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/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.

The yield criteria is pressure dependent. To compute the pressure an equation of state must be provided (such as /EOS/COMPACTION). This law is compatible only with solid elements.
Important: Starting in version 2019.1, the equation of state (EOS) parameters were removed from this material law. Any model using the old format that includes the EOS parameters will be converted during import into the updated material law format with an associated /EOS/COMPACTION.

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

  1. Original Drucker-Prager yield criterion has a linear pressure dependency.


    Figure 1. Original Drucker-Prager Yield Criteria
    Radioss is using the extended Drucker-Prager yield criteria whose pressure dependency is nonlinear.


    Figure 2. Extended Drucker-Prager Yield Criteria Implemented in Radioss
  2. 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 Criteria
    An 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(3sin(ϕ))α=2sin(ϕ)3(3sin(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)
  3. /MAT/LAW21 is also based on an extended Drucker-Prager yield criteria but pressure evolution can be described with user functions.
  4. 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.
  5. Starter checks the yield parameters A0, A1, and A2 and warns you in case of an unexpected situation.
    Figure 5.