/MAT/LAW62 (VISC_HYP)

Block Format Keyword This law describes the hyper visco-elastic 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/LAW62/mat_ID/unit_ID or /MAT/VISC_HYP/mat_ID/unit_ID
mat_title
ρ i                
ν N M μ max Flag_Visc      
Define N parameters (5 per Line)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
μ 1 μ 2 μ 3 μ 4 μ 5
α 1 α 2 α 3 α 4 α 5
Define M parameters (5 per Line)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
γ 1 γ 2 γ 3 γ 4 γ 5
τ 1 τ 2 τ 3 τ 4 τ 5

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)

 
ρ i Initial density.

(Real)

[ kg m 3 ]
ν Poisson's ratio.

Default = 0.0 (Real)

 
N Law order - must be positive.

(Integer)

 
M Maxwell model order.
=0
Law is hyper elastic.

(Integer)

 
μ max Maximum viscosity.

Default = 1030 (Real)

[ Pas ]
Flag_Visc Viscous formulation flag, used if M > 0.
=0 (Default)
Viscous stress is accounted for in the deviatoric stress only and thus should only be used for incompressible materials with Poisson’s ratio close to 0.5.
=1
Viscous stress is accounted for in both the deviatoric and volumetric stress which enables the lateral expansion effect for the entered Poisson’s ratio.
 
μ i ith parameter of the ground shear modulus.

(Real)

[ Pa ]
α i ith material parameter.

(Real)

 
γ i ith stiffness ratio.

(Real)

 
τ i ith time relaxation.

(Real)

[ s ]

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/LAW62/1/1
LAW62 RUBBER
#              RHO_I
                1E-9                   
#                 Nu         N         M              mu_max Flag_Visc
                .495         2         0                1000         1
#         mu_i
                   2                   1
#      alpha_i
                   2                  -2
#         gamma_i

#         tetha_i

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. Strain energy W is computed using the following equation:(1)
    W ( λ 1 , λ 2 , λ 3 ) = i = 1 N 2 μ i α i 2 ( λ 1 α i + λ 2 α i + λ 3 α i 3 + 1 β ( J α i β 1 ) )
    With
    • λ i are eigenvalue of F (F is deformation gradient matrix),
    • J is Jacobian determinant, with J = det F ,
    • N is the order of law,
    • μ i and α i are the material parameters:(2)
      β = ν ( 1 2 ν )
    • ν 0 and ν 1 / 2
    • ν is the Poisson's ratio.
  2. Coefficients ( G i , η i ) are used to describe rate effects through the Maxwell model:

    law82_maxwell_model
    Figure 1.
    The initial shear modulus is:(3)
    G 0 = i = 1 N μ i
    The sum of μ i should be greater than 0.(4)
    G 0 = G + i G i
    The stiffness ratio is:(5)
    γ = G G 0 = 1 i γ i
    (6)
    γ i = G i G 0
    With, (7)
    γ i [ 0 , 1 ] , i γ i < 1
    and (8)
    G 0 = G + i G i
    is the ground shear modulus
    The relative time, τ i must be positive:(9)
    τ i = η i G i
  3. Rate effects are modeled using a convolution integral using Prony series. This is an extension of small strain theory to large strain. Strain rate effect applies only to the deviatoric stress. The full expression of the deviatoric viscous stress can be found in the Radioss Theory Manual.
  4. There are several differences between /MAT/LAW42 (OGDEN) and /MAT/LAW62. Special care should be taken that the ground shear modulus expression depending on input values is not the same. Also, it corresponds to the long-term shear modulus in one case, whereas to the initial shear modulus in another case.