Helmholtz free energy of a non-linear elastic material
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
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.