/MAT/LAW133 (GRANULAR)

Block Format Keyword This material law models dry granular media, such as sands, using pressure-dependent elasto-plastic formulation.

The shear modulus $G (ρ)$ varies with density, and the plastic yield strength $Y (P)$ increases with pressure (hardening under confinement).

This model is typically used in combination with a compaction-type Equation of State.

Format


(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/MAT/LAW133/`mat_ID`/`unit_ID` or /MAT/GRANULAR/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$
`nu`		`Pmin`
`fct_ID`_G		`Gscale`
`fct_ID`_Y		`Yscale`

Definition


Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	(Optional) Unit identifier. (Integer, maximum 10 digits)
`mat_title`	Material title. (Character, maximum 100 characters)
$ρ_{i}$	Initial density. (Real)	$[\frac{kg}{m^{3}}]$
`nu`	Poisson’s ratio. (Real)
`Pmin`	Minimum pressure. Default = 0.0 (Real)	$[Pa]$
`fct_ID`_G	Shear modulus dependency function identifier, $G (ρ)$ . = 0 $G = G s c a l e$ > 0 $G = G s c a l e . G (ρ)$ (Integer)
`Gscale`	Shear modulus scale factor. Default = 1.0 (Real)	$[Pa]$
`fct_ID`_Y	Yield surface dependency function identifier, $Y (P)$ . = 0 $Y = Y s c a l e$ > 0 $Y = Y s c a l e . Y (P)$ (Integer)
`Yscale`	Yield surface scale factor. Default = 1.0 (Real)	$[Pa]$

Example

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
Unit example
                  kg                   m                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/GRANULAR/1/1
Dry Sand Sjobo - Consitutive Law (LAW133)
#        Init. dens.
              1674.0
#                 nu                Pmin
                0.22                -1e3
#  G(r).id                       G-scale
       100                           1.0
#  Y(P).id                       Y-scale
       200                           1.0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/EOS/COMPACTION_TAB/1/1
Dry Sand Sjobo – Equation of State
#            RHO_TMD             C_SOLID                                                      I_PLAS
              2641.0              4634.0
# Pc(r).id                      Pc-scale
       300                           1.0
#  c(r).id                       c-scale
       400                           1.0	
#  g(r).id                       g-scale
       500                           5.0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/100
G(rho) : density-dependent shear modulus (Dry Sand Sjobo kg,m,s)
#                  X                   Y
              1674.0           0.0769E+9                                  
              1745.6           0.8694E+9                                                            
              2086.3           4.0317E+9                                                             
              2146.8           4.9069E+9                                                      
              2300.0           7.7690E+9                                                                                     
              2572.0           14.801E+9                                                            
              2598.0           16.571E+9                                                             
              2635.0           36.718E+9                                                          
              2641.0           37.347E+9                                                        
              2800.0           37.347E+9                                                               
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/200
Y(P) : pressure-dependent yield surface (Dry Sand Sjobo kg,m,s)
#                  X                   Y
                0.00                 0.0                                                            
            3.401E+6            4.235E+6                                                           
           34.898E+6           44.695E+6                                                           
           101.32E+6           124.04E+6                                                           
           184.65E+6           226.00E+6                                                               
           500.00E+6           226.00E+6                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/300
Pc(rho) - plastic compaction curve (Dry Sand Sjobo kg,m,s)
#                  X                   Y
              1674.0                0.00
              1739.5            4.577E+6	
              1873.8            14.98E+6
              1997.0           29.151E+6
              2143.8           59.175E+6
              2250.0            98.10E+6
              2380.0           179.44E+6
              2485.0           289.44E+6
              2585.0           450.20E+6
              2671.3           650.66E+6
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/400
C_unload(rho) - elastic unloading soundspeed (Dry Sand Sjobo kg,m,s)
#                  X                   Y
              1674.0               265.2
              1745.6               852.1	
              2086.3              1721.7
              2146.8              1875.5
              2300.0              2264.8
              2572.0              2956.1
              2598.0              3112.2
              2635.0              4600.0
              2641.0              4634.0
              2800.0              4634.0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/500
gamma(rho) - shape function for unloading path
#                  X                   Y
                1674                 1.0
                1900                 1.0
                2641                 0.0
                3000                 0.0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

Using this material law with /EOS/COMPACTION_TAB allows you to model the Sjöbo Dry Sand model.
The Yield function $Y (P)$ allows you to define a customized surface.
Figure 1.

¹ Leo Laine & Ola Pramm Larsen, RE-IMPLEMENTATION AND CHARACTERIZATION OF SJOBO DRY SAND IN OPENRADIOSS: IMPROVING GROUND SHOCK PREDICTIONS THROUGH TRI-AXIAL AND WAVE VELOCITY TESTING, 15th International Conference on Shock & Impact Loads on Structures 12-13 June 2025, Gothenburg, Sweden