Ogden-Roxburgh model
The Ogden-Roxburgh model [1] is an approach which extends hyperelastic material models to allow for the Mullins effect. It is used in several commercial finite element codes.
The basis of pseudo-elastic material models is a hyperelastic second Piola–Kirchhoff stress , which is derived from a suitable strain energy density function :
The key idea of pseudo-elastic material models is that the stress during the first loading process is equal to the basic stress . Upon unloading and reloading is multiplied by a positive softening function . The function thereby depends on the strain energy of the current load and its maximum in the history of the material:
It was shown[2] that this idea can also be used to extend arbitrary inelastic material models for softening effects.