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Incompressibility in hyperelastic ABAQUS-Subroutine

Hello everybody,

in hyperelastic material models incompressibility is normally realised through Lagrange multipliers. But i can't find any instruction, whether i have to code that multiplier in a routine e.g. of type UHYPER, UANISOHYPER_INV or UANISOHYPER_STRAIN! The only instruction is on incompressibility (and hybrid element) flags, that have to be set, cf. Abaqus User Subroutines Reference Manual 1.1.20, 21 and 37.

 

The strain measures or invariants passed in to the routine are the modified deviatoric ones, except Ainv(3)=J=detF. So i assume, coding the routine without Lagrange multiplier would be right??

 

If i had to code the multiplier-terms, how could abaqus solve the undefined multiplier??

 

I read somewhere, that the multiplier takes the form p= -1/3 (Sigma11 + Sigma22 + Sigma 33), but to me that seems like a special case, am i right?

 

Thanks in advance!

 

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