Equivalent radius calculation for contact models?

MQ
MQ Altair Community Member
edited June 2022 in Community Q&A

Hi Everyone,

I have a bit of an ambiguity in mind, regarding calculation of equivalent radius (R*) for two interacting particles with radii R1 and R2 respectively. For instance, in carrying out calculations for Hertz-Mindlin force, we use:

double equivRadius(const NCalcForceTypesV3_0_0::SDiscreteElement & element1, const NCalcForceTypesV3_0_0::SDiscreteElement & element2)
{
return (element1.physicalRadius * element2.physicalRadius) / (element1.physicalRadius + element2.physicalRadius);
}

This calculation would halve the 'equivalent radius' of the particles having same radius (R1 = R2):

R* = R1R2/(R1+R2) = R1R1/(R1+R1) = R1^2/(2R1) = 0.5R1

In some literatures, I have also seen a factor of 2 being used to evaluate the equivalent radius, i.e., R* = 2R1R2/(R1+R2).

Can someone please help clarify this?

Thank you.

Best regards,

MQ

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Answers

  • RWood
    RWood
    Altair Employee
    edited June 2022

    Hi,

    If you're seeing another paper/textbook using a different definition for something like the equivalent radius then I suspect that there will be another slight difference later on in another term, in the stiffness calculation for example where perhaps the factor is reintroduced. 

    We've followed the approaches of those listed in the bibliography in our documentation but there will no doubt be slight variations on definitions and implementations by different authors, though I would expect the end results to be the same.

    Cheers,

    Richard

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