/MAT/LAW10 (DPRAG1)
Block Format Keyword This law, based on an extended Drucker-Prager yield criteria, is used to model materials with internal friction such as rock-concrete.
Format
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
/MAT/LAW10/mat_ID/unit_ID or /MAT/DPRAG1/mat_ID/unit_ID | |||||||||
mat_title | |||||||||
ρi | |||||||||
E | ν | ||||||||
A0 | A1 | A2 | Amax | ||||||
ΔPmin |
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) |
|
ρi | Initial
density. (Real) |
[kgm3] |
E | Young's
modulus. (Real) |
[Pa] |
ν | Poisson's
ratio. (Real) |
|
A0 | Yield criteria
coefficient. (Real) |
[Pa2] |
A1 | Yield criteria
coefficient. (Real) |
[Pa] |
A2 | Yield criteria
coefficient. (Real) |
|
Amax | Yield criteria limit (von
Mises limit). (Real) |
[Pa2] |
ΔPmin | Minimum
pressure. Default = -1030 (Real) |
[Pa] |
▸Example (Concrete)
Comments
- Original Drucker-Prager
yield criterion has a linear pressure dependency.Figure 1. Original Drucker-Prager Yield CriteriaRadioss is using the extended Drucker-Prager yield criteria whose pressure dependency is nonlinear.Figure 2. Extended Drucker-Prager Yield Criteria Implemented in Radioss
- Extended Drucker-Prager
yield criteria can be compared with Mohr-Coulomb criteria.Figure 3. Extended Drucker-Prager Yield Criteria Implemented in Radioss versus Mohr-Coulomb CriteriaAn extended Drucker-Prager yield criterion can be fitted from Mohr-Coulomb parameters:
- c
- Cohesion parameter
- ϕ
- Angle of internal friction
For this purpose, parameters A0,A1,A2 must be defined as:(1) A0=k(c,ϕ)2
A1=6k(c,ϕ)×α(ϕ)
A2=9α(ϕ)2
- Modeling Type
- Parameters
- Circumscribed Drucker-Prager criteria
- k=6c×cos(ϕ)√3(3−sin(ϕ))α=2sin(ϕ)√3(3−sin(ϕ))
- Middle Circle
- k=6c×cos(ϕ)√3(3+sin(ϕ))α=2sin(ϕ)√3(3+sin(ϕ))
- Inscribed Drucker-Prager criteria
- k=3c×cos(ϕ)√9+3sin2(ϕ)α=sin(ϕ)√9+3sin2(ϕ)
Figure 4. Fitting a Drucker-Prager Yield Criteria (blue colors) from Mohr-Coulomb Criterion (black) - /MAT/LAW21 is also based on an extended Drucker-Prager yield criteria but pressure evolution can be described with user functions.
- Young's modulus E and Poisson’s ratio ν are used to determined shear modulus G which is required for sound speed calculation in solid materials.
- Starter checks the yield
parameters A0, A1, and A2 and warns you in case of an unexpected situation.Figure 5.