/MAT/LAW75 (POROUS)

Block Format Keyword Describes the P-α porous material model. This material describes ductile Porous material with Herrmann model. It only works with 8-node brick element and is not compatible with ALE.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW75/mat_ID/unit_ID or /MAT/POROUS/mat_ID/unit_ID
mat_title
ρ i                
E υ            
mat_IDs Iflag1 Iflag2 itemax            
PE Ps n        
tol                

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 for porous material

(Real)

[ kg m 3 ]
E Young's modulus

(Real)

[ Pa ]
υ Poisson's ratio

(Real)

 
mat_IDs Material identifier of the solid (fully compacted) material.

(Integer)

 
Iflag1 Pressure formulation flag.
= 1 (Default)
Herrmann. 1
= 2
Modified Herrmann. 2

(Integer)

 
Iflag2 Deviatoric stresses formulation flag.
= 1 (Default)
Hydrodynamic
= 2
Elastic

(Integer)

 
itemax Maximum number of iterations on a calculation.

Default = 5 (Integer)

 
PE Elastic compact pressure (elastic limit). 3

(Real)

[ Pa ]
Ps Solid (matrix) compact pressure. 3

(Real)

[ Pa ]
n Exponent used for fitting the experiment data. 3

Default = 2 (Real)

 
tol Convergence tolerance on a calculation.

| Δ α | α < t o l

Default = 10-8 (Real)

 

Example (Porous Soil)

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. LOCAL_UNIT_SYSTEM:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
#              MUNIT               LUNIT               TUNIT
                   g                  cm                 mus
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  1. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW75/1/1
porous soil
#              RHO_I
                 1.7
#                 E                   NU
                   3                  .3
#  MAT_IDs    IFLAG1    IFLAG2    ITEMAX
         2         1         2         0
#                PE                   PS                   N
                 .01                 .05                   0
#               TOL
                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/HYD_JCOOK/2/1
soil
#              RHO_I               RHO_O
          1.76000004                   0
#                  E                  nu
           3.5999999          .300000012
#                  A                   B                   n              epsmax              sigmax
               10000                   0                   0                   0                   0
#               Pmin
                   0
#                  C           EPS_DOT_0                   M               Tmelt                Tmax
                   0                   0                   0                   0                   0
#              RHOCP                                                       Troom
                   0                                                           0
/EOS/POLYNOMIAL/2/1
EOS for soil
#                 C0                  C1                  C2                  C3
                   0          2.81999993                   2               -1.37
#                 C4                  C5                  E0                 Psh               RHO_0
          1.53999996          1.53999996                   0                   0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. The porosity α is defined as:(1)
    α = ρ s ρ

    Note that α ≥ 1 ( ρ s ρ )

    Where,
    ρ s
    Density of the solid (full compacted matrix) material
    ρ
    Density of the porous material
  2. If the EOS of the solid (matrix) material is:(2)
    P = f ( ρ s , e )
    Then the EOS of the porous material is:
    P = f ( α ρ , e )
    for Herrmann formulation
    P = 1 α f ( α ρ , e )
    for modified Herrmann formulation

    Where, ( e ) is the internal energy per unit mass. It is same in porous material and in the solid (matrix) material.

  3. If P < P E the behavior is elastic, and if P > P E describes plastic region.

    In the elastic region, the change of porosity α with pressure P is reversible.

    In the plastic region, the porosity α is assumed to depend on pressure as described below:(3)
    α = 1 + ( α P 1 ) [ P S P P S P E ] n
    Where,
    α P
    Porosity where pressure reach the elastic compact pressure P E
    α = 1
    Pressure reaches the solid (matrix) compact pressure P S
    α 0
    Iinitial porosity

    mat_law75_porosity
    Figure 1.
1 "Constitutive equation for the dynamic compaction of ductile porous materials", Herrmann W., J. Applied Physics 40, 1969
2 "Static and dynamic pore collapse relations for ductile porous materials", Carroll M.M., Holt A.C., J. Applied Physics 43, 1972