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Ogden Material:Closed-form expressions for the derivatives with respect to invariants

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Posts: 6
Topic starter
(@LennonCauser)
Active Member
Joined: 9 years ago

Hi everyone,

Im implementing an UMAT routine which is ready for any isotropic hyperelastic material as long as the derivatives dW/dI, dW/dJ, d2W/dIdI,d2W/dJdI are provided.

The routine is already validated for Neo-Hooke and Mooney-Rivlin models, where the quadratic convergence were achieved.

However, in the case of the Ogden model, the Abaqus Documentation suggest to get the closed-form expressions for those derivatives.

I used the chain rule involving the principal stretches and the definition of the Invariants, but Im having troubles to compute the second derivatives.

Anyone knows how to compute them?

Thanks in advance and best regards,

jferreira

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Posts: 6
Topic starter
(@LennonCauser)
Active Member
Joined: 9 years ago

Any tips? Literature links? Urgent!

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