/MAT/LAW81
Block Format Keyword This law is based on Drucker-Prager yield criteria with cap. It has a strain-hardening cap model based on the principles of Foster. Plasticity has an isotropic hardening.
Format
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
/MAT/LAW81/mat_ID/unit_ID | |||||||||
mat_title | |||||||||
K0 | G0 | c0 | Pb0 | ||||||
Eps_max | |||||||||
fct_IDK | fct_IDG | fct_IDC | fct_IDPb | Isoft | |||||
Kw | n0 | S0 | U0 | ||||||
Tol |
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) |
||
K0 | Initial bulk
modulus. (Real) |
|
G0 | Initial shear
modulus. (Real) |
|
c0 | Initial material
cohesion. (Real) |
|
Pb0 | Initial cap limit
pressure. (Real) |
|
Friction
angle. (Real) |
||
Plastic flow
angle. (Real) |
||
Ratio of:
Default = 0.5 (Real) |
||
Eps_max | Maximum dilatancy
(negative number limiting
). Default = -1020 (Real) |
|
Initial value of the
plastic volumetric strain. 3 (Real) |
||
fct_IDK | (Optional) Function
identifier for the bulk modulus scale factor versus the plastic
volumetric strain. 4 (Integer) |
|
fct_IDG | (Optional) Function
identifier for the shear modulus scale factor versus the plastic
volumetric strain. (Integer) |
|
fct_IDC | (Optional) Function
identifier for the material cohesion scale factor versus the
equivalent plastic strain. (Integer) |
|
fct_IDPb | (Optional) Function
identifier for the cap limit pressure scale factor versus the
plastic volumetric strain. (Integer) |
|
Isoft | Cap softening flag.
(Integer) |
|
Kw | Pore bulk modulus
(water). (Real) |
|
n0 | Initial
porosity. (Real) |
|
S0 | Initial
saturation. (Real) |
|
U0 | Initial pore
pressure. (Real) |
|
Tol | Tolerance for cap shift
viscosity. Default = 1.0E-4 (Real) |
|
Viscosity
factor. Default = 0.5 (Real) |
Example
#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
kg m s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#- 2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW81/1/1
LAW81
# RHO_I
1700
# K0 G0 c0 PB0
2.83E9 1.31E9 1 1
# PHI PSI
15 10
# ALPHA EPS_p_max EPS_0
.5 .02 .002
# Fct_IDK Fct_IDG Fct_IDc Fct_IDPb I_soft
0 0 3 4 1
# Kw n0 S0 U0
2.5E10 0.1 0.99 0.0
# Tol alpha_v
0.0001 0.5
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#- 3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/3
Yield Hardening
# X Y
0 2000
.1 2002000
1 2002000
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/4
Cap Hardening
# X Y
-1 1000
0 1000
.001 30000
.0022 70000
.0024 80000
.004 100000
.0056 200000
.0078 800000
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
Comments
- The yield surface is defined
as:
Where,
if
if
Where,- p
- Pressure
- q
- von Mises stress
- c
- Material cohesion
- P0
- Pressure, where
- pb
- Cap limit pressure
Figure 1.
In this material, yield surface and failure surface are the same.
- Plastic flow is governed by the
non-associated flow potential G, as:
if
if
if , the flow becomes associated on the cap.
- If cap softening is allowed, can decrease, therefore it is recommended to define the following curves on a relevant range. For example, if , negative values.
- The initial values for bulk
modulus, shear modulus, material cohesion, and cap limit pressure can be scaled
by defining a function as the scale factor curve for each respective value. If
the function is not defined, then the value is considered constant. For
example:
If fct_IDK = 0 then,
If fct_IDK ≠ 0 then, , with the function defined in fct_IDK
- The initial bulk modulus and shear
modulus can be calculated as:
;
With,- Poisson’s ratio
- Young’s modulus of concrete
- The porosity is defined so that
it represents the volume fraction of voids, with respect to the total material
volume.
In the elastic case, the void volume does not change. However, in the plastic case, the porosity change is defined by:
- Effect of pores filled with
water:
The initial state of the pores is defined by the initial porosity, initial saturation, and initial pore pressure n0, U0 and S0 which can be calculated as:
If the then the entered value for S0 is not used and instead S0 is recalculated.
- The following user variables are
available for post-treatment:
USR1 is the equivalent plastic strain EPSPD
USR2 is the plastic volumetric strain EPSPV
USR3 is the cohesion c
USR4 is the cap limit pressure Pb
USR5 pore pressure U
USR6 porosity n
USR7 saturation S
USR8 cap shift