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

Yuki Kaneko
Yuki Kaneko Altair Community Member
in Community Q&A

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

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Answers

  • AdrienR
    AdrienR
    Altair Employee

    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 :
    image.png

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

    image.png
    • 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

  • ThierryS
    ThierryS
    Altair Employee
    • 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

  • ThierryS
    ThierryS
    Altair Employee

    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…)

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