Ogden (hyperelastic model)

The Ogden material model is a hyperelastic material model used to describe the non-linear stress-strain behaviour of complex materials such as rubbers, polymers, and biological tissue. The model was developed by Raymond Ogden in 1972. The Ogden model, like other hyperelastic material models, assumes that the material behaviour can be described by means of a strain energy density function, from which the stress–strain relationships can be derived.

In the Ogden material model, the strain energy density is expressed in terms of the principal stretches ${\displaystyle \,\!\lambda _{j}}$, ${\displaystyle \,\!j=1,2,3}$ as:

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