A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber

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Deflections of a rubber membrane (2006, background): “It was observed that hysteretic or Mullins-type effects (i.e. the loading path differs from an unloading path; see e.g. Mullins, 1947, 1969; Johnson and Beatty, 1993, 1995; Beatty, 2001a; Ogden, 2004; Dorfmann and Ogden, 2004) were almost negligible at peak strains up to both 100% and 200%.”
Experimental tests and analytical model of high damping rubber dissipating devices (2006, background): “A number of experimental works on carbon filled rubber have been published in the scientific literature and a complete overview may be found in [8] and [9].”
A review of constitutive models for rubber-like materials (2010, background): “The residual strain are not accounted for when the mechanical properties of rubber are presented in terms of a strain energy function (Dorfmann and Ogden, 2004; Cheng and Chen, 2003).”
Improving reinforcement of natural rubber by networking of activated carbon nanotubes (2008, background): “5), which is hardly explained by a hydrodynamical model [46].”
A network evolution model for the anisotropic Mullins effect in carbon black filled rubbers (2009, background): “Among several phenomenological approaches Dorfmann and Ogden (2004) applied a theory of pseudo-elasticity which along with stress softening is able to take into account permanent set.”