/MAT/LAW95 (BERGSTROM_BOYCE)
Block Format Keyword This law is a constitutive model for predicting the nonlinear time dependency of elastomer like materials.
It uses a polynomial material model for the hyperelastic material response and the Bergstrom-Boyce material model 1 to represent the nonlinear viscoelastic time dependent material response. This law is only compatible with solid elements.
Format
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
/MAT/LAW95/mat_ID/unit_ID or /MAT/BERGSTROM_BOYCE/mat_ID/unit_ID | |||||||||
mat_title | |||||||||
C10 | C01 | C20 | C11 | C02 | |||||
C30 | C21 | C12 | C03 | sb | |||||
D1 | D2 | D3 | |||||||
A | C | M | Tau_ref |
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) |
|
Initial density. (Real) |
||
C10 | Material parameter for hyperelastic
model. Default = 0.0 (Real) |
|
C01 | Material parameter for hyperelastic
model. Default = 0.0 (Real) |
|
C20 | Material parameter for hyperelastic
model. Default = 0.0 (Real) |
|
C11 | Material parameter for hyperelastic
model. Default = 0.0 (Real) |
|
C02 | Material parameter for hyperelastic
model. Default = 0.0 (Real) |
|
C30 | Material parameter for hyperelastic
model. Default = 0.0 (Real) |
|
C21 | Material parameter for hyperelastic
model. Default = 0.0 (Real) |
|
C12 | Material parameter for hyperelastic
model. Default = 0.0 (Real) |
|
C03 | Material parameter for hyperelastic
model. Default = 0.0 (Real) |
|
Sb | Stress scaling factor for network B. Default = 0.0 (Real) |
|
D1 | Volumetric material parameter 1, for bulk modulus computation.
Default = 0.0 (Real) |
|
D2 | Volumetric material parameter 2. Default = 0.0 (Real) |
|
D3 | Volumetric material parameter 3. Default = 0.0 (Real) |
|
A | Effective creep strain rate. Default = 0.0 (Postive Real) |
|
C | Exponent characterizing the creep strain
dependence of the effective creep strain rate in
network B (-1 < C < 0). Default = -0.7 (Real) |
|
M | Positive exponent (
) characterizing the
effective stress dependence of the effective creep
strain rate in network B. Default = 1.0 (Real) |
|
Constant for regularization of the creep strain
rate near undeformed state. Default = 0.01 (Real) |
||
Tau_ref | Reference stress for the Effective creep strain
rate in secondary network. Default = 1.0 (Real) |
Example
#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
kg mm ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#- 2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW95/1/1
BERGSTROM
# RHO_I
1.42E-6
# C10 C01 C20 C11 C22
0.2019 0. 4.43E-5
# C30 C21 C12 C03 Sb
1.295E-4 0. 0. 0. 2.0
# D1 D2 D3
2.1839E-3 8.68E-5 -1.794E-5
# A EXPC EXPM KSI Tau_ref
1.0E-1 -0.7 5 0.01
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
Comments
- The response of the material can be represented using two parallel networks A and B. Network A is the equilibrium network with a nonlinear hyperelastic component. In network B, a nonlinear hyperelastic component is in series with a nonlinear viscoelastic flow element, and hence the time-dependent network.
- The same polynomial strain energy
potential is used for the hyperelastic components
in both networks. In network B, this potential is
scaled by a factor
Sb.
The strain energy density is then written for the
hyperelastic component of the
network:
(1) and(2) Where, - For special value of
, the polynomial model
can be reduced to the following material
models:
- Yeoh: j=0
Where, C10, C20, C30 are not zero
- Mooney-Rivlin: i+j =1
Where, C10 and C01 are not zero, and D2 =D3=0
- Neo-Hookean:
Only C10 and D1 are not zero
- Yeoh: j=0
- The initial shear modulus and the bulk
modulus are computed as:
(3) and(4) - If D1= 0, an incompressible material is considered.
- If =0, then only the hyperelastic polynomial material model is used with no viscoelastic time dependent response.
- The effective creep strain rate in
network
is given by the
expression:
(5) Where,- and
- Effective stress in Network B
- , , and
- Input material parameters