/EOS/COMPACTION2

Block Format Keyword Describes pressure for a porous media such as soil or foam which can be compacted and unloaded.

This Equation of State (EOS) is similar to /EOS/COMPACTION but is based on a user-function instead of a polynomial expression.

Format


(1)	(2)	(3)	(5)	(7)	(10)
	`P_func_ID`	`Fscale`	`Xscale`		`I`_form
$μ_{\min}$		$μ_{\max}$	`Bmin`	`Bmax`
`PSH`

Definition


Field	Contents	SI Unit Example
`P_func_ID`	Pressure versus volumetric strain function identifier. (Integer)
`Fscale`	Scale factor Ordinates for function P. Default = 1.0 (Real)	$[Pa]$
`Xscale`	Scale factor Abscissa for function P. Default = 1.0 (Real)
`I`_form	Unload formulation flag. 1 Constant modulus 2 (Default) Linear modulus from `Bmin` to `Bmax` on interval [ $μ_{\min}$ , $μ_{\max}$ ] (Integer)
$μ_{\min}$	Threshold value for compaction activation. Default = 0.0 (Real)
$μ_{\max}$	Maximum compaction. (Real)
`Bmin`	Tensile bulk modulus. (Real)	$[Pa]$
`Bmax`	Maximum unloading bulk modulus. (Real)	$[Pa]$
`PSH`	Pressure shift. (Real)	$[Pa]$

Example (Concrete)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                   g                  cm                 mus
#---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-02 
/EOS/COMPACTION2/1/1
Concrete EOS
#          P_func_ID              Fscale              Xscale                                   Iform
                  10                   0                   0                                       2
#              MUMIN               MUMAX                BMIN                BMAX 
                 0.0                0.44               0.256                2.56
#                PSH
                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/10
P versus volumetric strain
#                  X                   Y
                  -1              -0.256
                   0                   0
                0.05            0.013565
                 0.1             0.02916
                0.15            0.047535
                 0.2             0.06944
                0.25            0.095625
                 0.3             0.12684
                0.35            0.163835
                 0.4             0.20736
                0.45            0.258165
                 0.5               0.317
                0.55            0.384615
                 0.6             0.46176
                0.65            0.549185
                 0.7             0.64764
                0.75            0.757875
                 0.8             0.88064
                0.85            1.016685
                 0.9             1.16676
                0.95            1.331615
                   1               1.512
                1.05            1.708665
                 1.1             1.92236
                1.15            2.153835
                 1.2             2.40384
                1.25            2.673125
                 1.3             2.96244
                1.35            3.272535
                 1.4             3.60416
                1.45            3.958065
                 1.5               4.335
                1.55            4.735715
                 1.6             5.16096
                1.65            5.611485
                 1.7             6.08804
                1.75            6.591375
                 1.8             7.12224
                1.85            7.681385
                 1.9             8.26956
                1.95            8.887515
                   2               9.536
                2.05           10.215765
                 2.1            10.92756
                2.15           11.672135
                 2.2            12.45024
                2.25           13.262625
                 2.3            14.11004
                2.35           14.993235
                 2.4            15.91296
                2.45           16.869965
                 2.5              17.865
                2.55           18.898815
                 2.6            19.97216
                2.65           21.085785
                 2.7            22.24044
                2.75           23.436875
                 2.8            24.67584
                2.85           25.958085
                 2.9            27.28436
                2.95           28.655415
                   3              30.072
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

This equation of state is used to model pressure in porous media such as soil or foam. The compaction has an elastic response when it is less than the elastic limit $μ = μ_{\min}$ .
Figure 1.
Plastic compaction is along the path defined by curve.
$P = C_{0} + C_{1} μ + C_{2} μ^{2} + C_{3} μ^{3}$
Where,

$P$

Pressure in material

$μ$

Volumetric strain with $μ = \frac{ρ}{ρ_{0}} - 1$
Unloading and reloading are made along the straight line whose slope is $B$ which evolves from Bmin at $μ_{\min}$ to Bmax at $μ_{\max}$ .
Where, PSH is the pressure shift value used to model the relative pressure formulation. (Alternatively, $C_{0}$ can be set to 0).
In general case, $μ_{\min}$ is set to 0.
Figure 2. Pressure versus volumetric strain
The unloading path can be done with a constant modulus $B = B_{\max}$ when I_form=1.
Figure 3. I_form= 1, Unloading along a constant slope $B$