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Helmholtz free energy of a non-linear elastic material  


Sombrero
Posts: 2
(@sombrero)
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Joined: 4 months ago

Dear All, 

Given the stress-strain data of a particular mode of loading such as uniaxial tension on a hyperelastic material, how can one calculate the Helmholtz free energy per unit reference volume? otherwise known as strain energy density/stored energy/elastic potential. 

Thank you in advance

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stewie6514
Posts: 2
(@stewie6514)
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Joined: 11 months ago

Hello,

in simple terms your stress is the first derivative of the Helmholtz free energy after your strain. So you can just integrate your stress data over your change in strain data and you get your Helmholtz free energy. If you have large deformations in your data, just be careful with your kind of stress and strain.

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Sombrero
(@sombrero)
Joined: 4 months ago

New Member
Posts: 2

@stewie6514, Thank you. 

In simple terms, calculate the area under the stress-strain curve but since the relationship is not linear, methods such as trapezoidal are necessary. 

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