Hyper-elastic units

I am running ProPoMax in mm ton sec units, and want to add hyper elastic properties using the ARRUDA-BOYCE model. This will have to be entered manually which isn’t a problem but I suspect the units I started with are far off as the model won’t converge (it runs fine without hyper elastic properties and for a while with hooke before blowing up).

Should mu be in MPa or something else?



The unit for µ and D will be MPa in this case while λ_m is unitless.

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i’m not really familiar with this material. but reading some articles, the units of hyperelastic ( Arruda-Boyce) materials are example given:

  • Mu = 0.133 (MPa)
  • lamda = 1 (unitless)
  • D = 4.3 (1 / MPa)

another source notify D is half of bulk modulus, so the units should be in MPa. may this is the case of inconsistent unit.

Right, it’s hard to find information about this since units are often omitted, especially for D. But it seems that 1/MPa is most commonly used: html.scirp.org/file/_3-2190113_1.htm

Just like it is the case with incompressibility parameter for other hyperelasticity models.

According to Abaqus documentation, K_0 = 2 / D where K_0 is the initial bulk modulus. Wikipedia claims that D_1 = K / 2 where K is the bulk modulus but equation they use includes D_1*(((J^2-1)/2)-ln(J)) while Abaqus uses 1/D*(((J^2-1)/2)-ln(J)). This seems to explain the inconsistency.