/MAT/LAW102 (DPRAG2)
Block Format Keyword This law, based on extended Drucker-Prager yield criteria, is used to model materials with internal friction such as rock-concrete. The plastic behavior of these materials is dependent on the pressure in the material.
Format
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
/MAT/LAW102/mat_ID/unit_ID or /MAT/DPRAG2/mat_ID/unit_ID | |||||||||
mat_title | |||||||||
Iform | |||||||||
E | |||||||||
Amax | |||||||||
Pmin |
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) |
||
Iform | Formulation flag. 1
(Integer) |
|
E | Young's
modulus. (Real) |
|
Poisson's
ratio. (Real) |
||
Cohesion (Mohr-Coulomb
parameter). (Real) |
||
Internal friction angle
(Mohr-Coulomb parameter). (Real) |
||
Amax | Yield criteria
limit. Default = 1030 (Real) |
|
Pmin | Minimum pressure (usually
negative or zero, positive value for tension). Default = -1030 (Real) |
Example (Concrete)
#RADIOSS STARTER
/UNIT/1
unit for mat
g 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/DPRAG2/102/1
Concrete
# RHO_I
.0024
# Iform
2
# E NU
61000 .17
# c PHI AMAX
50 40 0.0
# P_min
0
/EOS/POLYNOMIAL/102/1
Concrete
# C0 C1 C2 C3
0 10000 0 0
# C4 C5 Psh Rho0
0 0 0 .0024
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
Comments
- An extended
Drucker-Prager yield criteria can be defined as:
The aim of this material law is to automatically compute A0, A1, A2 parameters from Mohr-Coulomb parameters (cohesion) and (angle of internal friction).
The Mohr-Coulomb criteria is usually defined by:(1) Where,- Shear stress
- Normal stress
- Cohesion
- Angle of internal friction
From the Mohr-Coulomb parameters three different extended Drucker-Prager yield criteria can be calculated.The following values are computed:
Where,Criteria α Circumscribed Middle Inscribed - Pressure
is defined through an equation of state
(/EOS).Where,
- Pressure in material.
- Volumetric strain with .
- Energy density.
Unloading:
If , then unloading bulk modulus, is used for unloading/reloading path. For each over , unloading path is the same as loading path.
- Drucker-Prager yield
criteria is given by:
(2) Where,- Second invariant of deviatoric stress, with
- P
- Pressure, with ( is the first stress invariant)
- Yield criteria is von Mises ( )
The polynomial expression should have at least one root and should be increasing.
- Pressure is always a total pressure. To model a relative pressure, the /EOS, Psh parameter must be used to shift the pressure output.
- The yield maximum
Amax is as the yield
function becomes:
(3)