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A simple hyperelastic (1-DoF) calculatin sheet - non-linear method required

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I am thinking about a possible mcad sheet for an hyperelastic material ie a rubber. Attached is a typical curve for such material.

I would like to predict the displacment (of some quantity, maybe stress) knowing the total force to be applied. I am not sure so will be happy to be corrected but is this a non linear problem (gien the shape of the curve)?

 

Known

  1. total force to the applied
  2. a (non-linear) relationship between say strain & stress

Find

The final "state" once all the toal force is applied

 

I haven't got a clue where to start.

Does the probleme require some kind of iterative solver?

 

Am I overthinking the whole think?

 

Any suggestion is welcome

 

Thanks

 

Regards

 

JXB


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