/MAT/LAW53 (TSAI_TAB)

Block Format Keyword Describes the law that is a uni-directional orthotropic elasto-plastic law and is only used with solid elements.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW53/mat_ID/unit_ID or /MAT/TSAI_TAB/mat_ID/unit_ID
mat_title
ρ i                
E11 E22            
G12 G23            
fct_ID11 fct_ID22 fct_ID12 fct_ID23 fct_ID45          
Fscale11 Fscale22 Fscale12 Fscale23 Fscale45

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)

[ kg m 3 ]
E11 Young's modulus

(Real)

[ Pa ]
E22 Young's modulus

(Real)

[ Pa ]
G12 Shear modulus

(Real)

[ Pa ]
G23 Shear modulus

(Real)

[ Pa ]
fct_ID11 Yield stress function identifier in direction 11

(Integer)

 
fct_ID22 Yield stress function identifier in direction 22

(Integer)

 
fct_ID12 Yield stress function identifier in direction 12

(Integer)

 
fct_ID23 Yield stress function identifier in direction 23

(Integer)

 
fct_ID45 Yield stress function identifier in direction 45

(Integer)

 
Fscale11 Scale factor for yield function 11

Default = 1.0 (Real)

[ Pa ]
Fscale22 Scale factor for yield function 22

Default = 1.0 (Real)

[ Pa ]
Fscale12 Scale factor for yield function 12

Default = 1.0 (Real)

[ Pa ]
Fscale23 Scale factor for yield function 23

Default = 1.0 (Real)

[ Pa ]
Fscale45 Scale factor for yield function 45

Default = 1.0 (Real)

[ Pa ]

Example (Plastic)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                 Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW53/1/1
plastic
#              RHO_I
               2E-10
#                E11                 E22
                 200                 200
#                G12                 G23
                 100                 100
# fct_ID11  fct_ID22  fct_ID12  fct_ID23  fct_ID45
         1         1         3         4         5
#           Fscale11            Fscale22            Fscale12            Fscale23            Fscale45
                   0                   0                   0                   0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1
function_1
#                  X                   Y
                   0                 200                                                           
                  .1                 200                                                           
                 .11                 100                                                           
                  .5                 100                                                           
                 1.5               20000                                                           
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/2
function_2
#                  X                   Y
                   0                   1                                                           
               10000                   1                                                           
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/3
function_3
#                  X                   Y
                   0                 200                                                           
                  .1                 200                                                           
                 .11                 100                                                           
                  .5                 100                                                           
                 1.5               20000                                                           
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/4
function_4
#                  X                   Y
                   0                 200                                                           
                  .5                 200                                                           
                 1.5               20000                                                           
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/5
function_5
#                  X                   Y
                   0                 100                                                           
                  .5                 100                                                           
                 1.5               20000                                                           
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. Orthotropic reference frame (1, 2, and 3) is defined in the appropriate property set of each finite element.
    For SOLID property set (/PROP/TYPE14), the global frame is used if Isolid = 1 or 2.

    clip0072
    Figure 1.
  2. The global frame is ( X MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiwaaaa@36D7@ , Y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiwaaaa@36D7@ , and Z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiwaaaa@36D7@ ).
  3. The local frame is ( t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiwaaaa@36D7@ , r MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiwaaaa@36D7@ , and s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiwaaaa@36D7@ ).
    σ 11 = E 11 ε 11 σ 12 = G 12 ε 12
    σ 22 = E 22 ε 22 σ 23 = G 23 ε 23
    σ 33 = E 33 ε 33 σ 13 = G 13 ε 13
  4. The law is othotropic, E33 = E22 and G13 = G12.
  5. The yield surface is Tsai-Wu yield criteria:(1)
    F = F 1 σ 11 + F 2 σ 22 + F 2 σ 33 + F 11 σ 11 2 + F 22 σ 22 2 + F 22 σ 33 2 + F 44 σ 12 2 + F 55 σ 23 2 + F 44 σ 13 2 + 2 F 12 σ 11 σ 22 + 2 F 23 σ 22 σ 33 + 2 F 12 σ 11 σ 33
    with (2)
    F 1 = 1 σ 1 y c + 1 σ 1 y t ; F 2 = 1 σ 2 y c + 1 σ 2 y t
    (3)
    F 11 = 1 σ 1 y c σ 1 y t ; F 22 = 1 σ 2 y c σ 2 y t ; F 44 = 1 σ 4 y c σ 4 y t ; F 55 = 1 σ 5 y c σ 5 y t
    (4)
    F 12 = 1 2 F 11 F 22 ; F 23 = 1 2 F 22

    The parameters: σ 1 y c , σ 1 y t , σ 2 y c , σ 2 y t , σ 4 y c , σ 4 y t , σ 5 y c , σ 5 y t are variable and introduced by yield function.

  6. If fct_ID45 ≠ 0,(5)
    F 12 = 2 σ 45 y 2 1 2 ( F 11 + F 22 + F 44 ) + F 1 + F 2 σ 45 y c