Ogden (hyperelastic Model) - Other Hyperelastic Models

Other Hyperelastic Models

For rubber and biological materials, more sophisticated models are necessary. Such materials may exhibit a non-linear stress-strain behaviour at modest strains, or are elastic up to huge strains. These complex non-linear stress-strain behaviours need to be accommodated by specifically tailored strain-energy density functions.

The simplest of these hyperelastic models, is the Neo-Hookean solid.

$W(\mathbf{C})=\frac{\mu}{2}(I_1^C-3)$

where is the shear modulus, which can be determined by experiments. From experiments it is known that for rubbery materials under moderate straining up to 30-70%, the Neo-Hookean model usually fits the material behaviour with sufficient accuracy. To model rubber at high strains, the one-parametric Neo-Hookean model is replaced by more general models, such as the Mooney-Rivlin solid where the strain energy is a linear combination of two invariants

$W(\mathbf{C})=\frac{\mu_1}{2}\left(I_1^C -3 \right) -\frac{\mu_2}{2}\left(I_2^C - 3\right)$

The Mooney-Rivlin material was originally also developed for rubber, but is today often applied to model (incompressible) biological tissue. For modeling rubbery and biological materials at even higher strains, the more sophisticated Ogden material model has been developed.

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