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strain energy density function

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Posts: 11
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(@MichaelRamsey)
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Joined: 11 years ago

what are strain energy density functions?

how are they useful in hyperelastic models?

can,t the same function be used in linear models?

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Posts: 8
(@K3v1n17)
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Joined: 12 years ago

Different strain energy density functions provide different stress-strain relations. It is necessary to have a variety of options for strain energy density functions since different materials exhibit different stress-strain behavior. The strain energy density functions used in solid mechanics (high fidelity FEA) are mostly 3D functions. Even though they are often characterized from limited test data (e.x. uniaxial data), they tend to work pretty well under any general kind of loading conditions, which is remarkable.

Hyperelastic functions are used for large strain (finite strain), nonlinear behavior, though hyperelasticity alone captures only the relaxed equlibrium response, - it is assumed in hyperelasticity that loading and unloading occur along the same path.

Not sure I understand your question about linear models. The Saint Venant-Kirchhoff strain energy density function is linear but works for large strains. I believe it would be classified as hyperelastic.

A different strain energy density function is used for materials where the elastic behavior can be assumed to be linear and the material only undergoes small infinitesimal strains. This is typically what is referred to as linear strain and it is not hyperelastic in the sense that it does NOT work for large strains. If you try to use the linear infinitesimal strain energy density function for large strains you get a lot of error very quick (something like 2% error for every one percent strain).

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Posts: 11
Topic starter
(@MichaelRamsey)
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Joined: 11 years ago

Thank you afreiden

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