/MAT/LAW10 (DPRAG1)

Block Format Keyword This law, based on an extended Drücker-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 2021.1, 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
ρ i                
E ν MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyVd4gaaa@37AE@            
A0 A1 A2 Amax    
Δ P min MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaam iuamaaBaaaleaaciGGTbGaaiyAaiaac6gaaeqaaaaa@3B2F@              

Definitions

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)

 
ρ i Initial density.

(Real)

[ kg m 3 ]
E Young's modulus.

(Real)

[ Pa ]
ν MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyVd4gaaa@37AE@ Poisson's ratio.

(Real)

 
A0 Yield criteria coefficient.

(Real)

[ P a 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca WGqbGaamyyamaaCaaaleqabaGaaGOmaaaaaOGaay5waiaaw2faaaaa @3A96@
A1 Yield criteria coefficient.

(Real)

[ Pa ]
A2 Yield criteria coefficient.

(Real)

 
Amax Yield criteria limit (von Mises limit).

(Real)

[ P a 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca WGqbGaamyyamaaCaaaleqabaGaaGOmaaaaaOGaay5waiaaw2faaaaa @3A96@
Δ P min MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaam iuamaaBaaaleaaciGGTbGaaiyAaiaac6gaaeqaaaaa@3B2F@ Minimum pressure.

Default = -1030 (Real)

[ Pa ]

Example (Concrete)

#RADIOSS STARTER
/UNIT/1
unit for mat
                   g                  cm                 mus
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW10/1/1
Concrete
#              RHO_I
                 2.4                   
#                  E                  Nu
                .576                 .25
#                 A0                  A1                  A2                Amax
            9.72E-10             4.32E-5                 .48                .013
#              P_min 
              -1E-20 
/EOS/COMPACTION/1/1
Concreate EOS
#                 C0                  C1                  C2                  C3
                 0.0               0.256               0.256                   1
#              MUMIN               MUMAX                BUNL
                 0.0                0.44               0.115
#                PSH                RHO0
                   0                2.40  
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA

Comments

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


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


    Figure 2. Extended Drücker-Prager Yield Criteria Implemented in Radioss
  2. Extended Drücker-Prager yield criteria can be compared with Mohr-Coulomb criteria.


    Figure 3. Extended Drücker-Prager Yield Criteria Implemented in Radioss versus Mohr-Coulomb Criteria
    An extended Drücker-Prager yield criterion can be fitted from Mohr-Coulomb parameters:
    c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yaaaa@36DF@
    Cohesion parameter
    ϕ
    Angle of internal friction
    For this purpose, parameters A 0 , A 1 , A 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIWaaabeaakiaacYcacaWGbbWaaSbaaSqaaiaaigdaaeqa aOGaaiilaiaadgeadaWgaaWcbaGaaGOmaaqabaaaaa@3C72@ must be defined as:(1)

    A 0 = k ( c , ϕ ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGbbWaaSbaaSqaaiaaicdaaeqaaOGaeyypa0Jaam4Aamaabmaa baGaam4yaiaacYcacqaHvpGzaiaawIcacaGLPaaadaahaaWcbeqaai aaikdaaaaaaa@4255@

    A 1 = 6 k ( c , ϕ ) × α ( ϕ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGbbWaaSbaaSqaaiaaigdaaeqaaOGaeyypa0JaaGOnaiaadUga daqadaqaaiaadogacaGGSaGaeqy1dygacaGLOaGaayzkaaGaey41aq RaeqySde2aaeWaaeaacqaHvpGzaiaawIcacaGLPaaaaaa@4934@

    A 2 = 9 α ( ϕ ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGbbWaaSbaaSqaaiaaikdaaeqaaOGaeyypa0JaaGyoaiabeg7a HnaabmaabaGaeqy1dygacaGLOaGaayzkaaWaaWbaaSqabeaacaaIYa aaaaaa@4231@

    Modeling Type
    Parameters
    Circumscribed Drücker-Prager criteria
    k = 6 c × cos ( ϕ ) 3 ( 3 sin ( ϕ ) ) α = 2 sin ( ϕ ) 3 ( 3 sin ( ϕ ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGRb Gaeyypa0ZaaSaaaeaacaaI2aGaam4yaiabgEna0kGacogacaGGVbGa ai4CaiaacIcacqaHvpGzcaGGPaaabaWaaOaaaeaacaaIZaaaleqaaO WaaeWaaeaacaaIZaGaeyOeI0Iaci4CaiaacMgacaGGUbGaaiikaiab ew9aMjaacMcaaiaawIcacaGLPaaaaaaabaGaeqySdeMaeyypa0ZaaS aaaeaacaaIYaGaci4CaiaacMgacaGGUbGaaiikaiabew9aMjaacMca aeaadaGcaaqaaiaaiodaaSqabaGcdaqadaqaaiaaiodacqGHsislci GGZbGaaiyAaiaac6gacaGGOaGaeqy1dyMaaiykaaGaayjkaiaawMca aaaaaaaa@5F3D@
    Middle Circle
    k = 6 c × cos ( ϕ ) 3 ( 3 + sin ( ϕ ) ) α = 2 sin ( ϕ ) 3 ( 3 + sin ( ϕ ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGRb Gaeyypa0ZaaSaaaeaacaaI2aGaam4yaiabgEna0kGacogacaGGVbGa ai4CaiaacIcacqaHvpGzcaGGPaaabaWaaOaaaeaacaaIZaaaleqaaO WaaeWaaeaacaaIZaGaey4kaSIaci4CaiaacMgacaGGUbGaaiikaiab ew9aMjaacMcaaiaawIcacaGLPaaaaaaabaGaeqySdeMaeyypa0ZaaS aaaeaacaaIYaGaci4CaiaacMgacaGGUbGaaiikaiabew9aMjaacMca aeaadaGcaaqaaiaaiodaaSqabaGcdaqadaqaaiaaiodacqGHRaWkci GGZbGaaiyAaiaac6gacaGGOaGaeqy1dyMaaiykaaGaayjkaiaawMca aaaaaaaa@5F27@
    Inscribed Drücker-Prager criteria
    k = 3 c × cos ( ϕ ) 9 + 3 sin 2 ( ϕ ) α = sin ( ϕ ) 9 + 3 sin 2 ( ϕ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGRb Gaeyypa0ZaaSaaaeaacaaIZaGaam4yaiabgEna0kGacogacaGGVbGa ai4CaiaacIcacqaHvpGzcaGGPaaabaWaaOaaaeaacaaI5aGaey4kaS IaaG4maiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOmaaaakiaa cIcacqaHvpGzcaGGPaaaleqaaaaaaOqaaiabeg7aHjabg2da9maala aabaGaci4CaiaacMgacaGGUbGaaiikaiabew9aMjaacMcaaeaadaGc aaqaaiaaiMdacqGHRaWkcaaIZaGaci4CaiaacMgacaGGUbWaaWbaaS qabeaacaaIYaaaaOGaaiikaiabew9aMjaacMcaaSqabaaaaaaaaa@5D3E@


    Figure 4. Fitting a Drücker-Prager Yield Criteria (blue colors) from Mohr-Coulomb Criterion (black)
  3. /MAT/LAW21 is also based on an extended Drücker-Prager yield criteria but pressure evolution can be described with user functions.
  4. Young's modulus E and Poisson’s ratio ν MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyVd4gaaa@37AE@ are used to determined shear modulus G which is required for sound speed calculation in solid materials.