/MAT/LAW94 (YEOH)

Block Format Keyword This law describes the YEOH material model, which can be used to model incompressible hyperelastic behavior. This law is only compatible with solid elements.

Format

(1)	(3)	(5)
/MAT/LAW94/`mat_ID`/`unit_ID` or /MAT/YEOH/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$
Blank
`C`₁₀	`C`₂₀	`C`₃₀
`D`₁	`D`₂	`D`₃

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)	$[\frac{kg}{m^{3}}]$
`C`₁₀	Deviatoric material parameter 1 Default = 0.0 (Real)
`C`₂₀	Deviatoric material parameter 2 Default = 0.0 (Real)
`C`₃₀	Deviatoric material parameter 3 Default = 0.0 (Real)
`D`₁	Volumetric material parameter 1, for bulk modulus computation. $K = \frac{2}{D_{1}}$ Default = 0.0 (Real)
`D`₂	Volumetric material parameter 2 Default = 0.0 (Real)
`D`₃	Volumetric material parameter 3 Default = 0.0 (Real)

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/LAW94/1/1
plastic
#              RHO_I        
             1.19E-9 		
#Blank

#                C10                 C20                 C30
              1.3169             0.02758            0.003686
#                 D1                  D2                  D3
             7.26e-3
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

The YEOH energy density.(1)
$W = \sum_{i = 1}^{3} [C_{i 0} {({\bar{I}}_{1} - 3)}^{i} + \frac{1}{D_{i}} {(J - 1)}^{2 i}]$

Where,(2)
${\bar{I}}_{1} = {\bar{λ}}_{1}^{2} + {\bar{λ}}_{2}^{2} + {\bar{λ}}_{3}^{2}$

and(3)
${\bar{λ}}_{i} = J^{- \frac{1}{3}} λ_{i}$

The Cauchy stress is computed as:(4)
$σ_{i} = \frac{λ_{i}}{J} \frac{\partial W}{\partial λ_{i}}$
The initial shear modulus and the bulk modulus are computed as:(5)
$G = 2 \cdot C_{10}$

and(6)
$K = \frac{2}{D_{1}}$
If D₁= 0, an incompressible material is considered.
This material has similar compatibilities as LAW42, except it is for Hexa elements only. Verifications for tetrahedral elements is ongoing.
This material is based on Yeoh, O. H., 1993, "Some forms of the strain energy function for rubber", Rubber Chemistry and Technology, Volume 66, Issue 5, November 1993, Pages 754-771.