/EOS/COMPACTION

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

Format

(1)	(3)	(5)	(7)	(10)
/EOS/COMPACTION/`mat_ID`/`unit_ID`
`eos_title`
`C`₀	`C`₁	`C`₂	`C`₃	`I`_form
$μ_{\min}$	$μ_{\max}$	`B`
`P`_sh

Definition

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier. (Integer, maximum 10 digits)
`eos_title`	EOS title. (Character, maximum 100 characters)
`C`₀	EOS parameter. (Real)
`C`₁	EOS parameter. (Real)
`C`₂	EOS parameter. (Real)
`C`₃	EOS parameter. (Real)
`I`_form	Flag formulation for unloading behavior. 5 0 Default is 1 1 (Default) Constant unloading slope 2 Linear unloading slope (Integer)
$μ_{\min}$	Elastic limit. No compaction below $μ < μ_{\min}$ . $P_{e} = C_{0} + C_{1} μ_{\min} + C_{2} μ_{\min}^{2} + C_{3} μ_{\min}^{3}$ Default = 0.0 (Real)
$μ_{\max}$	Maximum compaction. Default = 10²⁰ (Real)
`B`	Unloading bulk modulus. (Real)	$[Pa]$
`P`_sh	Pressure shift. (Real)	$[Pa]$

Example

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW06/6/1
law06
#              RHO_I        
             2.33e-3          
#                 NU                PMIN
                0.22               -0.02
/EOS/COMPACTION/6/1
law06-compaction
#                 C0                  C1                  C2                  C3               Iform
                1E-2               0.256               0.256                   1                   1
#              MUMIN               MUMAX                BUNL
                 0.0               0.115                1.44
#                PSH               
                   0                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata

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 path defined by curve:(1)
$P = C_{0} + C_{1} μ + C_{2} μ^{2} + C_{3} μ^{3}$

Where,

$P$

Pressure in material

$μ$

Volumetric strain with $μ = \frac{ρ}{ρ_{0}} - 1$

Unloading and reloading are made along straight line whose slope is B.

P_sh

Pressure shift value used to model the relative pressure formulation.

Figure 2. Pressure versus Volumetric Strain
In versions prior to 2019.1, this equation of state was embedded in /MAT/LAW10 with a fixed elastic limit, $μ_{\min} = 0$ .
Equations of state are used by Radioss to compute the hydrodynamic pressure and are compatible with the material laws:
- /MAT/LAW3 (HYDPLA)
- /MAT/LAW4 (HYD_JCOOK)
- /MAT/LAW6 (HYDRO or HYD_VISC)
- /MAT/LAW10 (DPRAG1)
- /MAT/LAW12 (3D_COMP)
- /MAT/LAW49 (STEINB)
- /MAT/LAW102 (DPRAG2)
- /MAT/LAW103 (HENSEL-SPITTEL)
The unloading path runs along a constant slope $B$ by default. You can define a variable slope which increases with the compaction using I_form=2. The slope will then evolve from C₁ at $µ_{\min}$ to $B$ at $μ_{\max}$ .
Figure 3. I_form=1 Unloading along a constant slope $B$

Figure 4. I_form=2 Unloading slope evolves from C₁ to $B$ in $[µ_{\min}, µ_{\max}]$