I'm using a constitive model for an FEA analysis that is outlined as follows: enter image description here

In which Young's Modulus is an structure strain invariant defined by the following tensor: enter image description here

And I need to use the SMSHookeToLame function in order to compensate for poisson's ratio (v) and E, however, I'm not really sure how to go about it due to the tensorial nature E.

I apologize if this is a stupid question but I am just learning to use AceFem.

Thank you and have a great day :)

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    $\begingroup$ Welcome to MSE. Please post code rather than an image. $\endgroup$ – Rohit Namjoshi Nov 7 '19 at 2:41
  • $\begingroup$ Welcome to Mathematica.SE! I suggest the following: 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Take the tour and check the faqs! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! $\endgroup$ – Pinti Nov 7 '19 at 8:16
  • $\begingroup$ Are you sure about tensorial nature of Young's modulus in your equation? You seem to define it as a trace (Tr) of something and that should return a scalar. $\endgroup$ – Pinti Nov 7 '19 at 8:30
  • $\begingroup$ The Young's modulus is defined for isotropic materials and by nature is a scalar and cannot be a tensor. $\endgroup$ – KratosMath Nov 18 '19 at 10:21

SMSHookeToLame is a small utility function which converts Young's modulus and Poisson ratio to Lame's constants. They are more suitable for direct use in constitutive equations.

{λ, g} = SMSHookeToLame[e, ν]

{(e ν)/((1 - 2 ν) (1 + ν)), e/(2 (1 + ν))}

You can also enter Young's modulus as a tensor (3 x 3 matrix), but I am not sure if that is physically correct approach.

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