Filled elastomers especially composite solid propellants demonstrate strain rate dependent, large deformation/large strain, thermo-rheological, stress relaxation, stress softening due to microstructural damage and compressible constitutive behavior. This paper presents a micromechanism inspired framework capturing all the above mentioned features by combining both continuum formulation of hyperelasticity, statistical formulation of viscoelasticity, compressibility and damage. The mechanical response is decomposed into equilibrium and time dependent parts. The equilibrium and time dependent parts are further decomposed into dilational and deviatoric parts. Deviatoric parts are modelled using Mooney- Rivlin hyperelastic strain energy density functions. Compressibility is modelled by considering dilatational part of strain energy density as the function of the dilation with quadratic and quartic terms. The stress softening during cyclic loading (Mullins effect) due to microstructural damage is described by polynomial function of the current strain energy density and its previous maximum value. The predictions based on the proposed model are in good agreement with the experimental results.