.0                 0.0
#                R11                 R22                 R12
                 .11                 .11                 .11
#                R33                 R13                 R23
                 .11                 .11                 .11
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/141
plasticity curve
#                  X                   Y
               0.000           26.900000
            0.005000           46.700000
            0.015000           69.100000
            0.025000           84.300000
            0.035000           94.500000
            0.045000           101.20000
            0.055000           106.10000
            0.065000           110.00000
            0.075000           113.60000
            0.085000           117.10000
            0.095000           120.50000
            0.105000           124.00000
            0.112000           126.30000
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#ENDDATA
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Comments

1. The yield stress is defined by a user function and the yield stress is compared to equivalent stress in the orthotropic frame.(1)
   $${\sigma }_{eq}=\sqrt{\left(G+H\right){\sigma }_1^2+\left(F+H\right){\sigma }_2^2-2H{\sigma }_1{\sigma }_2+2N{\sigma }_{12}}$$
   Where,(2)

   $$F=\frac{1}{2}(\frac{1}{R_{22}^2}+\frac{1}{R_{33}^2}-\frac{1}{R_{11}^2})$$

   (3)

   $$G=\frac{1}{2}(\frac{1}{R_{33}^2}+\frac{1}{R_{11}^2}-\frac{1}{R_{22}^2})$$

   (4)

   $$H=\frac{1}{2}(\frac{1}{R_{22}^2}+\frac{1}{R_{11}^2}-\frac{1}{R_{33}^2})$$

   (5)

   $$N=\frac{3}{2R_{12}^2}$$
   Two different ways (parameter input or curve input) to describe the Yield criteria in LAW93. The yield will be compared with equivalent stress ${\sigma }_{eq}$ as:(6)

   $$\Phi ={\sigma }_{eq}-\left[{\sigma }_y+R({\epsilon }_p)\right]$$

   • For parameter input, the hardening can be defined as:(7)
     $$R({\epsilon }_p)={\displaystyle \sum _i^{2}Q{R}_i\cdot \left(1-e^{-C{R}_i\cdot {\epsilon }_p}\right)}$$
   • Using curve input, the parameter input will be ignored
     The Yield can be defined with using stress vs plastic strain curve taking account the strain rate effect. When the stress vs strain curves are defined this is the default way for defining the hardening.

     1. If $\dot{\epsilon }\le {\dot{\epsilon }}_n$ , the yield is interpolated between ${\mathrm{f}}_n$ and ${\mathrm{f}}_{n-1}$ .
     2. If $\dot{\epsilon }\le {\dot{\epsilon }}_1$ function, ${\mathrm{f}}_1$ is used.
     3. Above ${\dot{\epsilon }}_{\max }$ , yield is extrapolated.

        
        
        Figure 1.