/MAT/LAW75 (POROUS)
Block Format Keyword Describes the P$\alpha $ porous material model. This material describes ductile Porous material with Herrmann model. It only works with 8node brick element and is not compatible with ALE.
Format
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/MAT/LAW75/mat_ID/unit_ID or /MAT/POROUS/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
E  $\upsilon $  
mat_ID_{s}  Iflag_{1}  Iflag_{2}  ite_{max}  
P_{E}  P_{s}  n  
tol 
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) 

${\rho}_{i}$  Initial density for porous
material (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
E  Young's modulus (Real) 
$\left[\text{Pa}\right]$ 
$\upsilon $  Poisson's ratio (Real) 

mat_ID_{s}  Material identifier of the solid (fully
compacted) material. (Integer) 

Iflag_{1}  Pressure formulation flag. (Integer) 

Iflag_{2}  Deviatoric stresses formulation flag.
(Integer) 

ite_{max}  Maximum number of iterations on a
calculation. Default = 5 (Integer) 

P_{E}  Elastic compact pressure (elastic
limit). 3 (Real) 
$\left[\text{Pa}\right]$ 
P_{s}  Solid (matrix) compact pressure. 3 (Real) 
$\left[\text{Pa}\right]$ 
n  Exponent used for fitting the experiment
data. 3 Default = 2 (Real) 

tol  Convergence tolerance on a calculation. $\frac{\left\text{\Delta}\alpha \right}{\alpha}<tol$ Default = 10^{8} (Real) 
Example (Porous Soil)
#12345678910
# 2. LOCAL_UNIT_SYSTEm:
#12345678910
/UNIT/1
unit for mat
# MUNIT LUNIT TUNIT
g cm mus
#12345678910
#12345678910
# 1. MATERIALS:
#12345678910
/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
#12345678910
/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
#12345678910
#enddata
#12345678910
Comments
 The porosity $\alpha $
is defined as:$$\alpha =\frac{{\rho}_{s}}{\rho}$$
Note that $\alpha $ ≥ 1 ( ${\rho}_{s}\ge \rho $ )
Where, ${\rho}_{s}$
 Density of the solid (full compacted matrix) material
 $\rho $
 Density of the porous material
 If the EOS of the solid (matrix)
material is:$$P=\mathrm{f}\left({\rho}_{s},e\right)$$Then the EOS of the porous material is:
 $P=\mathrm{f}\left(\alpha \rho ,e\right)$
 for Herrmann formulation
 $P=\frac{1}{\alpha}\mathrm{f}\left(\alpha \rho ,e\right)$
 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.
 If
$P<{P}_{E}$
the behavior is elastic, and if
$P>{P}_{E}$
describes plastic region.
In the elastic region, the change of porosity $\alpha $ with pressure $P$ is reversible.
In the plastic region, the porosity $\alpha $ is assumed to depend on pressure as described below:
$$\alpha =1+\left({\alpha}_{P}1\right){\left[\frac{{P}_{S}P}{{P}_{S}{P}_{E}}\right]}^{n}$$Where, ${\alpha}_{P}$
 Porosity where pressure reach the elastic compact pressure ${P}_{E}$
 $\alpha =1$
 Pressure reaches the solid (matrix) compact pressure ${P}_{S}$
 ${\alpha}_{0}$
 Initial porosity