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Hyperelastic Plane Stress

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(@coolmallu)
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Joined: 14 years ago

Hi Dr. Jorgen,

Im a PhD. student in CU Boulders Mechanical Engineering department. I recently wrote some code for calculating the internal forces in a nearly incompressible hyperelastic plane stress element, but Im unsure about how I should calculate the out of plane component of the deformation gradient. The abaqus theory manual starts from a linear elastic assumption in order to derive an equation for the thickness change, but they dont explain when and why that is valid. Would it be possible for you to point me towards some resources that explain methods for calculating the out of plane component of the deformation gradient for hyperelastic plane stress elements?

Thanks,

Chris DeLuca

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(@jorgen)
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Joined: 4 years ago

Im curious, who do you work with at CU Boulder? And whats your thesis topic?

You basically have three options for calculating the out of plane deformation. The first approach is to solve for the out of plane deformation that give a zero stress in the out of plane direction. This should give you good results but can be computationally and theoretically expensive.

The other option is to assume that your material is fully incompressible, that will significantly simplify the derivation of the out of plane deformations.

A third option is to calculate the stresses based on an incompressible approach, and then calculate the out of plane deformation based on a fixed transverse Poissons ratio. The actual transverse strain can be very strongly influencing the large deformation resonse in plane stress.

-Jorgen

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Topic starter
(@coolmallu)
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Joined: 14 years ago

Thanks for responding so fast!

We dont exactly have my research topic nailed down yet, but Im working in Kurt Mautes optimization group under both Kurt Maute and Martin Dunn. Do you know either of them?

I think the first option will be too expansive for what we are doing, and we really dont want to be limited to modeling incompressible materials, so I think Ill explore the third option.

Ive been looking through the abaqus manuals for a while trying to find an explanation for why they calculate the out of plane component the way they do, and I cant find one anywhere. Do you know of any resources that might explain why abaqus calculates the thickness change the way that they do?

Thanks again,

Chris DeLuca

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