Ogden–Roxburgh model
The Ogden–Roxburgh model is an approach which extends hyperelastic material models to allow for the Mullins effect. It is used in several commercial finite element codes, and is named for R.W. Ogden and D. G. Roxburgh. The basis of pseudo-elastic material models is a hyperelastic second Piola–Kirchhoff stress formula_1, which is derived from a suitable strain energy density function formula_2: The key idea of pseudo-elastic material models is that the stress during the first loading process is equal to the basic stress formula_1. Upon unloading and reloading formula_1 is multiplied by a positive  softening function formula_6. The function formula_6 thereby depends on the strain energy formula_2 of the current load and its maximum formula_9 in the history of the material: It was shown that this idea can also be used to extend arbitrary inelastic material models for softening effects.