/MAT/LAW82

Format

(1)	(3)	(5)
/MAT/LAW82/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$
`N`	`v`
$μ_{1}$	$μ_{2}$	$μ_{3}$
. . . `N` values of $μ$ (five per line)
$α_{1}$	$α_{2}$	$α_{3}$
. . . `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)
$ρ_{i}$	Initial density (Real)	$[\frac{kg}{m^{3}}]$
`N`	Order of the Ogden model. (Integer, maximum 10 digits)
`v`	Poisson's ratio Default value depends on `D`₁ input. 2 (Real)
$μ_{i}$	`i`^th Parameter (`i`= 1,`N`). (Real)
$α_{i}$	`i`^th Parameter (`i` = 1,`N`). (Real)
`D`_i	`i`^th 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 $W$ is computed using the following equation:(1)
$W = \sum_{i = 1}^{N} \frac{2 μ_{i}}{{α_{i}}^{2}} ({\bar{λ}}_{1}^{α_{i}} + {\bar{λ}}_{2}^{α_{i}} + {\bar{λ}}_{3}^{α_{i}} - 3) + \sum_{i = 1}^{N} \frac{1}{D_{i}} {(J - 1)}^{2 i}$

with $\bar{λ} = J^{- \frac{1}{3}} λ$ and J = $λ$ ₁ $λ$ ₂ $λ$ ₃

where, $λ_{i}$ is the i^th principal stretch.
The initial shear modulus:(2)
$μ = \sum_{i = 1}^{N} μ_{i}$
The Bulk Modulus is calculated as $K = \frac{2}{D_{1}}$ , based on the following rules:
- If $ν = 0$ , then D₁ should be entered entered.
- If $ν \neq 0$ , D₁ input is ignored and will be recalculated and output in the Starter output using the formula:(3)
  $D_{1} = \frac{3 (1 - 2 v)}{μ (1 + v)}$
- If $ν = 0$ and D₁ = 0, then a default value of $υ = 0.495$ 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.