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Hello,
I’m trying to figure out how hyper-elastic materials function. For this, I’d like to use Python or Matlab to implement the simplest instance feasible.
A beam fixed on one side is subjected to a traction test, which is solved using a 1D finite element approach.
The mesh is nothing more than a series of 1D elements with 1 degree of freedom connected by nodes.
It’s simple to write the stiffness matrix and calculate F=KUĀ in the case of a linear material.
If I want to utilize a hyperelastic behavior law (such as Moonley Rivlin or Neo Hookean), I can’t figure out how to create the stiffness matrix; for me, it would be something nonlinear like K(u), which would necessitate an iterative approach to inverse the matrix.

In 1D and static, I can’t find any examples of straightforward implementation/discretization of a hyper-elastic behavior law.
Is there anyone who knows how to code this? Or the overarching concept of hyper-elastic law?
The majority of the resources I found are too theoretical to be useful in practice.
Thank you for your assistance.

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Hello,

If you want to use only the coding platform, I have a suggestion. You can use the ABAQUS subroutine called UHYPER. There you would be able to write any conditions or use any theory you want to model a hyper-elastic material. Actually, there is an example with Neo-Hookean theory in the link below. I think it could help you.

https://caeassistant.com/product/uhyper-subroutine-in-abaqus/#Workshop-13323-8da6

Best regards.

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