MATX21

Bulk Data Entry Defines additional material properties for Rock-Concrete material for geometric nonlinear analysis.

This law is based on the Drücker-Prager yield criteria and 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. This law is only applicable to solid elements.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATX21 MID A0 A1 A2 AMAX        
  TPID KT FSCAL P B MUMAX P    

Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT1 102 3.1E10   0.33 1000.0        
MATX21 102     3          
  1 1E10              

Definitions

Field Contents SI Unit Example
MID Material ID of the associated MAT1. 1

No default (Integer > 0)

 
A0 Coefficient.

(Real)

 
A1 Coefficient.

(Real)

 
A2 Coefficient.

(Real)

 
AMAX von Mises limit.

Default = 1030 (Real > 0)

 
TPID Identification number of a TABLES1 that defines the volumetric strain vs. pressure function.

No default (Integer > 0)

 
KT Tensile bulk modulus.

Recommended to set equal to 1/100 of unloading bulk modulus. Must be positive.

(Real > 0.0)

 
FSCAL Scale factor for pressure function.

Default = 1.0 (Real)

 
P Minimum pressure.

Default = -1030 (Real)

 
B Unloading bulk modulus.

Recommended to set equal to the initial slope of function describing P ( μ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGqbWaaeWaaeaacqaH8oqBaiaawIcacaGLPaaaaaa@3CEB@ . Must be positive.

(Real > 0.0)

 
MUMAX Maximum compression volumetric strain.

(Real)

 
P External pressure.

Required if relative pressure formulation is used. In this specific case, yield criteria and energy integration require the value of total pressure.

Default = 0.0 (Real)

 

Comments

  1. The material identification number must be that of an existing MAT1 Bulk Data Entry. Only one MATX21 material extension can be associated with a particular MAT1.
  2. MATX21 is only applied in geometric nonlinear analysis subcases which are defined by ANALYSIS=EXPDYN. It is ignored for all other subcases.
  3. Hydrodynamic behavior is given by a user-defined function P = f ( μ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGqbGaeyypa0JaamOzamaabmaabaGaeqiVd0gacaGLOaGaayzk aaaaaa@3EDC@ .
    Where,
    P
    Pressure in the material
    μ
    Volumetric strain


    Figure 1.
  4. Drücker-Prager yield criteria uses a modified von Mises yield criteria to incorporate the effects of pressure for massive structures:(1)
    F = J 2 ( A 0 + A 1 P + A 2 P 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGgbGaeyypa0JaamOsamaaBaaaleaacaaIYaaabeaakiabgkHi TmaabmaabaGaamyqamaaBaaaleaacaaIWaaabeaakiabgUcaRiaadg eadaWgaaWcbaGaaGymaaqabaGccaWGqbGaey4kaSIaamyqamaaBaaa leaacaaIYaaabeaakiaadcfadaahaaWcbeqaaiaaikdaaaaakiaawI cacaGLPaaaaaa@4865@
    Where,
    J 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGkbWaaSbaaSqaaiaaikdaaeqaaaaa@3A8E@
    Second invariant of deviatoric stress
    P
    Pressure
    A 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGbbWaaSbaaSqaaiaaicdaaeqaaaaa@3A83@ , A 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGbbWaaSbaaSqaaiaaicdaaeqaaaaa@3A83@ , and A 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGbbWaaSbaaSqaaiaaicdaaeqaaaaa@3A83@
    Material coefficients
    A 1 = A 2 = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGbbWaaSbaaSqaaiaaigdaaeqaaOGaeyypa0JaamyqamaaBaaa leaacaaIYaaabeaakiabg2da9iaaicdaaaa@3F0C@ means that the yield criteria is von Mises ( σ vm = 3 A 0 ).


    Figure 2.
  5. This card is represented as an extension to a MAT1 material in HyperMesh.