Density Variation Calculation over Time for MAT/LAW1 and MAT/LAW6 in RADIOSS

Question

When using MAT/LAW1 or MAT/LAW6, an initial density is set. How is the density change over time calculated in these cases?

ThierryS · Answer

What mentionned Adrien for /MAT/LAW1 is correct : for information  P=E/3/(1-2nu)*mu is deduced from P=-1/3 trace(sigma) where sigma is calculated using Hooke's law. Resulting EoS is depedent on strain tensor (large strain, small strain, etc…)

ThierryS · Answer

* For lagrangian case : rho[0].V[0] = rho[n].V[n] ⇒  rho[n] = rho[0] . V[0}/V[n]
* For ALE/EULER case : you have to take into account mass transfer (convection / remaping / inlet-outlet). rho[n] = mass[n] / V[n]

For example in OpenRadioss this is done in ./engine/.source/elements/solide/srho3.F for /BRICK elements.

After that Pressure is defined with

* P=-1/3 trace(sigma) if you do not define an EoS. 
* P=P(µ,E) if you do define an EoS.   (µ=rho/rho0-1 is volumetric strain and E=rho0.e)

Regards

Thierry

AdrienR · Answer

Hi Yuki, that's quite a vast question.

Obviously, the density is changing with the compression or expansion of the material, which can be directly linked to the element deformation in case of lagrangian formulation. So it is linked to strain / node displacement, which of course depends on forces and material bulk stiffness.

Then the question could be how does the density change with X variable. If X is the pressure, then I can tell that :

* for /MAT/LAW1 with large strain formulation, the density changes linearly with the pressure :

where E is the Young's modulus, nu is the Poisson's ratio and

* for /MAT/LAW6 : it depends on the /EOS selected/linked to the material. Each Equation Of State (EOS) is different, so you need to refer to the documentation of the specific /EOS that you use.

I hope it helps.

Adrien