A constitutive model for the Mullins effect with changes in material symmetry

Unified constitutive modeling of rubber-like materials under diverse loading conditions

“…Experimental data (e.g. Dargazany & Itskov, 2009;Diani, Brieu, & Vacherand, 2006;Dorfmann & Pancheri, 2012;Itskov, Haberstroh, Ehret, & Vhringer, 2006;Machado, Chagnon, & Favier, 2012) confirm that stress softening introduces some anisotropy in the material response. Diani et al (2006) and Dargazany and Itskov (2009) present micromechanical directional models to handle softening induced anisotropy.…”

“…infinite-directional) network. Dorfmann and Pancheri (2012) build on the tensorial approach outlined by Horgan et al (2004) and derive a simple phenomenological model accounting for stress softening and changes in material symmetry. The model applies, in its current form, to pure homogeneous deformations; however, it may be extended to more general loading conditions by the addition of an evolution law.…”

“…Alternatively, phenomenological models rely on mathematical developments that are associated with conceptual representations or analogies with the purpose of replicating the material's behavior as observed at the macroscopic scale (e.g. Dorfmann & Ogden, 2004;Dorfmann & Pancheri, 2012;Gent, 1996;Hoo Fatt & Ouyang, 2007Huber & Tsakmakis, 2000;Liu, 2010;Liu & Hoo Fatt, 2011;Ogden & Roxburgh, 1999;Pioletti, Rakotomanana, Benvenuti, & Leyvraz, 1998). In some mixed approaches, constitutive equations are founded on macroscopic models that contain statistical parameters reflecting a certain representation of the microscopic structure (e.g.…”

“…Alternatively, Hoo Fatt and Ouyang (2008) propose a finite strain constitutive model for virgin Styrene Butadiene rubber subjected to a high strain rate monotonic loading. Furthermore, Liu and Hoo Fatt (2011) present constitutive equations, in finite strain, for the dynamic response of rubber under cyclic loading while D' Ambrosio et al (2008), De Tommasi et al (2006 and many others (e.g Chagnon, Verron, Gornet, Marckmann, & Charrier, 2004;Chagnon, Verron, Marckmann, & Gornet, 2006;Dorfmann & Ogden, 2004;Dorfmann & Pancheri, 2012;Horgan et al, 2004;Marckmann et al, 2002;Ogden & Roxburgh, 1999) focus on characterizing main features of the rate independent softening behavior of elastomers, i.e. the Mullins effect 0020-7225/$ -see front matter Ó 2012 Elsevier Ltd. All rights reserved.…”

Time-dependent behavior of passive skeletal muscle

“…The inelastic behavior is characterized by the permanent set of the material at completion of the first loading-unloading cycle. Reloading differs from the primary loading path indicating preconditioning of the material similar to the Mullins effect observed in rubberlike materials [49][50][51]. For convenience of comparison, experimental behavior for loading-unloading cycles of the preconditioned material are included as dashed curves in Fig.…”