/MAT/LAW82
Block Format Keyword This keyword defines the Ogden material. This law is compatible with solid and shell elements. In general it is used to model polymers and elastomers.
Format
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
/MAT/LAW82/mat_ID/unit_ID | |||||||||
mat_title | |||||||||
N | v | ||||||||
. . . N values of (five per line) | |||||||||
. . . N values of α (five per line) | |||||||||
D1 | D2 | D3 | |||||||
. . . N values of D (five per line) |
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) |
|
Initial
density (Real) |
||
N | Order of the Ogden
model. (Integer, maximum 10 digits) |
|
v | Poisson's ratio Default value depends on D1 input. 2 (Real) |
|
ith Parameter (i
= 1,N). (Real) |
||
ith Parameter
(i =
1,N). (Real) |
||
Di | ith Parameter
(i =
1,N). (Real) |
Example (Rubber)
#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/LAW82/1/1
LAW82 RUBBER
# RHO_I
1E-9 0
# N Nu
2 .495
# Mu_i
2 1
# Alpha_i
2 -2
# D_i
0 0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
Example (Hyper-elastic Rubber)
#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/LAW82/1/1
Rubber
# RHO_I
2E-9
# N Nu
3 0
# Mu_i
1.061898 .0578289 .0159176
# Alpha_i
.428246 5.71269 -4.59726
# D_i
1E-4 0 0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
Comments
- The strain energy density
is computed using the following
equation:
(1) with and J = 1 2 3
where, is the ith principal stretch.
- The initial shear
modulus:
(2) The Bulk Modulus is calculated as , based on the following rules:- If , then D1 should be entered entered.
- If
, D1
input is ignored and will be recalculated and output in the Starter
output using the formula:
(3) - If and D1 = 0, then a default value of is used and D1 is calculated using Equation 3
- To get a material without Poisson ratio effect, v should be defined with a small value (1e-10).
- Further explanation about this law can be found in "Non-Linear Elastic Deformations", by R.W Ogden, Ellis Horwood, 1984.