/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  
${\rho}_{i}$  
N  v  
${\mu}_{1}$  ${\mu}_{\text{\hspace{0.05em}}2}$  ${\mu}_{\text{\hspace{0.05em}}3}$  
. . . N values of $\mu $ (five per line)  
${\alpha}_{1}$  ${\alpha}_{2}$  ${\alpha}_{3}$  
. . . N values of α (five per line)  
D_{1}  D_{2}  D_{3}  
. . . N values of D (five per line) 
Definitions
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) 

${\rho}_{i}$  Initial
density (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{3}}\right]$ 
N  Order of the Ogden
model. (Integer, maximum 10 digits) 

v  Poisson's ratio Default value depends on D_{1} input. 2 (Real) 

${\mu}_{i}$  i^{th} Parameter (i
= 1,N). (Real) 

${\alpha}_{i}$  i^{th} Parameter
(i =
1,N). (Real) 

D_{i}  i^{th} Parameter
(i =
1,N). (Real) 
Example (Rubber)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
Mg mm s
#12345678910
# 2. MATERIALS:
#12345678910
/MAT/LAW82/1/1
LAW82 RUBBER
# RHO_I
1E9 0
# N Nu
2 .495
# Mu_i
2 1
# Alpha_i
2 2
# D_i
0 0
#12345678910
#ENDDATA
/END
#12345678910
Example (Hyperelastic Rubber)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
Mg mm s
#12345678910
# 2. MATERIALS:
#12345678910
/MAT/LAW82/1/1
Rubber
# RHO_I
2E9
# N Nu
3 0
# Mu_i
1.061898 .0578289 .0159176
# Alpha_i
.428246 5.71269 4.59726
# D_i
1E4 0 0
#12345678910
#ENDDATA
/END
#12345678910
Comments
 The strain energy density
$W$
is computed using the following
equation:
(1) $$W=\sum _{i=1}^{N}\frac{2{\mu}_{i}}{{{\alpha}_{i}}^{2}}\left({{\overline{\lambda}}_{1}}^{{\alpha}_{i}}+{{\overline{\lambda}}_{2}}^{{\alpha}_{i}}+{{\overline{\lambda}}_{3}}^{{\alpha}_{i}}3\right)+\sum _{i=1}^{N}\frac{1}{{D}_{i}}{\left(J1\right)}^{2i}$$with $\overline{\lambda}={J}^{\frac{1}{3}}\lambda $ and J = $\lambda $ _{1} $\lambda $ _{2} $\lambda $ _{3}
where, ${\lambda}_{i}$ is the i^{th} principal stretch.
 The initial shear
modulus:
(2) $$\mu ={\displaystyle \sum _{i=1}^{N}{\mu}_{i}}$$The Bulk Modulus is calculated as $K=\frac{2}{{D}_{1}}$ , based on the following rules: If $\nu =0$ , then D_{1} should be entered entered.
 If
$\nu \ne 0$
, D_{1}
input is ignored and will be recalculated and output in the Starter
output using the formula:
(3) $${D}_{1}=\frac{3(12v)}{\mu (1+v)}$$  If $\nu =0$ and D_{1} = 0, then a default value of $\upsilon =0.495$ is used and D_{1} is calculated using Equation 3
 To get a material without Poisson ratio effect, v should be defined with a small value (1e10).
 Further explanation about this law can be found in "NonLinear Elastic Deformations", by R.W Ogden, Ellis Horwood, 1984.