Short survey on isotropic viscohyperelastic constitutive equations for damageable filled rubberlike materials

Using a classic thermomechanical framework, including irreversible processes characterized by state variables, general constitutive equations for isotropic viscohyperelastic materials with damage are reviewed. The modelling equations are based on classic multiplicative splits of the deformation gradient tensor into, viscoelastic and elastic parts (Sidoroff 1974), and deviatoric and volumetric parts (Flory 1961, Ogden 1976). A comparison of the pioneering finite strain viscohyperelastic models following such decompositions (Le Tallec, Rahier, & Kaiss 1993, Lion 1997, Reese & Govindjee 1998) is carried out. Damage has been introduced to possibly reproduce the softened behaviors of filled elastomers undergoing Mullins effect, as well as, solid propellants exhibiting debonding at the matrix/filler interface. Contrary to the former, the latter induces a significant change of the material compressibility. Existing hydrostatic and deviatoric damage variables and damage evolution functions are reported. The impact of the damage framework as well as the variable choice is studied. Finally, examples of the type of stretch-stress responses that can be obtained are presented revealing some limitations that could be addressed in the future.