Hyper-elastic units

General Questions
1

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?

Thanks

Luke

2

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

1 Like
3

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.

4

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.