/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 | |||||||||
ρiρi | |||||||||
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) |
|
ρiρi | Initial density (Real) |
[kgm3][kgm3] |
E11 | Young's modulus (Real) |
[Pa][Pa] |
E22 | Young's modulus (Real) |
[Pa][Pa] |
G12 | Shear modulus (Real) |
[Pa][Pa] |
G23 | Shear modulus (Real) |
[Pa][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][Pa] |
Fscale22 | Scale factor for yield function 22 Default = 1.0 (Real) |
[Pa][Pa] |
Fscale12 | Scale factor for yield function 12 Default = 1.0 (Real) |
[Pa][Pa] |
Fscale23 | Scale factor for yield function 23 Default = 1.0 (Real) |
[Pa][Pa] |
Fscale45 | Scale factor for yield function 45 Default = 1.0 (Real) |
[Pa][Pa] |
▸Example (Plastic)
Comments
- Orthotropic reference frame (1, 2, and 3) is defined in the appropriate property set of each finite element.
- The global frame is ( XX , YY , and ZZ ).
- The local frame is (
tt
,
rr
, and
ss
).
σ11=E11ε11σ11=E11ε11 σ12=G12ε12σ12=G12ε12 σ22=E22ε22σ22=E22ε22 σ23=G23ε23σ23=G23ε23 σ33=E33ε33σ33=E33ε33 σ13=G13ε13σ13=G13ε13 - The law is othotropic, E33 = E22 and G13 = G12.
- The yield surface is Tsai-Wu yield
criteria:
(1) F=F1σ11+F2σ22+F2σ33+F11σ211+F22σ222+F22σ233 +F44σ212+F55σ223+F44σ213+2F12σ11σ22+2F23σ22σ33 +2F12σ11σ33F=F1σ11+F2σ22+F2σ33+F11σ211+F22σ222+F22σ233+F44σ212+F55σ223+F44σ213+2F12σ11σ22+2F23σ22σ33+2F12σ11σ33with(2) F1=−1σc1y+1σt1y;F2=−1σc2y+1σt2yF1=−1σc1y+1σt1y;F2=−1σc2y+1σt2y(3) F11=1σc1yσt1y;F22=1σc2yσt2y;F44=1σc4yσt4y;F55=1σc5yσt5yF11=1σc1yσt1y;F22=1σc2yσt2y;F44=1σc4yσt4y;F55=1σc5yσt5y(4) F12=−12√F11F22;F23=−12F22The parameters: σc1y,σt1y,σc2y,σt2y,σc4y,σt4y,σc5y,σt5y are variable and introduced by yield function.
- If fct_ID45 ≠
0,
(5) F12=2σ245y−12(F11+F22+F44)+F1+F2σc45y