/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)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW94/mat_ID/unit_ID or /MAT/YEOH/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
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) 

${\rho}_{i}$  Initial density (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{3}}\right]$ 
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
#12345678910
/UNIT/1
unit for mat
Mg mm s
#12345678910
# 2. MATERIALS:
#12345678910
/MAT/LAW94/1/1
plastic
# RHO_I
1.19E9
#Blank
# C10 C20 C30
1.3169 0.02758 0.003686
# D1 D2 D3
7.26e3
#12345678910
#ENDDATA
#12345678910
Comments
 The YEOH energy
density.
(1) $$W={\displaystyle \sum _{i=1}^{3}\left[{C}_{i0}{\left({\overline{I}}_{1}3\right)}^{i}+\frac{1}{{D}_{i}}{\left(J1\right)}^{2i}\right]}$$Where,(2) $${\overline{I}}_{1}={\overline{\lambda}}_{1}^{2}+{\overline{\lambda}}_{2}^{2}+{\overline{\lambda}}_{3}^{2}$$and(3) $${\overline{\lambda}}_{i}={J}^{\frac{1}{3}}{\lambda}_{i}$$The Cauchy stress is computed as:(4) $${\sigma}_{i}=\frac{{\lambda}_{i}}{J}\frac{\partial W}{\partial {\lambda}_{i}}$$  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 D_{1}= 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 754771.